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A multi-level multi-product supply chain network design of vegetables products considering costs of quality: A case study
Quality costs management in agricultural products’ supply chain
https://orcid.org/0000-0003-3954-071X
Khazaeli Sareh Methodology Writing – original draft Writing – review & editing 1 *
Kalvandi Ramazan Supervision 2
Sahebi Hadi Conceptualization 1
1 Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, IR
2 Agricultural Garden, Yaman Avenue, Shahid Chamran Highway, Tehran, IR
Islam Md. Monirul Editor
Bangladesh Agricultural University, BANGLADESH
Competing Interests: The authors have declared that no competing interests exist.

* E-mail: khazaeli_sareh@ind.iust.ac.ir
3 9 2024
2024
19 9 e03030548 9 2023
18 4 2024
© 2024 Khazaeli et al
2024
Khazaeli et al
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Effective logistics management is crucial for the distribution of perishable agricultural products to ensure they reach customers in high-quality condition. This research examines an integrated, multi-echelon supply chain for perishable agricultural goods. The supply chain consists of four stages: supply, processing, storage, and customers. This study investigates the quality-related costs associated with product perishability to maximize supply chain profitability. Key factors considered include the network design, location of processing and distribution centers, the ability to process raw products to minimize post-harvest quality degradation, the option to sell the excess produce to a secondary market due to unpredictable yields, and the decision not to fulfill demand from distant customers where significant quality loss and price drops would be involved, instead diverting those products to the aforementioned secondary market. Quantitative methods and linear mathematical programming are employed to model and validate the proposed supply chain using actual data from a real-world case study on vegetable supply chains. The main contribution of this research is the incorporation of quality costs into the objective function, which allows the supply chain to prioritize meeting nearby customers’ demands with minimal quality loss over serving distant customers where high quality loss is unavoidable. Additionally, deploying a faster transportation fleet can significantly improve the overall profitability of the perishable product supply chain.

The author(s) received no specific funding for this work. Data AvailabilityThe most critical data are presented in Supporting Information files. All are not presented due to the high space they need. If there is no space limitation in the paper, it can be published.
Data Availability

The most critical data are presented in Supporting Information files. All are not presented due to the high space they need. If there is no space limitation in the paper, it can be published.
==== Body
pmc1. Introduction

Vegetables are perishable, edible, agricultural products that deteriorate during a limited shelf life [1]. Quality of perishable products is essential to the customer because such products deteriorate fast and endanger the consumer’s health [2]. There is a consensus in the literature on the reasons why people buy organic food; however, there is also a gap between the consumers’ generally positive attitude toward organic food and their relatively low level of actual purchases [3]. Quality of vegetables is one of the important measures to its customers due to the quality deterioration rate of products which relates to the health of consumers [2]. Time decay and shortages are common phenomena in products with short life cycles, and financial volatility necessitates a more accurate characterization of inventory costs based on time-adjusted value [4]. The supply chain management concept evolved when manufacturers experienced a strategic partnership with their direct suppliers. Then the logistics and transportation experts improved it one step forward and involved the distribution and transportation operations. Next, the concept of integrated logistics was recognized as the supply chain management [5]. Product quality is another novel concept in the supply chain management [6]. Moreover the quality deterioration often happens in traditional supply chains which, for the most part, are poorly planned [7]. From a product quality perspective, when processed products decay at a faster rate than raw materials, storing raw materials is favored [8]. Alternatively, when processing decreases the quality decay rate, a short time until processing is favored [9]. The supply chain (SC) of vegetables consists of four echelons: 1) purchasing raw materials, 2) processing, 3) distribution, and 4) customers to which products are delivered [10]. Since perishable products (agri-foods) have limited shelf life, logistic-related topics are important in business [11]. Transportation share in supply chain costs reached about 92% in the distribution sector in some traditional chains [12]. The post-harvest pre-customer-sent product loss [13] accounts for more than 40% of the supply chain costs even in industrialized and developed countries [14]. It occurs in terms of both the product quantity and agri-food quality loss throughout the chain and imposes quality costs on the chain [15]. Although considering the shelf life losses is in relation to an increase in transportation costs, it worth investing on transportation infrastructure due to less quality loss. Moreover, from a system’s point of view, integrating warehousing and transportation in the supply chain can highly affect the total cost, customer satisfaction and inventory level. Integrated models of providing and storing perishable products help to maximize meeting demands [11]. Integration of storing and distributing decisions leads to more efficiency than other operational integration [16, 17]. Integration of strategic decision making and operational processes appears relevant, especially for such perishable products as agri-foods [18]. Recently some strategies were studied in supply chain management of perishable products to control the perishability of products which are inventory management [19], reverse logistic management [20], pricing [7], and robust optimization [21].

Notably, product quality is characterized by the product’s remaining shelf life and thus is time-dependent [22]. Taguchi described the deviation in performance using the quality loss function that measures the product’s quality loss in terms of the total loss to society due to functional variation and harmful side effects [23]. For perishable foods, product quality degradation must be identified because it significantly affects consumers’ decisions and retailer profitability [22]. On the other hand, computing the cost of quality loss for an integrated supply chain allows for exploring the interrelationships among business entities. It enables the supply chain to achieve a minimum total cost by investing in quality and, hence, increasing the overall benefit [24]. Today, lateral marketing is the most effective way of competing in mature/immature markets, where micro-segmentation and plenty of brands don’t leave any space for new opportunities [25]. One of problems in the perishable agricultural products’ supply chain is a high quality loss post-harvest, which leads to different quality costs and the customer dissatisfaction. A brief review of the literature reveals that rarely is there any established advanced multi-echelon vegetable supply chain wherein the profit is maximized by considering such features as product quality degradation, quality loss-related costs, and settling lateral markets. Due to this research gap, current study is aimed to maximize the profit of perishable products supply chain considering their related quality costs. The question in this research is how considering both the cost of qualities and the second market in the supply chain network design (SCND) of perishable products can affect the benefits of stakeholders, such as farmers and customers in the supply chain.

The research objective is to formulate a SCND of perishable products by considering different costs of qualities in the supply chain and settling a lateral market and processing the part of perishable products that have not entered the supply chain due to its high level of perishability and enters to the second market be used in specific form satisfying customers, in the mathematical mixed integer linear programming. The current study intends to make affecting decisions in different levels of decision making as: 1) strategic level; locating different centers in the supply chain, 2) tactical level; determining the processing type, and quantities of different products be delivered to the customers, and 3) operational level; selecting a suitable mode of transportation and quantities in the SCND. To address this challenging problem, vegetables, important perishable products, were examined in a case study by first studying the multi-echelon agri-food supply chain (AFSC) based on the post-harvest quality features.

The remainder of this paper is structured as follows: In the next section, a brief overview of related literature reviews on the quality management of perishable agricultural products is given. Section 3 describes the research methodology, a quantitative supply chain modeling approach in a linear programming framework. The case study and sensitivity analysis results in the optimum point are presented in Section 4, the research conclusions in Section 5, managerial implications in Section 6, and future research and limitations in Section 7.

2. Literature review

2.1. Agricultural products supply chain

Customers pay special attention to the quality and safety of agri-foods because they directly affect their health [26]. This quality can be measured by such different criteria as the purchasability [27], lifetime (day) left [28], color [29], freshness [30] and light-greenness of vegetables (L. in the Hunter Laboratory) [31, 32]. Creating an efficiency-responsiveness balance in quality-based customer-oriented supply chains is worth considering [9]. The optimal operation strategy is acquired based on product quality [6]. Organizations that have instituted a system of quality cost measures have experienced dramatic positive results because it translates the implications of poor quality, activities of a quality program, and quality improvement efforts into a monetary language for managers to understand which factors are important in affecting profitability and the consumer need [24].

Decisions made in the supply chain of perishable products are strategic, tactical and, operational; strategic decisions that have long-term effects on firms are those made on the network design, supply chain network design [33] and the location of different equipment in the processing, distribution and, hub centers to make the best use of the capacity of the existing facilities [34]. In the strategic level of decision-making in the perishable products’ supply chain design, different ways to cope with increasing product quality decay can be identified. On the one hand, the network can be centralized to decrease handling time (for each transport to a hub, a fixed handling time is incorporated in the transport time) and hence decay. On the other hand, more hubs can be opened to decrease transport time and decay [9]. Moreover, technical models are popular and have public applications in harvest programming, product selection, and labor capacity in agricultural products supply chains. Besides strategic and tactical decisions, the supply chain also involves operational decisions for which it is assumed that the former two are already known and sufficient knowledge is available about production, demand, and transportation [35]. Pasha et al. studied an integrated bi-objective quality-based production-distribution agri-food MILP supply chain model in which profitability is maximized by defining the quality as a function of such decisions as the location of hubs and transportation strategy throughout the supply chain [17], whereas making decisions in an integrated way will reduce costs compared to individual decisions made at each level [36, 37]. Moreover, in the greenery supply chains, De Keizer et al. presented a model in which decisions made on the greenhouse location (strategic) are based on the plant’s lifetime in that location [9]. As changes in the temperature and enthalpy levels change the food quality [38], Khazaeli et al. and Rong et. al determined the temperature of distribution centers and deliveries to meet the expectations of different customers as the operational decision-making in a supply chain management [39, 40].

2.2. Quality of agricultural products

In most supply chain designs, cost, profit, quality, responsiveness and environment are the general decision-making factors [34]. Although cost and profit are still the main criteria in almost all quantitative mathematical programming models of the supply chain of perishable agricultural products, in recent years, other criteria, such as product quality [9, 17, 18, 41, 42] and environmental protection [43] have also been considered in some studies. The quality function of perishable agricultural products can be either complex or simple [44]. It has been shown that, the decrease of a single quality attribute of agricultural products can be approximated by one of the four basic types of mechanism which are zero-order reactions having linear kinetics, Michaelis Menten kinetics, first-order reactions having exponential kinetics, and autocatalytic reactions with logistic kinetics [45, 46]. For the concept of keeping quality, it is convenient to assume zero-order reaction kinetics [28], and mostly the Michaelis Menten kinetics reduces to a linear one in the initial region of decay, which is the most important in quality assessment [47]. Therefore, the quality variable of vegetables in the initial region of decay can be considered in a widely used equation, in which the quality function changes by the time linearly. It is shown in Eq 1.

dQdt=kQ(t)=Q0−k.t (1)

Where, Q0 is the initial quality, t is time and k is a degradation rate. In a dynamic environment, the well-known Arrhenius equation shows that the degradation rate (k) depends on the activation energy of the material, and the environmental factors [28, 48, 49].

