Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
05
24
Optimal design of cross docking supply chain networks with time-varying uncertain demands
1
20
EN
Javad
Behnamian
Department of Industrial Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran
behnamian@basu.ac.ir
Seyed Mohammad Taghi
Fatemi Ghomi
0000-0003-4363-994X
Department of Industrial Engineering,Amirkabir University of Technology,Tehran,Iran
fatemi@aut.ac.ir
Fariborz
Jolai
Department of Industrial Engineering,University of Tehran
fjolai@ut.ac.ir
M.
Telgerdi
Department of Industrial Engineering,Amirkabir University of Technology, Tehran, Iran
m_telgerdi@aut.ac.ir
This paper proposes an integrated network design model for a post-distribution cross-docking strategy, comprising multi product production facilities with shared production resources, capacitated cross docks with setup cost and customer zones with time windows constraints. The model is dynamic in terms of time-varying uncertain demands, whereas uncertainty is expressed with scenario approach and contains both ‘‘wait-and-see’’ and ‘‘here-and-now’’ decisions. Inventory is just permitted in plants and over several time periods. The objective of the model is to minimize the sum of the fixed location costs for establishing cross docking centers and inventory related costs across the supply chain while ensuring that the limited service rate of cross docking centers and production facilities, and also the lead time requirements of customers are not violated. The problem is formulated as a mixed-integer linear programming problem and solved to global optimality using CPLEX. Due to the difficulty of obtaining the optimum solution in medium and large-scale problems, two heuristics that generate globally feasible, near optimal solution, Imperialistic competitive algorithm (ICA) and simulated annealing (SA), are also proposed as heuristics. We find that CPLEX is not able to solve some of the sets to optimality and turned out to run out of memory, but it performs quite well for small test sets, as compared with the two heuristics. While SA is a faster heuristic method in terms of runtime, ICA generates better results on average, but in more time.
Facilities planning and design,cross-docking,mixed integer model,heuristics
http://www.jise.ir/article_57038.html
http://www.jise.ir/article_57038_e153c6963b818db665cafd171f454224.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
08
01
A New Formulation for Cost-Sensitive Two Group Support Vector Machine with Multiple Error Rate
21
30
EN
Amir Abbas
Najafi
Faculty of Industrial Engineering, K.N.Toosi University of Technology
aanajafi@kntu.ac.ir
Ali
Nedaie
Faculty of Industrial Engineering, K.N.Toosi University of Technology
alinedaie@kntu.ac.ir
Support vector machine (SVM) is a popular classification technique which classifies data using a max-margin separator hyperplane. The normal vector and bias of the mentioned hyperplane is determined by solving a quadratic model implies that SVM training confronts by an optimization problem. Among of the extensions of SVM, cost-sensitive scheme refers to a model with multiple costs which considers different error rates for misclassification. The cost-sensitive scheme is useful when misclassifications cannot be considered equal. For example, it is true for medical diagnosis. In such cases, misclassifying a patient as healthy implies more loss in comparison to the opposite loss. Therefore, cost-sensitive scheme poses as a modified model and hereby aims at minimizing loss function instead of generalization error. This paper, concentrates on a new formulation cost-sensitive classification considering both misclassification cost and accuracy measures. Also, in the training phase a new heuristic algorithm will be used to solve the proposed model. The superiority of the novel method is affirmed after comparing to the traditional ones.