The perishable products’ quality model shown in Eq 1 has been frequently used to capture the degradation of food products over time. For example, in the grocery retail chain, Wang and Li presented a pricing model to maximize food retailer’s profit in a dynamically identified food shelf life by using Eq 1 [50]. Chen and Chen proposed an on-site direct-sale dynamic supply chain inventory model, considering time-dependent quality losses for perishable foods [22]. Lejarza and Baldea presented a closed-loop, feedback-based control framework, that employs real-time product quality measurements for optimal supply chain management [51]. Moreover, Xu et al. presented a real time decision support framework to mitigate the quality degradation in the journey of agricultural perishable products from farm to the retailer in the supply chain based on the Eq 1 [52].

Generally, cost, benefit, and quality factors are the most important factors that are to be optimized in network designs. Mostly, agri-food should make a logical balance between two topics, which are the price reduction and the customer service improvement [38]. In the field of multi-objective supply chain network design, De Keizer et al. and Khazaeli et al. showed that, the quality of agricultural products causes cost in the supply chain’s network [18, 39]. A review of quantitative supply chain research on the perishability of agri-food by considering related quality costs is summarized in Table 1.

10.1371/journal.pone.0303054.t001 Table 1 Summary of mathematical SC models based on the quality of perishable products.

Author/ Year
Feature of the model	[7]	[39]	[51]	[17]	[22]	[12]	[34]	[53]	[52]	[54]	[9]	[27]	[43]	[41]	[18]	[42]	[35]	[40]	Current research	

Mathematical models	Optimization- (LP)					*															
Optimization- (MILP)						*	*	*			*	*	*		*			*	*	
Optimization- (NLP)			*		*				*					*						
Optimization- (MINLP)	*	*		*						*										
General mathematical models																*				

Dynamic or static	Static										*	*	*			*					
Dynamic	*	*	*	*	*	*	*	*	*					*		*	*	*	*	

Flow direct	Forward	*	*		*	*	*	*	*	*	*	*	*	*	*	*	*	*	*	*	
Backward			*										*	*						

Uncertainty	Certain	*	*	*	*	*			*		*	*	*	*	*		*		*	*	
Stochastic															*					
Robust				*			*		*						*		*			

Decision level	Strategic with location	*	*	*			*	*	*			*	*							*	
Strategic without location										*										
Tactical	*	*	*		*		*	*	*		*		*		*	*	*		*	
Operational	*	*		*		*					*		*	*				*	*	

Objectives of programming	Economical	*		*	*		*	*	*	*	*	*	*	*	*	*	*		*	*	
Environmental	*						*					*								
Social	*																			
Quality- based		*		*	*	*		*	*		*	*		*	*	*			*	

No. of product	One- product			*		*					*		*	*			*		*		
Multi product	*	*	*	*			*	*	*		*			*	*		*		*	

Network element	Material supply	*	*	*	*	*	*	*	*	*	*	*		*	*	*	*	*		*	
Storage								*	*	*	*		*				*	*	*	
Process	*	*					*	*	*		*				*		*		*	
Distribution	*	*		*		*		*	*	*		*		*		*	*	*	*	
Retailer/ Customer	*	*	*		*	*	*	*	*	*	*		*		*				*	
Transportation	*	*	*			*	*			*	*		*	*		*		*	*	
Number of echelons of the supply chain	4	4	2	2	2	3	3	4	5	4	4	1	3	2	3	2	5	3	4	
Study field	Livestock/agriculture food	*			*			*			*	*	*	*				*			
Vegetables/ flowers/ Herbal plants			*		*	*		*	*					*	*	*		*	*	
Pharmacy and herbal medicines		*																		
Source(s): Authors’ work

2.3. Research gaps and contributions

Due to the importance and necessity of developing SCM from a larger perspective to provide a win-win situation for each participant in the supply chain, in this paper, we aim to develop a novel mathematical model to design a supply chain network, based on quality function elements in the vegetables’ sector. The summary of the literature review outlines the gaps in the literature as follows:

Despite the importance of the cost of qualities in designing supply chains due to the perishability of the products, the cost of quality concept has not been widely incorporated by researchers in the design of agricultural products’ supply chains.

No research has paid attention to the lateral market to look at the quality problems from the side covering some target customers.

Few researchers have considered the benefits of several stakeholders of the agricultural supply chains simultaneously. The stakeholders in agricultural Products’ supply chain are consumers, farmers, the environment, and society.

The proposed SCND is a multi-product, multi-echelon model with exact (certain) demand that makes decisions at strategic, tactical, and operational levels. It has focused on “quality” by considering the quality deterioration which is time-dependent in the initial region of decay, moreover, by defining costs of quality degradation in the quality-cost functions. Features that differentiate the present research from others are displayed in the last row in Table 1. As previous researches have demonstrated, traditional supply chain of agri-food is unstructured, which generally leads to low quality and low benefit of agricultural products, the presented research is developed, in which the main contributions are as follows:

✓ Providing a network design model for an integrated multi-level supply chain of perishable products wherein profit is optimized by considering quality decay aspect of the products.

✓ Optimizing the profit of the supply chain of perishable products considering different quality costs for them due to unmet demand, product waste and reduced revenue of low-quality products.

✓ Introducing a strategy of selling perishable products to lateral markets before letting products enter the chain to prevent the production of low-quality products along it.

✓ Enabling the purchase of the farmer’s total agricultural product above the contract ceiling due to unpredictable production to prevent waste production and its scattering in the environment.

✓ Introducing a strategy of producing semi-processed, low-quality products (from those that did not enter the chain) to meet part of the market demand for lower-quality lower-price products.

The developed model is a four-echelon supply chain of perishable agricultural products in which the time-dependent quality of the products is considered. In addition, a lateral market is considered in the designed supply chain that does not stand higher than vertical marketing and completes the primary market.

In the end, the developed model is applied to a case study of a firm in the agricultural products industry with four echelons of farm-processing-distribution-customer centers. The vegetables selected as candidates for the present supply chain network design are Yarrow, Borage flower, and Melisa, due to their priority in agricultural studies and their application in various industries [55].

Although there are some studies done to minimize quality losses of perishable products by multi-objective problem-solving approaches [17, 19, 20, 21, 39], the programming in the present research is done as a single objective problem solving by profit objective function underlying quality loss costs.

3. Problem description and formulation

From the perspective of the research approach, this research is quantitative, done as a mathematical mixed integer linear programming (MILP) modeling with the objective function of profit by considering the cost of quality factors of products in the multi-echelon perishable products’ supply chain. It is applicable to the related supply chains. It focuses on an integrated multi-product SCND of agricultural products that provides, processes, stores and distributes materials. It considers customer demands and sells the farmers’ in-excess products to the second market. The designed model was solved using GAMS 24.1.2 software by exact solution method by epsilon-constraint. The model is validated by applying it in the case study of a multi-vegetable supply chain of a firm in a fertile area in Iran country. The designed supply chain of the firm is shown in Fig 1.

10.1371/journal.pone.0303054.g001 Fig 1 Flow diagram of the agricultural products’ SC.

First, products through related contracts and in-excess products are bought from farmers in the study area. In the second echelon of the proposed supply chain, some or all of the purchased products are processed at related centers resulting in different degrees of product quality. Third, the products in the former echelon are stored in cool storage centers until being distributed and fourth, they are sold to wholesalers. Another part of the purchased products are transferred to the second market as lower quality products in different industries (tea bags, spices in food, etc.). Different road modes of transport are used between different echelons of the supply chain.

The modeling makes decisions at different echelons of the supply chain. Decisions made are (1) selecting farms and the quantity of raw products to be purchased from each of them, (2) the quantity of products sold to the second market, (3) the number of processing and storage facilities to be settled in the supply chain, (4) product flow and the vehicles to carry out the transportation between the active facilities i. e. from farms to wholesalers and (5) assignment of processing facilities to the products. They are made based on minimizing the total cost of the supply chain design considering the cost of qualities. In the following, assumptions and the modeling are described.

3.1. Assumptions

The location of production centers is specified.

Capacities of the processing centers, and also storage centers are determined.

Customer demand for each type of processed product is pre-determined.

Shortage to customer demand is allowed.

The quality of products post-harvest in the supply chain is considered time-dependent.

The deterioration rate of each product is considered specific, based on the activation energy of the material.

The approach of quality costs is considered in measuring the quality of products in the objective function modeling.

The transportation speed of each mode is assumed uniform.

In-excess products are sold to the second market.

Over-time quality loss-related cost, unmet customer demand and product waste are considered as quality costs.

The cost of the lost product quality equals the price drop in proportion to the quality drop by a factor of ten (The coefficient (10) is proposed by experts based on pairwise comparisons of cost and quality criteria).

The quality cost of the customer credit for each demand equals the revenue lost due to not meeting one unit demand.

The quality cost of the product waste equals the revenue from the product sales not realized, causing that product to enter the environment as waste.

Products are bought from farmers: 1) at a price for first-grade products based on the amount in the contract and 2) at a price for second-grade products for those over that in the contract (According to experts, the purchase-price-drop coefficient is 0.3 in the market).

Products are sold to the supply chain customers at a price for first-grade products and those outside the supply chain are sold in the second market at a price for second-grade products (According to experts, the sell-price-drop coefficient is 0.3 in the market).

The mathematical model, its objective and its constraints are presented in the following.

3.2. Mathematical modelling

Symptoms used in the model consist of sets, related indexes, parameters and variables, objective functions and constraints, are as follows:

Sets and indexes

10.1371/journal.pone.0303054.t002 i∈I	Set of contracted farms	
j∈J	Set of potential processing centers	
k∈K	Set of potential storage centers	
l∈L	Set of customer centers	
n∈N	Set of harvested products	
p∈P	Set of processing technologies	
m∈M	Set of transportation modes	

Parameters

10.1371/journal.pone.0303054.t003 pdin	Amount of product n produced at location i (ton)	
prin	Price of product n (USD/ ton)	
pri′n	Price of purchasing second-degree product n from farmers (USD/ ton)	
Sanp	The sale price of processed product n in type-p form (USD/ ton)	
sa′n	Price of selling second-degree product n to the second market (USD/ ton)	
capjp	Processing center j capacity for the type-p processed product (ton)	
capkp	Storage center k capacity for the type-p processed product (ton)	
capmp	Transportation mode m capacity for type-p processed product (ton)	
dij	Distance between farm i and processing center j by Google (km)	
djk	Distance between processing center j and storage center k by Google map (km)	
dkl	Distance between storage center k and wholesaler l by Google map (km)	
Vm	The average speed of transportation in mode m (km/hour)	
dlnp	The demand of wholesaler l for type-p processed product n (ton)	
Cfj	Fixed cost of opening one processing center chamber (USD)	
Cfk	Fixed cost of opening one storage center chamber (USD)	
Costtrm	Cost of transportation per unit load per unit distance (USD.ton-1.km-1)	
Corderm	Cost of ordering mode m of transportation (USD/ unit vehicle)	
Cpronp	Cost of type-p processing of each unit of product n (USD.ton-1)	
Csto	Cost of each unit of product to be stored (USD.ton-1)
	

Variables

10.1371/journal.pone.0303054.t004 Integer variables	
qin	Amount of product n purchased from farm i and entered the supply chain (ton)	
qim→jn	Amount of product n which is transported from farm i to processing center j by mode m (ton)	
Extqin	Amount of product n purchased from farm i to be sold to the second market (ton)	
qjnp	Amount of type-p processed product n produced at center j (ton)	
qjm→knp	Amount of type-p processed product n transported from processing center j to storage center k by mode m (ton)	
qknp	Amount of type-p processed product n stored in storage center k (ton)	
qkm→lnp	Amount of type-p processed product n transported from storage center k to customer center l by mode m (ton)	
qlnp	Amount of type-p processed product n delivered to customer l (ton)	
t	Time duration (hour)	
Nim→j	No. of mode-m vehicles for transferring harvested products from farm i to center j	
Njm→k	No. of vehicles of mode-m for transferring products from center j to center k	
Nkm→l	No. of vehicles of mode-m for transferring products from center k to center l	
exlnp	Weight of processed product n in type-p over the demand of customer l (ton)	
shlnp	Weight of processed product n in type-p less than the demand of customer l (ton)	
Binary variables	
Xjnp	1, if the equipment for processing type-p product n is installed in center j; 0 otherwise	
Xknp	1, if the equipment for storing type-p product n is installed in center k; 0 otherwise	

Profit objective function and constraints are described as follows:

Profit objective function

The objective function is defined to maximize the supply chain profit. It is equal to the revenue from both, selling products to customers and the second market minus the total supply chain and quality costs (Eq 2).

Profit=Totalrevenue–Totalcost=[∑1l∑1n∑1psanp.(qlnp−exlnp)+∑1i∑1nsa′n.(pdin−qni)]–[∑1i∑1nprin.qni+∑1i∑1l∑1n∑1pprin.(dlnp−qni)+∑1i∑1l∑1n∑1ppri′n.(pdin−dlnp)]‐∑1j∑1n∑1pCfj.Xjnp+∑1k∑1n∑1pCfk.Xknp]‐∑1j∑1n∑1pCpronp.qjnp]−[∑1k∑1n∑1pCsto.qknp]‐[∑1mCosttrm.(∑1i∑1n∑1jqnim→j.dij+∑1j∑1n∑1p∑1kqjm→knp.djk+∑1k∑1n∑1p∑1lqkm→lnp.dkl)+∑1mCorderm.(∑1i∑1jNim→j+∑1j∑1kNjmk→+∑1k∑1lNkm→l)]‐[∑1i∑1j∑1m∑1nsan(p=1).qim→jn.kn(p=1).dijvm∑1j∑1k∑1m∑1n∑1psanp.qjm→knp.knp.djkvm+∑1k∑1l∑1m∑1n∑1psanp.qkmlnp.knp.dklvm)]−[∑1l∑1n∑1psanp.shlnp]−[∑1l∑1n.∑1psanp.extlnp] (2)

Revenue consists of: 1) that obtained by selling the supplied demanded product, which is equal to the unit price of the sold product multiplied by the customer met demand; the latter equals the amount supplied in the supply chain minus that over the customer demand, and 2) that obtained by selling: a) the supply chain-decided products and b) in-excess products sent to the second market which is equal to the price of each unit of the low-quality product multiplied by the amounts in a and b.

Costs relate to: 1) purchasing high-quality (on contract) and low-quality (in-excess) products from farmers (with their own related prices), 2) locating processing and storage centers, 3) processing operations, 4) storing products in storage centers, 5) different supply chain distances (ton-km), 6) ordering different transportation modes, 7) revenue lost due to reduced product quality, 8) credit lost due to unmet demand and 9) unsold wasted product.

Constraints

Quantities equations

qni≤pdni;∀i,n (3)

qni=∑1j∑1mqim→jn;∀n,i (4)

∑1i∑1m∑1nqim→jn=∑1n∑1pqjnp;∀j (5)

∑1i∑1m∑1jqim→jn=∑1j∑1m∑1k∑1pqjm→knp;∀n (6)

qjnp=∑1k∑1mqjm→knp;∀j,n,p (7)

∑1i∑1mqim→jn=∑1k∑1m∑1pqjm→knp;∀j,n (8)

∑1j∑1mqjmknp=∑1l∑1mqkmlnp;∀k,n,p (9)

∑1k∑1mqkm→lnp=qlnp;∀l,n,p (10)

extqin=pdni−qni;∀n,i (11)

Constraints (3) to (10) ensure the product weight in different supply chain steps—from the farm to the customer (considering the amount of the farm production). Constraint (11) addresses in-excess low-grade products to be sold in the second market; these are produced, but not delivered to customers through the supply chain for different reasons.

qjnp≤capjp.Xjnp;∀j,n,p (12)

qknp≤capkp.Xknp;∀k,n,p (13)

Xjnp≤qjnp;∀j,n,p (14)

Xknp≤qknp;∀k,n,p (15)

Constraints (12) to (15) indicate that quantities of processed and stored products, respectively, in activated processing and storage centers are determined based on the capacities of these centers. If centers are not active, the quantities would be zero.

Travel time in the supply chain equation

t=dv (16)

Constraint (16) indicates that the vehicles used in the transportation system of the supply chain have uniform speeds.

Number of vehicles

Nim→j=∑1n(qim→jn/capm(p=1));∀i,m,j (17)

Njm→k=∑1n∑1p(qjm→knp/capmp);∀j,m,k (18)

Nkm→l=∑1n∑1p(qkm→lnp/capmp);∀k,m,l (19)

Nm=∑1i∑1jNim→j+∑1j∑1kNjm→k+∑1k∑1lNkm→l;∀I,j,k,m,l (20)

Constraint (17) to (20) determines needed vehicles in different modes to transfer materials in different supply chain steps and the whole supply chain assuming full-capacity active vehicles.

Shortage and extra quantities constraints

dlnp−qlnp=shlnp−extlnp;∀l,n,p (21)

extlnp≤M.y;∀l,n,p (22)

shlnp≤M.(1‐y);∀l,n,p (23)

Constraints (21) to (23) determine the in-excess and shortage amounts.

qni,qim→jn,qjn,qjnpqjm→knp,qknp,qkml→np,qlnp,Extlnp,Shlnp,Extqin,Nim→j,Njm→k,Nkm→l,Nm,≥0andIntegers (24)

Xjnp,Xknp∈{0,1} (25)

Constraints (24) and (25) illustrate non-negativity and binary variables.

4. Case study

In this section, we implement the proposed model in an Iranian raw and processed vegetable products’ company, the Razian Company, as a case study. Iran country has been bestowed with a wide range of climate and physio-geographical conditions and as such is most suitable for growing various kinds of vegetables, its production of vegetables is increasing. Moreover, agricultural products are profitable fields for investment. Since Iran possesses a large variety of flora with manufacturers, in equal measure, analysis of the working of the vegetable market is critical [55]. There is an apparent shortage of related supply chain in Iran country. The goal of the case study is to evaluate the efficacy of the proposed model under real-world conditions and to address the needs of the firm in question. The case study used a four-echelon SCND, and materials were supplied, processed, and stored (echelons 1–3) in the firm area (origin) while the last-level centers were located all over the country; in addition, a center was established as a second market to collect the in-excess products, as shown in Fig 1. The mentioned lateral market imposes no costs on the supply chain because it is closest to farms, and customers pay the transportation costs.

At first, the firm seasonally provided the vegetables from the suppliers. Suppliers were specified and contracted in advance in fertilized source centers (i = 4) of selected vegetables (n = 3). The farm centers were, in Kaboudrahang, Razan, Nahavand, and Malayer, and the vegetable products were Yarrow, Borage flower, and Melisa. Secondly, the firm used the related processing on vegetables, or the products remained raw. There are potential processing center (j = 5) candidates in the case study. Thirdly, the firm stored the products in the storage centers for packaging. There are potential storage center (k = 5) candidates in the case study. The five potential processing and storage center candidates were Kaboudrahang, Razan, Nahavand, Malayer, and Asadabad. Finally, the firm delivered the demanded products to the customer centers. The customers were trade representatives of each province all over the country (l = 30). Due to the importance of the case study data for the application of the presented model, some were obtained from the enterprise resource planning (ERP) of Razian company [56]. In addition, data on fixed and variable costs of different transportation modes were obtained from the recent case study research done in Iran [39]. Data on the price of different raw and processed vegetable products were gathered from the statistics of the Ministry of Agriculture [57]. Details of the most critical data of the case study are presented in the table in S1 Table in the supporting information.

The designed mathematical mixed integer linear programming (MILP) model was implemented and solved using GAMS 24.1.2 software and an Intel 2.13-GHz processor by exact solution method by epsilon-constraint. The designed network, product type, amount (tons) produced and sent to, e.g., Tehran (Capital), the transportation mode at different supply chain levels, and amount (tons) delivered to the second market are shown in Fig 2.

10.1371/journal.pone.0303054.g002 Fig 2 Supply chain network design of multi-product (multi-vegetable) in Hamadan province (Quantities are in tons).

(R indicates Yarrow product, C indicates Borage flower product, T indicates Melisa product). Optimally, 564 trailers and 33068 trucks were needed in the designed supply chain network. Generally, in presented agricultural products’ supply chain, some products have high quality-loss rates as well as demands for distances far from the cultivation center. This leads to a long post-harvest time for the product to reach the customer and, hence, a high rate of quality loss and a drop in the product price. This fact makes the supply chain decision maker set the lateral market due to not delivering those products to those customers and hence delivering them to the second market. It is considered newly in the present research due to make quality loss of products in the supply chain, the less, hence the profit the more.

4.1. Results

As shown in Fig 2, in the optimum point of maximizing profit by considering quality costs in perishable vegetables supply chain in the proposed MILP model, the processing, storage, and distribution centers are settled in similar locations, spatially. It leads to set process-storage-transfer type of hub centers, in compliance with the supply chain network proposed by Khazaeli et al. [39]. Out of 5 potential processing and storage/transfer centers, the model found all for the supply chain No. of facilities based on the center capacity and its setup costs (related parameters are listed in the table in S1 Table). It is similar to the model proposed by De Keizer et al., in which to decrease transport time and hence decay in related supply chain design, the centers were decentralized, [9]. Therefore, more hubs were opened.

The model determined the amount and type of the delivered products between all supply chain levels, by the supply chain programming, and provided the information on the product (ton) if it was possible to supply to meet the customer demand. The details of provided products are presented in the table in S2 Table in the supporting file. Here, the supply chain management decides not to offer part of products to the customer and sells them at a second-grade price to the second market to maximize the chain profit by minimizing the quality loss-related cost along the chain (highlighted as unmet demands in the table in S2 Table). In such a case, saving the low-quality cost of the perishable product will bring more revenue for the chain.

The model also selected the center-to-center transportation mode considering the vehicle speed to reduce time and, hence, the quality degradation and transportation costs. The table in S2 Table in the supporting file lists the number of each vehicle type required to transfer products. In result, the supply chain used trucks about 60 times more than trailers because of being faster. It used trailers, although with higher order costs, only in long distances, e.g., from storage centers to customer centers due to their more than ten times more capacity than trucks which led to fewer vehicle orders and, hence, less vehicle order costs. As shown in Fig 2, in all supply chain steps, except the last, the model suggests using trucks because of their higher speed than trailers and their less order costs than trailers (The vehicle-related parameters are shown in the table in S1 Table).

In this chain, some produced, but supply chain-decided undelivered to the supply chain were sold to the second market with price of high-grade products. The products produced more than that guaranteed in the farmer’s purchase contract, were sold to the second market with a much cheaper price (0.3 that of high-grade products). Both, amounted to 1820 tons of product Yarrow in Razan, 10020 tons of product Borage flower in Nahavand and 93.5 tons of product Melisa in Malayer and Nahavand, all were delivered to the second market.

Demands for all types of products were met except for fresh products, for which the demands were responded in centers closer to the previous echelon due, maybe, to their higher corruptibility and quality-loss rate than other types of products (The table in S1 Table in the supporting information lists the perishability rate of each processed products than the fresh one) and, hence, a price decline that makes them uneconomical to deliver to customers.

4.2. Benefit and quality loss of the products in the supply chain

In the designed supply chain, as shown for the optimum solution point in Fig 3A, the revenue and total cost are, respectively, 27.3 and 18.5 million USD; therefore, the benefit is 8.8 million USD. The final product quality and quality loss in the supply chain are 28,357 and 643 (Unit of quality), respectively (Fig 3B).

10.1371/journal.pone.0303054.g003 Fig 3 (a). Profit/ cost of the SC designed. (b). Final quality/ quality losses in the SC design.

The revenue of the supply chain (27.3 million USD) is due to: 1) selling the chain-demanded supplied products 21.9 (Million USD), 2) selling products not supplied to the chain and sold to the secondary market based on the chain management decision 0.08 (Million USD) and 3) selling products supplied more than that specified in the contract 5.32 to the secondary market (Million USD) (Fig 4A).

10.1371/journal.pone.0303054.g004 Fig 4 (a). Supply chain revenue parts. (b). Farmers’ revenue parts.

The revenue of farmers as main stakeholders, is 12.5 million USD, which goes to them by selling: 1) contract-demanded products delivered to the supply chain (10.2 million USD), 2) contract-demanded products supply chain-decided undelivered products (2.07 million USD) and 3) in-excess-of-contract products to the second market (0.24 million USD) (Fig 4B).

Total supply chain benefit (8.8 million USD) comes from supplying products to customers considering the demand (5.7 million USD) and products to the second market (3.1 million USD). In addition, the total revenue of farmers is (12.5 million USD) (Fig 5).

10.1371/journal.pone.0303054.g005 Fig 5 Revenue of farmers and network designed profits.

4.3. Supply chain cost breakdown considering quality cost and other supply chain costs

The supply chain cost (18.5 million USD) consists of 8 elements, among which purchasing, including buying raw materials for the supply chain (10.2 million USD) and in-excess materials (2.3 million USD) for selling to the second market, is the costliest, and revenue lost due to reduced product quality along the chain (5.4 million USD) stand next. Other costs in the case studied, in the order of higher values, include quality cost of unmet demand of fresh products in long distances (0.38 million USD), processing (0.1 million USD), logistic transportation (0.07 million USD), storage (0.03 million USD), establishing facility centers (0.02 million USD); product waste has zero cost. The percent share of total costs, including those of the network, supply chain logistics and quality costs is shown in Fig 6.

10.1371/journal.pone.0303054.g006 Fig 6 Supply chain different costs.

As shown in Fig 6, 29% of the costs (5.4 million USD) in the supply chain of perishable product supply relate to the revenue lost due to the product quality loss by unmet fresh products. On the other hand, the quality cost of unmet demand for fresh products in long distances is 0.38 million USD. The most part of the mentioned costs are compensated by revenue earned by selling these products to the second market by 5.32 million USD.

The designed supply chain has other profits, which are: 1) preventing low-quality products from being produced at the request of the chain customers and 2) sending products produced over that specified in the contract (due to unpredicted agricultural products produced) to the secondary market and, hence, preventing them from entering the environment as waste.

The model accuracy was verified by changing its parameters and examining its responses to the changes. The validity of the proposed model has also been confirmed by comparing the results of the present SCND, with a vicinity secondary market (Fig 2), and those of the existing chain, without such a market. Related experts have evaluated the proposed model, validated it, and concluded that the chain profit has increased due to its reduced quality costs. The sensitivity analysis is presented to evaluate the effect of changing some parameters on variables and the objective function, in the following.

4.4. Sensitivity analysis

Parameters to which model responses investigated in reaction, are the reaction rate of products and speed of different transportation modes as they relate to the quality loss of products and cost of supply chain during the time after harvest. Model responses to changes have been analyzed and explained orderly in the following:

Quantity of products and revenue versus reaction rate (k) of products

The quality loss rate (k) of different products varies depending on their reactivity, and processing reduces this rate in fresh products. To prevent the quality cost resulting from the products’ quality loss and price decline, the chain provides just part of the fresh product demands, not far than a specific distance (The table in S2 Table in the supporting information). When the quality loss rate (k) changes, the amount of the customer-demanded met products as well as those not enter the chain change too; the latter are processed at the beginning of the chain immediately after they are purchased and then sold as low-grade products to the second market. The ratio of the customer-offered to customer demand for different types of products and the amount sold to the second market were examined considering the product quality loss rate (k). The effects of the quality loss rate (k) on the stakeholders’ profit and revenue have also been studied. A summary of the results is shown in Fig 7.

10.1371/journal.pone.0303054.g007 Fig 7 Analysis of changes in reaction rate (k).

(a) Changes in quantities of products. (b) Changes in revenue/ profit of farmers and SC parts.

In the current chain, 96% of the demand for fresh products is met, and the rest is sold to the second market. As shown in Fig (7a), an increase in the quality loss rate (k) reduces the amount of fresh products. It increases the amount of those sold to the second market and supplied before entering the chain due to a sharp drop in fresh products, undesirability for customers, quality loss and price drop in the chain over time. A more increase in the mentioned rate (twice more) reduces the meeting rate of the customer-demanded fresh product from 96% to 35%; products sold to the second market increase from 64% to 100%, and the processed, dried and essence products, fully met, remain unchanged. Moreover, as shown in Fig (7b), an increase in the rate of product quality loss (k) does not reduce the farmer revenue, because the contract-specified products are bought from farmers at the original price.

As shown in Fig (7b), an increase in the quality-loss rate (k) of perishable products reduces the chain profit because some of these products, purchased from the farmer at the original contract price, do not enter the chain and are sold in the secondary market at lower prices (here, 0.3 times the contract price). Therefore, considering higher quality-loss rates (k) in the SCND will result in sharper reduced profits for the supply chain and the secondary market.

Supply chain cost/revenue versus speed of vehicles (v) changes

Under present conditions and the speed (v) of the current fleet in the case study (Vtrailer = 80 and Vtruck = 100 (km/ hour)), the model meets 96% of the demand for fresh products and all that for the dried and essence products; Faster fleet speeds enable more demands to be met (Fig 8A).

10.1371/journal.pone.0303054.g008 Fig 8 Analysis of supply chain designed results versus change in vehicles speed (v).

(a) Change in quantities of products (b). Change in number of vehicles (c). Change in cost/ revenue.

Increasing the speed (v) up to 50% will help the demand for fresh products to be met up to 100% and that for other products stays constant at 100%; however, reducing it up to 80% will not change the amount of processed products, but will cause the amount of the freshly supplied products to reach about 20% (Fig 8a).

As shown in Fig (8b), increasing the speed (v) leads to more use of faster vehicles (here, trucks). As shown, increasing the speed (v) to 100% will increase the number of needed trucks by 2%, but will not change the number of needed trailers. As mentioned earlier, trailers are used for outside-province long distances to respond to customers located far from the supply center. This will result in lower total long-distance transportation costs than trucks due to lower ton-km costs despite higher-order costs (The table in S1 Table in the supporting file).

Fig (8c) shows the minor increases in transportation costs and a noticeable reduction in the unmet-demand lost revenue due to the increased vehicle speed (v). Increasing the speed (v) up to 100% will increase the transportation costs by 11%, but reduces the unmet-demand lost revenue by 100%. This increased transportation cost of 0.008 million USD will prevent a revenue loss of 0.34 million USD, which is quite a significant figure.

It demonstrates that increasing the speed (v) will increase the number of vehicles, hence increase the transportation costs and the responded demand and ultimately prevent the revenue loss. Hence, increasing the speed (v) will lead to increased costs and enhanced chain revenue (Fig 9).

10.1371/journal.pone.0303054.g009 Fig 9 Analysis of different stakeholders’ cost/ revenue/ profit versus vehicles’ speed (v) change.

Since the increased revenue is greater than the increased cost, increasing the speed (v) will increase the chain profit; increasing the speed (v) up to 100% will increase the profit by 2.9 million USD (increased by 100%). Increasing the speed (v) will not affect the farmers’ revenue. The results comply with the findings of Patidar and Agrawal in research on traditional agricultural chains in India, in which the transportation share in supply chain costs reached about 92% in the distribution sector [12]. It shows the importance of transportation strategies in this sector.

A comparison of designed supply chain with traditional supply chain in the case study is demonstrated in Fig 10.

10.1371/journal.pone.0303054.g010 Fig 10 Designed SC with a second market in comparison with SC without a second market.

Regarding demands for fresh products, as shown in Fig 10, their amounts in the two cases (with and without a secondary market) are 10868 and 10068 tons, respectively, showing an increase of about 0.08 times; this leads to a quality increase and, hence, customer satisfaction and profit increase. In both cases, demands for dry and essence products are fully satisfied. The comparison between the results of the present supply chain design in the case study and the results with the lateral market indicates that a lateral market in the supply chain will increase the chain profit and farmer income. However, in the optimal mode in this case study, they are increasing from 9.7 and 5.85 to 12.5 (about +50%) and 8.8 (about +20%), respectively.

The results show that newly designed supply chain is applicable in the field of the perishable products supply chain. It confirms the necessity of supplying innovative products of perishable ones such as processed agricultural products to meet new customer needs in a lateral market to the competitiveness. It complies with the findings of Malynka and Perevozova, who proposed the lateral markets in mature and immature markets in the brand creation process [25].

4.5. Managerial insight

Some lessons and insights for managers are as follows.

All of the contract products are supposed to enter the chain; if not (for different reasons, e.g., chain management decision), some are sent to the second market, the presence of which prevents the produced products and resources (land, labor, energy, etc.) spent for those not entering the chain (for different reasons) from being wasted.

Not considering a second market for fresh perishable agricultural products e. g., vegetables will lead to ignoring the post-harvest quality loss-related costs.

Increasing the fleet speed is of great benefit to all the chain stakeholders including customers, chain management and environment because, on the one hand, it leads to increased response to the customer demand for more fresh products and selling customer-demanded high-quality products at prices proportionate to their grades will increase the chain profit and, hence, the total revenue, on the other, it prevents environmental pollution by letting more products to enter the supply chain and preventing wastes to be generated.

5. Conclusions

In this paper, a new approach is presented to optimize a logistics network design for distributing multiple products that are highly perishable and sensitive in quality and health of products to consumers, such as vegetables. Echelons of supply chain design include supply, processing, storage and customer. Considering the unpredictable amount of production of agricultural products and their perishability post-harvest, the second market which is accompanied by processing technologies to produce innovative products from the perishable products has been considered in the related supply chain network design, beside the main chain. The supply chain network design has been done based on maximization of profit by considering different quality costs in the supply chain. Quality costs include those due to: 1) quality-loss price-drop, 2) product waste and 3) losing credit with the customer for not meeting the desired demand. Since the chain integrity of these types of products is essential, the integrated one considered in this study is managed by the chain management deployed in the product supply center. Programming has been done based on the maximization of profit by the MILP model considering the quality costs of products in the supply chain. To evaluate the modeling, a case study was used on three vegetables cultivated and harvested in a fertile area in Iran country in September 2023. The model was subsequently validated by multiple sensitivity analyses performed on some of the essential parameters that had a greater effect on the results.

In this supply chain design, as it is demonstrated in Fig 2, different decisions have been made at strategic, tactical and operational levels in order to maximize profit by considering the costs of quality in the supply chain. Decisions made are on the location of processing centers and storage centers, and product flow allocations in the designed supply chain. Moreover, the model decides on the operations of processing after harvest, such as drying and extracting, which leads to mitigated products’ quality decay. In the next echelon after processing in the supply chain, there are storage centers in which products are stored to be distributed to the retailers. In the tactical level of decision making, the presented model decides on the allocation of farmers to processing centers and also processing centers to storage centers, moreover the allocation of storage centers to the retailers as the customers, also the number of products produced by farmers enters the supply chain and remains to be supplied to the second market and not deployed in the supply chain is determined. In the operational level of decision-making, the quantity of products and mode of transportation between different levels in the supply chain have been determined to meet the customers’ needs.

Results of this research were compared with those of related recent studies [9, 12, 25, 39]. The comparisons demonstrated good conformity, especially, in compliance with recent research in lateral besides vertical markets [25]. It seems innovative second markets are required to meet other parts of demand. Settling the lateral market seems strategic, especially in perishable products. The lateral market regulates supply and demand and helps reduce the quality-loss-related costs of the chain and responds to another part of the market that has specific customers.

6. Managerial implications

The proposed model is generic and can help managers in food quality, customer service, and other related operations as a tool to assist in decision-making in the perishable agricultural products supply chain. Specially, the research done can have the following applications:

The decisions stemming from the presented model are determined based on the products’ degradation pattern to maximize its quality. The decisions include supplier selection, supply chain design, processing technology deployment, and vehicle deployment.

A second market besides the chain and not higher than the vertical one in supply-based products such as vegetables, may result in a considerable increase in the chain profit without changing the resources, no reduction in the farmer income for unpredictable amounts of agricultural products production, and no wasted products preventing the environment from being polluted.

The usage of lateral marketing is relevant, as it is the most effective way of competition in mature markets. However, when chains are designed for perishable products for optimum profit, the demand for some products with high quality-loss rates is not met due too long distances from distribution centers (if it is met, high-quality costs will be imposed on the chain). The related products are processed for secondary customers and delivered to them in the second market.

Increased perishability rate of agricultural products reveals the effects and necessity of second markets next to the chain.

Although, high-speed shipping fleets are expensive, using them will increase the chain profit because they reduce the post-harvest travel time and, hence, reduce the quality-loss-related costs of perishable products significantly. This way, the demands of more customers are met, customer credit costs will be prevented and the supply chain management and customers will both be benefitted. By applying the proposed model in the perishable agricultural products supply chain, the products are sold in the second market to meet the lateral part of the market.

As a result, different stakeholders such as farmers, customers, the environment, and the owner of the supply chain may benefit from the new supply chain network design.

7. Future research and limitations

Our framework is limited in some respects. With that said, this modeling limitations serve as a platform for extending it in future researches. One primary limitation of the presented model is that it does not consider the uncertainty in the amount of customers’ demand. Therefore, the proposed model does not work for the problem in uncertain conditions. Also, the proposed model in this research has been solved by the exact-type solving method of mathematical programming, which is proper for solving the small size of problems such as the studied case. Considering the limitations above, using mathematical models by uncertainty considerations in the supply chain parameters and applying meta-heuristic methods to solve medium and large-sized problems are suggested in the future research. From the managerial perspective, the presented research works by the assumption of that upstream suppliers, freight transportation, processing centers, and storage facilities are integrated and it needs to build alignment between their organizations to deploy the solutions proposed by the output of the proposed framework. For these efforts to be successful, for future research, it is suggested to study how to cooperate all parties involved in the supply chain, and design the coordination infrastructure in the supply chain to yield the positive effects of proposed supply chain network design, in practice.

Supporting information

S1 Table Parameters of case study network design.

(DOCX)

S2 Table Quantity (tons) of each product delivered to customers and number of vehicles in logistics of designed SC.

(DOCX)

The authors are indebted to Mr. Ja’fary, the manager of “Razian” Co. (https://razian.co/), for his invaluable help to gather data in the case study. Also, the authors are grateful to the two anonymous referees for their valuable comments, which have led to significant improvements in this paper.

10.1371/journal.pone.0303054.r001
Decision Letter 0
Islam Md. Monirul Academic Editor
© 2024 Md. Monirul Islam
2024
Md. Monirul Islam
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version0
30 Oct 2023

PONE-D-23-27530A Multi-level Multi-Product Supply Chain Network Design of Vegetables Products Considering Quality Costs: A Case StudyPLOS ONE

Dear Dr. khazaeli,

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Additional Editor Comments:

Reviewer -1:

It should be recommended to add exact discussion about considering linear behavior for a perishable supply chain.

Some sensitivity analysis are so trivial and should be omitted.

Literature review should be checked. some significant published work has not been considered.

Comparative analysis should be covered difference between present condition of case study and proposed approach.

Reviewer-2:

Although the problem studied in this article is ok but the exposition is incomplete and inaccurate. Most of the viewpoints are simply explained abut not fully explained, and there are many problems in the model setting. Simplifying the model may get better results. Based on these concerns, I have to recommend that this paper should be considered for major revision.

While the paper provides a clear outline of the paper's objectives and methodology, it lacks specific details on the theories and approaches employed. To enhance the clarity and comprehensibility, I suggest incorporating the following :

1. Provide a brief summary of the approach: Explain the key principles and advantages of the method included to provide readers with a better understanding of its relevance to the proposed models.

2. Elaborate on the multiple-objective programming tools: Highlight the specific tools and techniques utilized and how they contribute to addressing the presence of such a huge network problem. This would help the readers comprehend the novelty and significance of the approach. Research gaps can be improved by using https://doi.org/10.3390/math9172093 and https://doi.org/10.1007/s11276-019-02246-6

https://link.springer.com/article/10.1007/s10100-023-00870-4

https://doi.org/10.1007/s10100-023-00874-0

3. Expand on the sufficient conditions to estimate the model: Provide further insights/assumptions into the conditions established by the proposed models, explain how these conditions are derived, and clarify their role in the overall analysis for the case data. Separate section to be considered for Case considerations.

4. Enhance the explanation of the application in the food sector/ perishable products : Give specific information about how the suggested models were used in the food sector/ perishable industry (please cite https://doi.org/10.1080/00207543.2012.752587), such as the data sources, variables that were looked at, and any results or insights that were gained from the use of the current data sets.

5. The results of the paper are simply stated without good explanations. The discussion of the obtained results must be well improved, highlighting the insights of the research findings and support from earlier literature such as https://doi.org/10.1038/s41598-022-26449-8.

6. It would be better if providing a more complete process instead of just states how to calculate it.

This submission looks like the student’s assignment and not a research paper .

7. Limitation of the work to be included along with the future research directions.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Partly

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: No

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: No

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: It should be recommended to add exact discussion about considering linear behavior for a perishable supply chain.

Some sensitivity analysis are so trivial and should be omitted.

Literature review should be checked. some significant published work has not been considered.

Comparative analysis should be covered difference between present condition of case study and proposed approach.

Reviewer #2: Although the problem studied in this article is ok but the exposition is incomplete and inaccurate. Most of the viewpoints are simply explained abut not fully explained, and there are many problems in the model setting. Simplifying the model may get better results. Based on these concerns, I have to recommend that this paper should be considered for major revision.

While the paper provides a clear outline of the paper's objectives and methodology, it lacks specific details on the theories and approaches employed. To enhance the clarity and comprehensibility, I suggest incorporating the following :

1. Provide a brief summary of the approach: Explain the key principles and advantages of the method included to provide readers with a better understanding of its relevance to the proposed models.

2. Elaborate on the multiple-objective programming tools: Highlight the specific tools and techniques utilized and how they contribute to addressing the presence of such a huge network problem. This would help the readers comprehend the novelty and significance of the approach. Research gaps can be improved by using https://doi.org/10.3390/math9172093 and https://doi.org/10.1007/s11276-019-02246-6

https://link.springer.com/article/10.1007/s10100-023-00870-4

https://doi.org/10.1007/s10100-023-00874-0

3. Expand on the sufficient conditions to estimate the model: Provide further insights/assumptions into the conditions established by the proposed models, explain how these conditions are derived, and clarify their role in the overall analysis for the case data. Separate section to be considered for Case considerations.

4. Enhance the explanation of the application in the food sector/ perishable products : Give specific information about how the suggested models were used in the food sector/ perishable industry (please cite https://doi.org/10.1080/00207543.2012.752587), such as the data sources, variables that were looked at, and any results or insights that were gained from the use of the current data sets.

5. The results of the paper are simply stated without good explanations. The discussion of the obtained results must be well improved, highlighting the insights of the research findings and support from earlier literature such as https://doi.org/10.1038/s41598-022-26449-8.

6. It would be better if providing a more complete process instead of just states how to calculate it.

This submission looks like the student’s assignment and not a research paper .

7. Limitation of the work to be included along with the future research directions.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Professor (Dr.) Sadia Samar Ali

**********

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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

10.1371/journal.pone.0303054.r002
Author response to Decision Letter 0
Submission Version1
18 Dec 2023

Editor points:

Dear editor,

Thank you for the comments which led us to make the paper ready to be sent the journal in its standards. We have done the changes in the paper as follows.

We add authors’ information in the manuscript.

We do the requirements of the journal in the paper to be the paper proper for the journal.

We add data in an appendix in a supplementary file and mentioned it in a manuscript.

We make ready three other files as, manuscript, manuscript with track changes and response to the reviewers’ comments and attached them in the revision process.

Point-by-Point Response Letter

Reviewer 1:

Dear reviewer,

Thank you for your insightful comments and suggestions which led us to improve the paper. We have modified the manuscript thoroughly according to your valuable comments and helpful suggestions. Please find the revised version of the paper enclosed. The following are our responses to your comments. Please note that the referees’ comments are written in green and our responses in black. Also, the by-one-by response to the comments are as follows.

It should be recommended to add exact discussion about considering linear behavior for a perishable supply chain.

Thank you for your comment. The linear behavior for a perishable agricultural products, independent of environmental factors such as temperature variations has been re-explained in the “literature review” as follows:

In practice the decrease of a single quality attribute can be approximated by one of the four basic types of mechanism which are zero order reactions having linear kinetics, Michaelis Menten kinetics, first order reactions having exponential kinetics and autocatalytic reactions with logistic kinetics (HAYAKAWA and TIMBERS, 1977; Varoquaux and Wiley, 1994). Although linear kinetics are relatively rare, Michaelis Menten kinetics are observed more frequently. The Micaelis Menten kinetics reduces to a linear one in the initial region of decay, which is the most important in quality assessment. Therefore the variable of quality in vegetables in the initial region of decay can be considered as the function of time post-harvest linearly (Tijskens and Polderdijk, 1996). It is shown in Equation 1.

Q(t)=Q_0-k .t (1)

Where, Q0 is the initial quality, t is time and k is a degradation rate. In a dynamic environment, as the quality function works by the exponential kinetics, the degradation rate of quality (k) depends on the type of chemical synthesis, the activation energy of material and the gas constant by Arrhenius relation (Chang, 1900).

Some sensitivity analysis are so trivial and should be omitted.

Thank you for your comment. Two last part of the sensitivity analysis section has been improved not to be trivial as follows:

Since the increased revenue is greater than the increased cost, increasing the speed (v) will increase the chain profit; increasing the speed (v) up to 100% will increase the profit by 2.9 million USD (increased by 100%). Increasing the speed (v) will not affect the farmers’ revenue. The results comply with findings of Patidar and Agrawal in research of traditional agricultural chains in India, in which the transportation share in SC costs reached about 92% in the distribution sector (Patidar and Agrawal, 2020). It shows the importance of transportation strategies in this sector.

Regarding demands for fresh products, as shown in Figure 2, their amounts in the two cases (with and without a secondary market) are 10868 and 10068 tons, respectively, showing an increase of about 0.08 times; this leads to a quality increase and, hence, customer satisfaction and profit increase. In both cases, demands for dry and essence products are fully satisfied. The results show that new designed supply chain is applicable in the field of perishable products supply chain. It confirms the necessity of supplying innovative products of perishable ones such as processed agricultural products to meet new customer needs in a lateral market in order to the competitiveness. It complies with the findings of Malynka and Perevozova, who proposed the lateral markets in mature and immature markets in brand creation process (Malynka and Perevozova, 2019).

Literature review should be checked. Some significant published work has not been considered

Thank you for your comment. The related papers have been studied, hence the “Introduction” and “literature review” has been updated by relevant papers. Also, the recent quantitative models have been studied, as all are shown orderly on pages 2-5, as follows:

In the introduction section:

Quality of vegetables is one of important measures to its customers due to quality deterioration rate of products which relates to the health of consumers (Forman et al., 2012). Time decay and shortages are a common phenomenon in products with short life cycles, and financial volatility necessitates more accurate characterization of inventory costs based on time-adjusted value (Ali et al., 2013). Moreover the quality deterioration often happens in traditional supply chains which, for the most part, are poorly planned

Recently some strategies studied in supply chain management of perishable products due to control the perishability of products which are inventory management (Ali et al., 2021), reverse logistic management (Ali et al., 2020), pricing (Mohammadi et al., 2023) and robust optimization (Goli et al., 2023).

Today, lateral marketing is the most effective way of competing on the mature/immature markets, where micro-segmentation and plenty of brands don’t leave any space for new opportunities (Malynka and Perevozova, 2019).

In the literature review section:

The optimal operation strategy is acquired based on product quality (Guo et al., 2021).

Making decisions in an integrated way will reduce costs compared to individual decisions made at each level (Salehi et al., 2020; Song and Wu, 2022), Pasha et al. studied an integrated bi-objective quality-based production-distribution agri-food MILP SC model in which profitability is maximized by defining the quality as a function of such decisions as the location of hubs and transportation strategy throughout the SC. Moreover, in the greenery SCs, De Keizer et al. presented a model on which decisions made on the greenhouse location (strategic) based on the plant’s lifetime in that location (De Keizer et al., 2017). As changes in the temperature and enthalpy levels change the food quality (Soysal et al., 2012), Khazaeli et al. and Rong et. al determined the temperature of distribution centers and deliveries so as to meet the expectations of different customers as the operational decision making in a supply chain programming (Khazaeli et al., 2023; Rong et al., 2011).

In a dynamic environment, as the quality function works by the exponential kinetics, the degradation rate of quality (k) depends on the type of chemical synthesis, the activation energy of material and the gas constant by Arrhenius relation (Chang, 1981). In the most of network designs, cost and benefit and quality factors are the most important factors that are to be optimized. Mostly, agri-food should make a logical balance between two topics of price reduction and customer service improvement (Soysal, Bloemhof-Ruwaard et al. 2012). Usually, the economic criteria are considered based on resource utilization and customer responsiveness; the latter means meeting part of the customer demand in due delivery time.. De Keizer et al. and Khazaeli et al. indicated quality of agricultural products causes cost in supply chain’s network designs. They showed that there is a conflict between factors of cost and quality (De Keizer et al., 2015; Khazaeli et al., 2023).

Comparative analysis should be covered difference between present condition of case study and proposed approach.

Thank you for your feedback. As the following comparison between present condition of case study and proposed approach were suggested by the reviewer to be included in the paper, we have done our best to clarify this issue by Figure 10 and its descriptions as follows:

The comparison between results of present supply chain design in the case study and the results with lateral market indicates that a lateral market in the supply chain will increase the chain profit and farmer income. However, in the optimal mode in this case study, they are increasing from 9.7 and 5.85 to 12.5 (about +50%) and 8.8 (about +20%), respectively.

The results show that new designed supply chain is applicable in the field of perishable products supply chain. It confirms the necessity of supplying innovative products of perishable ones such as processed agricultural products to meet new customer needs in a lateral market in order to the competitiveness. It complies with the findings of Malynka and Perevozova, who proposed the lateral markets in mature and immature markets in brand creation process (Malynka and Perevozova, 2019).…

 

Reviewer 2:

Dear reviewer,

Thank you for the time you put in to evaluate our manuscript. Your feedback has been invaluable to our work. Please find the revised version of the paper enclosed. The following are our responses to your comments. Please note that the referees’ comments are written in green and our responses in black. Also, the by-one-by response to the comments are as follows.

Although the problem studied in this article is ok but the exposition is incomplete and inaccurate. Most of the viewpoints are simply explained about not fully explained, and there are many problems in the model setting. Simplifying the model may get better results. Based on these concerns, I have to recommend that this paper should be considered for major revision. While the paper provides a clear outline of the paper's objectives and methodology, it lacks specific details on the theories and approaches employed. To enhance the clarity and comprehensibility, I suggest incorporating the following

We appreciate your positive feedback on the topic. We have modified the manuscript according to the reviewer’s helpful comments and suggestions. We’ve done our best to more precisely clarify the confusing and poorly written component. In our opinion, now the manuscript is more suitable to the Journal.

Provide a brief summary of the approach: Explain the key principles and advantages of the method included to provide readers with a better understanding of its relevance to the proposed models.

Thank you for your comment. The present study -past researches relationship is shown in the “the research gap and contributions”, as follows:

A review of quantitative SC researches on the perishability of agri-food by considering quality costs in Section 2, outlines the gaps in the literature as follows:

1. Despite the importance of cost of qualities in designing SCs due to the perishability of the products, the cost of quality concept has not been widely incorporated by researchers in the design of agricultural products’ SCs.

2. No research has paid attention to the lateral market to look at the quality problems from the side in which covering some target customers.

3. Few researchers have considered benefits of several stakeholders of the agricultural SCs simultaneously. The stakeholders in agricultural Products’ SC are consumers, farmers, environment and society.

Due to the importance and necessity of developing supply chain management (SCM) from a larger perspective to provide a win-win situation for each participant in the SC, in this paper, we aim to develop a novel mathematical model in order to design a SC network, based on quality function elements in the vegetables’ sector.

The main contributions are as follows:

Providing a network design model for an integrated multi-level SC of perishable products wherein profit is optimized by considering quality decay aspect of the products.

Optimizing the profit of the SC of perishable products considering different quality costs for them due to unmet demand, product waste and reduced revenue of low-quality products.

Introducing a strategy of selling perishable products to lateral markets before letting products enter the chain to prevent the production of low-quality products along it.

Enabling the purchase of the farmer’s total agricultural product above the contract ceiling due to unpredictable production to prevent waste production and its scattering in the environment.

Introducing a strategy of producing semi-processed, low-quality products (from those that did not enter the chain) to meet part of the market demand for lower-quality lower-price products.

The key principles and advantages of the method included to provide readers with a better understanding of its relevance to the proposed models are mentioned as follows.

The proposed SCND is a multi-product, multi-echelon model with exact (certain) demand that makes decisions at strategic, tactical and operational levels. It has focused on “quality” by considering the quality deterioration in a Micaelis Menten kinetics in the initial region of decay reduced to a linear one, moreover, by defining costs of quality degradation in the quality-cost functions.

The developed model is a four-echelon SC of perishable agricultural products in which static decade rate of the products is considered. Moreover, a lateral market is considered in the SC that does not stand higher than the vertical marketing and complete the main market. In the end, the developed model is applied to a case study of a firm in agricultural products’ industry with four echelons of farm-processing-distribution-customer centers. The vegetables selected as candidate for the present SC network design are Yarrow, Borage flower and Melisa, due to their priority in agricultural studies and their application in various industries (Agriculture ministry of Iran, 2022).

Elaborate on the multiple-objective programming tools: Highlight the specific tools and techniques utilized and how they contribute to addressing the presence of such a huge network problem. This would help the readers comprehend the novelty and significance of the approach. Research gaps can be improved by using https://doi.org/10.3390/math9172093

Although there are some researches done in order to minimize quality losses of perishable products by multi-objective problem solving approaches (Ali et al., 2021, 2020; Goli et al., 2023; Khazaeli et al., 2023; Pasha et al., 2021), the programming in present research is a single objective problem solving by profit objective function underlying quality loss costs. Hence the proposed model is not a multi-objective, but also a single objective one.

The mentioned reference is cited as a related research in other parts of the manuscript, “the literature review”.

Expand on the sufficient conditions to estimate the model: Provide further insights/assumptions into the conditions established by the proposed models, explain how these conditions are derived, and clarify their role in the overall analysis for the case data. Separate section to be considered for Case considerations.

Firstly, the conditions and assumptions of the modeling are presented in first part of section 3 as follows.

The designed supply chain of the firm is shown in Figure 1.

Figure 1. Flow diagram of the agricultural products’ SC.

Source(s): Authors’ work

First, products through related contracts and in-excess products are bought from farmers in the study area. In the second echelon of the proposed SC, some or all of the purchased products are processed at related centers resulting in different degrees of product quality. Third, the products in former echelon are stored in cool storage centers until being distributed and fourth, they are sold to wholesalers. Another part of the purchased products are transferred to the second market as lower quality products in different industries (tea bags, spices in food, etc.). Different road modes of transport are used between different echelons of the SC.

The modeling makes decisions at different echelons of the SC. Decisions made are (1) selecting farms and the quantity of raw products to be purchased from each of them, (2) the amount of products sold to the second market, (3) the number of processing and storage facilities to be settled in the SC, (4)

Attachment Submitted filename: Response to Reviewers.docx

10.1371/journal.pone.0303054.r003
Decision Letter 1
Islam Md. Monirul Academic Editor
© 2024 Md. Monirul Islam
2024
Md. Monirul Islam
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version1
2 Jan 2024

PONE-D-23-27530R1A Multi-level Multi-Product Supply Chain Network Design of Vegetables Products Considering Quality Costs: A Case StudyPLOS ONE

Dear Dr. khazaeli,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Reviewer-1

Respond to first comment "It should be recommended to add exact discussion about considering linear behavior for a perishable supply chain" is not acceptable because used references are old.

Reviewer-2

1. Consider adding an Implications section that zeroes in on managerial and policy-maker implications, as this may enhance the practical relevance of the research.

2. A dedicated section for Future Research and Limitations can provide readers with a clearer understanding of potential avenues for further inquiry and the boundaries of the current study.

3. Refraining from using bullets, especially in Future research, limitations, and uniqueness of the study can help maintain a consistent and professional format throughout the manuscript.

4. Why Quality as a keyword is used in the title? Replace with some other word.

Please submit your revised manuscript by Feb 16 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Md. Monirul Islam, PhD

Academic Editor

PLOS ONE

Additional Editor Comments:

Dear Author

Thank you so much for your effort. Please provide the necessary corrections as suggested by the expert review panel. Good Luck.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: (No Response)

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Partly

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Respond to first comment "It should be recommended to add exact discussion about considering linear behavior for a

perishable supply chain" is not acceptable because used references are old.

Reviewer #2: I truly appreciate the effort dedicated to revising the manuscript. While reviewing the document, I have a few constructive suggestions for further improvement:

1. Consider adding an Implications section that zeroes in on managerial and policy-maker implications, as this may enhance the practical relevance of the research.

2. A dedicated section for Future Research and Limitations can provide readers with a clearer understanding of potential avenues for further inquiry and the boundaries of the current study.

3. Refraining from using bullets, especially in Future research, limitations, and uniqueness of the study can help maintain a consistent and professional format throughout the manuscript.

4. Why Quality as a keyword is used in the title ? Replace with some other word.

I hope these recommendations prove helpful in refining the manuscript.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

**********

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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

10.1371/journal.pone.0303054.r004
Author response to Decision Letter 1
Submission Version2
30 Jan 2024

Point-by-Point Response Letter

Reviewer 1:

Dear reviewer,

Thank you for your insightful comment which led us to improve the paper. We have modified the manuscript thoroughly according to your valuable comment. Please find the revised version of the paper enclosed. In newly enclosed revised version of the paper, the new changes in this second revised version of the manuscript are highlighted in yellow color. Track changes show the changes in the first revision of the manuscript.

The following is our response to your comment. Please note that the referees’ comment is written in green and our responses in black.

Respond to first comment "It should be recommended to add exact discussion about considering linear behavior for a perishable supply chain" is not acceptable because used references are old.

Thank you for your comment. The linear behavior for perishable agricultural products, independent of environmental factors such as temperature variations has been re-explained in the “literature review” with some new references as follows:

The quality function of perishable agricultural products can be either complex or simple (Centobelli et al., 2021). It has been shown that, the decrease of a single quality attribute of agricultural products can be approximated by one of the four basic types of mechanism which are zero-order reactions having linear kinetics, Michaelis Menten kinetics, first-order reactions having exponential kinetics, and autocatalytic reactions with logistic kinetics (HAYAKAWA and TIMBERS, 1977; Varoquaux and Wiley, 1994). For the concept of keeping quality, the actual mechanism does not play a role. For this reason, it is convenient to assume zero-order reaction kinetics (Tijskens and Polderdijk, 1996), and mostly the Michaelis Menten kinetics reduces to a linear one in the initial region of decay, which is the most important in quality assessment (Hertog et al., 2014). Therefore, the variable of quality in vegetables in the initial region of decay can be considered as the function of time post-harvest linearly, which is shown in Equation 1.

Q(t)=Q_0-k .t (1)

Where, Q0 is the initial quality, t is time and k is a degradation rate. Borghi D de Freitas et al. minimized the losses of fruits and vegetables that happen during its storage in a mathematical model, based on Equation 1 (Ferreira et al., 2005).

Reviewer 2:

Dear reviewer,

Thank you for the time you put in to evaluate our manuscript. Your feedback has been invaluable to our work. Please find the revised version of the paper enclosed. In newly enclosed revised version of the paper, the new changes in this second revised version of the manuscript are highlighted in yellow color. Track changes show the changes in the first revision of the manuscript.

The following are our responses to your comments. Please note that the referees’ comments are written in green and our responses in black. Also, the by-one-by response to the comments are as follows.

Consider adding an Implications section that zeroes in on managerial and policy-maker implications, as this may enhance the practical relevance of the research.

Thank you for your comment. To enhance the practical relevance of the research, the managerial implications section is added as Section 6 to the end of the manuscript, as follows:

The proposed model is generic and can help logistic managers as a tool to assist in decision-making related to the logistics of perishable agricultural products in the supply chain. Specially, the research done can have the following applications:

A second market besides the chain and not higher than the vertical one in supply-based products such as vegetables, may result in a considerable increase in the chain profit without changing the resources, no reduction in the farmer income for unpredictable amounts of agricultural products production, and no wasted products preventing the environment from being polluted.

The usage of lateral marketing is relevant, as it is the most effective way of competition in mature markets.

When chains are designed for perishable products for optimum profit, the demand for some products with high quality-loss rates is not met due too long distances from distribution centers (if it is met, high-quality costs will be imposed on the chain).

Increased perishability rate of agricultural products reveals the effects and necessity of second markets next to the chain.

Although, high speed shipping fleets are expensive, using them will increase the chain profit because they reduce the post-harvest travel time and, hence, reduce the quality-loss-related costs of perishable products significantly. This way, the demands of more customers are met, customer credit costs will be prevented and the supply chain management and customers will both be benefitted. By applying the proposed model in the perishable agricultural products supply chain, the products are sold in the second market to meet the lateral part of the market. As a result, different stakeholders such as farmers, customers, the environment, and the owner of the supply chain may benefit from the new supply chain network design

A dedicated section for Future Research and Limitations can provide readers with a clearer understanding of potential avenues for further inquiry and the boundaries of the current study.

A separate section has been dedicated to future research and limitations to provide readers with a clearer understanding of potential avenues for future research and the boundaries of the current study in Section 7 as follows:

The limitations of this study include not considering pricing policies. The proposed solution method computed the optimal solution by the exact-type solving method of mathematical programming with certain parameters and it does not work for the problem in uncertain conditions. Due to the size of the case study problem and related certain parameters, this solution method is not applicable to large-size problems. Considering the limitations of and the results obtained in this study, directions for future research include considering pricing policies for products sold to the second market to maximize the profit of the stakeholders. As it is computed the optimal solution by the exact-type solving method of mathematical programming with certain parameters, using mathematical models to consider uncertainties in the SC parameters is suggested. Moreover, applying meta-heuristic methods to solve medium and large-sized problems is suggested in future research.

Refraining from using bullets, especially in Future research, limitations, and uniqueness of the study can help maintain a consistent and professional format throughout the manuscript.

Thank you for your comment. We refrain from using bullets in future research and limitations.

Why Quality as a keyword is used in the title? Replace with some other word.

Thank you for your comment. The word “Quality” in the title is not a separate word and it is part of the concept of “Cost of quality”, which is introduced by Feigenbaum and Crozby in the Total Quality Management philosophy. “Cost of quality” concept is a technique to measure the non-conformance with quality features. To the above-mentioned concept be clearer, the title is modified as follows.

“A Multi-level Multi-Product Supply Chain Network Design of Vegetables Products Considering Costs of Quality: A Case Study”.

Attachment Submitted filename: Response to Reviewers2.docx

10.1371/journal.pone.0303054.r005
Decision Letter 2
Islam Md. Monirul Academic Editor
© 2024 Md. Monirul Islam
2024
Md. Monirul Islam
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version2
4 Mar 2024

PONE-D-23-27530R2A Multi-level Multi-Product Supply Chain Network Design of Vegetables Products Considering Costs of Quality: A Case StudyPLOS ONE

Dear Dr. khazaeli,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Comments:1. The abstract needs to have a smooth flow in terms of the discussions . Don't include pointwise discussions.

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1. The abstract needs to have a smooth flow in terms of the discussions . Don't include pointwise discussions.

2. Many subsections were included, which prevented the readers from having a smooth reading. Kindly adjust and remove the subsection numbers.

3. Data availability references and tables/data-based in-depth information are not given .

4. The paper needs clearer insights into future trends and the ability of researchers to pursue them based on existing research. More detailed discussions on future research directions, trends, challenges, and opportunities are needed.

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Comments to the Author

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Reviewer #1: (No Response)

Reviewer #2: (No Response)

Reviewer #3: All comments have been addressed

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Reviewer #1: Respond of authors about linear behavior for a perishable supply chain is not suitable nowadays thence originality of work is weak.

Reviewer #2: 1. The abstract needs to have a smooth flow in terms of the discussions . Don't include pointwise discussions.

2. Many subsections were included, which prevented the readers from having a smooth reading. Kindly adjust and remove the subsection numbers.

3. Data availability references and tables/data-based in-depth information are not given .

4. The paper needs clearer insights into future trends and the ability of researchers to pursue them based on existing research. More detailed discussions on future research directions, trends, challenges, and opportunities are needed.

Reviewer #3: No comment

Good work

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10.1371/journal.pone.0303054.r006
Author response to Decision Letter 2
Submission Version3
17 Apr 2024

Point-by-Point Response Letter

Academic Editor:

Dear academic editor,

Thank you for your attention to our manuscript. As you emphasized on the second reviewer questions, the questions you mentioned are answered in pages 3-4.

 

Reviewer 1:

Dear reviewer,

Thank you for your insightful comment which led us to improve the paper. We have modified the manuscript thoroughly according to your valuable comment. Please find the revised version of the paper enclosed. In newly enclosed revised version of the paper, the new changes in this third revised version of the manuscript are highlighted in yellow color. Track changes show the changes in the second revision of the manuscript.

The following is our response to your comment. Please note that the referees’ comment is written in green and our responses in black.

Respond of authors about linear behavior for a perishable supply chain is not suitable nowadays thence originality of work is weak.

Thank you for your comment. The linear behavior for perishable agricultural products is widely used in the literature in modeling of the products’ perishability. It has been re-explained in the “literature review”, precisely. Moreover, some new references, which uses this modeling approach in the quality definition of perishable agricultural products are mentioned to demonstrate that the application of the linear behavior of the perishable products’ quality in time has been recently used in different mathematical modeling of quality behavior, as follows:

The quality function of perishable agricultural products can be either complex or simple [44]. It has been shown that, the decrease of a single quality attribute of agricultural products can be approximated by one of the four basic types of mechanism which are zero-order reactions having linear kinetics, Michaelis Menten kinetics, first-order reactions having exponential kinetics, and autocatalytic reactions with logistic kinetics [45], [46]. For the concept of keeping quality, it is convenient to assume zero-order reaction kinetics [47], and mostly the Michaelis Menten kinetics reduces to a linear one in the initial region of decay, which is the most important in quality assessment [48]. Therefore, the quality variable of vegetables in the initial region of decay can be considered in a widely used equation, in which the quality function changes by the time linearly. It is shown in Equation 1.

dQ/dt=k Q(t)=Q_0-k .t (1)

Where, Q0 is the initial quality, t is time and k is a degradation rate. In a dynamic environment, the well-known Arrhenius equation shows that the degradation rate (k) depends on the activation energy of the material, and the environmental factors [47], [49], [50].

The perishable products’ quality model shown in Equation 1 has been frequently used to capture the degradation of food products over time. For example, in the grocery retail chain, Wang and Li presented a pricing model to maximize food retailer’s profit in a dynamically identified food shelf life by using Equation 1 [51]. Chen and Chen proposed an on-site direct-sale dynamic supply chain inventory model, considering time-dependent quality losses for perishable foods [22]. Lejarza and Baldea presented a closed-loop, feedback-based control framework, that employs real-time product quality measurements for optimal supply chain management [52]. Moreover, Xu et al. presented a real time decision support framework to mitigate the quality degradation in the journey of agricultural perishable products from farm to the retailer in the supply chain based on the Equation 1 [53].

Reviewer 2:

Dear reviewer,

Thank you for the time you put in to evaluate our manuscript. Your feedback has been invaluable to our work. Please find the revised version of the paper enclosed. In newly enclosed revised version of the paper, the new changes in this second revised version of the manuscript are highlighted in yellow color. Track changes show the changes in the second revision of the manuscript.

The following are our responses to your comments. Please note that the referees’ comments are written in green and our responses in black. Also, the by-one-by response to the comments are as follows.

The abstract needs to have a smooth flow in terms of the discussions. Don't include pointwise discussions.

Thank you for your comment. To make the abstract have a smooth flow, especially in terms of the discussion, we re-write the abstract, as follows:

Effective logistics management is crucial for the distribution of perishable agricultural products to ensure they reach customers in high-quality condition. This research examines an integrated, multi-echelon supply chain for perishable agricultural goods. The supply chain consists of four stages: supply, processing, storage, and customers. This study investigates the quality-related costs associated with product perishability to maximize supply chain profitability. Key factors considered include the network design, location of processing and distribution centers, the ability to process raw products to minimize post-harvest quality degradation, the option to sell the excess produce to a secondary market due to unpredictable yields, and the decision not to fulfill demand from distant customers where significant quality loss and price drops would be involved, instead diverting those products to the aforementioned secondary market. Quantitative methods and linear mathematical programming are employed to model and validate the proposed supply chain using actual data from a real-world case study on vegetable supply chains. The main contribution of this research is the incorporation of quality costs into the objective function, which allows the supply chain to prioritize meeting nearby customers' demands with minimal quality loss over serving distant customers where high quality loss is unavoidable. Additionally, deploying a faster transportation fleet can significantly improve the overall profitability of the perishable product supply chain

Many subsections were included, which prevented the readers from having a smooth reading. Kindly adjust and remove the subsection numbers.

Thank you for your comment. The subsection numbers are made to only one and second level. The third level of the subsection numbers is removed, as it is apparent in the manuscript. Please check it in the new one.

Data availability references and tables/data-based in-depth information are not given.

Thank you for your comment. The more precise data availability references and data-based in-depth information are stated in the case study section, as follows:

In this section, we implement the proposed model in an Iranian raw and processed vegetable products’ company, the Razian Company, as a case study.

The case study used a four-echelon SCND, and materials were supplied, processed, and stored (echelons 1-3) in the firm area (origin) while the last-level centers were located all over the country; in addition, a center was established as a second market to collect the in-excess products, as shown in Fig. 1. The mentioned lateral market imposes no costs on the supply chain because it is closest to farms, and customers pay the transportation costs.

At first, the firm seasonally provided the vegetables from the suppliers. Suppliers were specified and contracted in advance in fertilized source centers (i=4) of selected vegetables (n=3). The farm centers were, in Kaboudrahang, Razan, Nahavand, and Malayer, and the vegetable products were Yarrow, Borage flower, and Melisa. Secondly, the firm used the related processing on vegetables, or the products remained raw. There are potential processing center (j=5) candidates in the case study. Thirdly, the firm stored the products in the storage centers for packaging. There are potential storage center (k=5) candidates in the case study. The five potential processing and storage center candidates were Kaboudrahang, Razan, Nahavand, Malayer, and Asadabad. Finally, the firm delivered the demanded products to the customer centers. The customers were trade representatives of each province all over the country (l=30). Due to the importance of the case study data for the application of the presented model, some were obtained from the enterprise resource planning (ERP) of Razian company (https://razian.co/). In addition, data on fixed and variable costs of different transportation modes were obtained from the recent case study research done in Iran [39]. Data on the price of different raw and processed vegetable products were gathered from the statistics of the Ministry of Agriculture [56]. Details of the most critical data of the case study are presented in Table S1 in the Appendix.

Of course, the Appendix is a separate file attached.

The paper needs clearer insights into future trends and the ability of researchers to pursue them based on existing research. More detailed discussions on future research directions, trends, challenges, and opportunities are needed.

Thank you for your comment. As you mentioned in this valuable comment, we re-write the limitations and future research section, with a more detailed discussion on the future research directions and opportunity to do valuable research in the future for those whom are passionate about the field of agricultural products supply chain design, as follows:

Our framework is limited in some respects. With that said, this modeling limitations serve as a platform for extending it in future researches. One primary limitation of the presented model is that it does not consider the uncertainty in the amount of customers’ demand. Therefore, the proposed model does not work for the problem in uncertain conditions. Also, the proposed model in this research has been solved by the exact-type solving method of mathematical programming, which is proper for solving the small size of problems such as the studied case. Considering the limitations above, using mathematical models by uncertainty considerations in the supply chain parameters and applying meta-heuristic methods to solve medium and large-sized problems are suggested in the future research. From the managerial perspective, the presented research works by the assumption of that upstream suppliers, freight transportation, processing centers, and storage facilities are integrated and it needs to build alignment between their organizations to deploy the solutions proposed by the output of the proposed framework. For these efforts to be successful, for future research, it is suggested to study how to cooperate all parties involved in the supply chain, and design the coordination infrastructure in the supply chain to yield the positive effects of proposed supply chain network design, in practice.

Reviewer 3:

Dear reviewer,

Thank you for the time you put into evaluating our manuscript. We are grateful to you for your positive feedback to our work.

Attachment Submitted filename: Response to Reviewers-R3.docx

10.1371/journal.pone.0303054.r007
Decision Letter 3
Islam Md. Monirul Academic Editor
© 2024 Md. Monirul Islam
2024
Md. Monirul Islam
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version3
19 Apr 2024

A Multi-level Multi-Product Supply Chain Network Design of Vegetables Products Considering Costs of Quality: A Case Study

PONE-D-23-27530R3

Dear Dr. sareh khazaeli,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Md. Monirul Islam, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Dear author

Well done. Best of luck.

Reviewers' comments:

10.1371/journal.pone.0303054.r008
Acceptance letter
Islam Md. Monirul Academic Editor
© 2024 Md. Monirul Islam
2024
Md. Monirul Islam
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
22 May 2024

PONE-D-23-27530R3

PLOS ONE

Dear Dr. khazaeli,

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==== Refs
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