Cost-sensitive Learning,Classification,Support Vector Machine,Supervised Learning
http://www.jise.ir/article_59552.html
http://www.jise.ir/article_59552_f44503642f2159cf052a6ed3d35f93d4.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
08
02
The effects of misclassification errors on multiple deferred state attribute sampling plan
31
46
EN
Robab
Afshari
Ferdowsi University of Mashhad
robab.afshari@mail.um.ac.ir
Bahram
Sadeghpour Gildeh
0000-0003-0863-676X
Ferdowsi University of Mashhad
sadeghpour@um.ac.ir
Multiple deferred state (MDS) sampling plan by attribute in which current lot and future lots information is utilised on sentencing submitted lot, is constructed under the assumption of perfect inspection. But sometimes the inspection may not be free of inspection errors. In this paper, we develop MDS-plan by attribute to the state where misclassification errors exist during the inspection. In the following, we consider effects of the inspection errors on operating characteristic curve, expected disposition time and average sample number (ASN) for decision in MDS- plan. In order to discuss influence of the inspection errors on these mentioned measures, we have more focus on a specific feature of MDS(0,1,2)-plan. Also, some applicable examples are given to make more understanding. The results show that accuracy and performance of MDS(0,1,2)-plan can be affected by the inspection errors. Also we show that the inspection errors not only cause the considerable difference between true and observed curves of the expected disposition time in MDS(0,1,2)-plan but also have a negative influence on the ASN curve of the mentioned plan.
Multiple deferred state sampling plan,inspection errors,operating characteristic curve,average sample number
http://www.jise.ir/article_59609.html
http://www.jise.ir/article_59609_afe6782afe2d7abb93bd06d3004cbeb9.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
08
23
An Optimal Preventive Maintenance Model to Enhance Availability and Reliability of Flexible Manufacturing Systems
47
61
EN
Bakhtiar
Ostadi
Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran
bostadi@modares.ac.ir
<span lang="EN-US">General preventive maintenance model for the components of a system, which improves the reliability to ‘as good as new,’ was used to optimize the maintenance cost. The cost function of a maintenance policy was minimized under given availability constraint. On the other hand, in order to ensure appropriate reliability and availability, the development of the optimal maintenance policy is the one of the main issues in system to perform preventive maintenance (PM) in equipment. In this paper, maintenance characteristics of a typical flexible manufacturing system (FMS) have been determined. These characteristics can be used to understand and prevent the complex reality of failures and repairs. </span><span lang="EN-US">Also, an optimal </span><span lang="EN-US">model for the preventive maintenance management of a FMS has been presented based on preview literature in order to enhance availability and reliability of this system and to reduce the cost of maintenance tasks. Finally, proposed framework has been applied for a robot paint sprayer and its results shown in a form of the preventive maintenance plan, distribution fitting and Reliabilities’ parameters for each component s of robot paint sprayer, and the maintenance scheduling timetable.</span>
Maintenance management,preventive maintenance,Flexible manufacturing systems,Availability,Reliability,Maintenance scheduling
http://www.jise.ir/article_54749.html
http://www.jise.ir/article_54749_b68c3aa12d86cf85c55b47cfaff8583d.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
07
A multi-objective Two-Echelon Capacitated Vehicle Routing Problem for perishable products
62
84
EN
Rashed
Sahraeian
Industrial Engineering Department, College of Engineering, Shahed University, Tehran, Iran
sahraeian@shahed.ac.ir
Mehraneh
Esmaeili
Industrial Engineering Department, College of Engineering, Shahed University, Tehran, Iran
m_esmaili@shahed.ac.ir
This article addresses a general tri-objective two-echelon capacitated vehicle routing problem (2E-CVRP) to minimize the total travel cost, customers waiting times and carbon dioxide emissions simultaneously in distributing perishable products. In distributing perishable products, customers’ satisfaction is very important and is inversely proportional to the customers waiting times. The proposed model is a mixed integer non-linear programming (MINLP). By applying some linearization methods, the MINLP model exchanged to a mixed integer linear programming (MILP). This paper uses a non-dominated sorting genetic (NSGA-II) algorithm to solve the presented mathematical model. The related results would be compared with Lp-metric results in small-sized test problems and with multi objective particle swarm optimization (MOPSO) algorithm in medium and large sized test problems. In order to evaluate the quality of the solution sets, the results of two metaheuristic algorithms are compared based on four comparison metrics in medium sized problems. The obtained results indicate the efficiency of the NSGA-II algorithm.
2E-CVRP,carbon dioxide emissions,perishable products,customers waiting times,linearization,Multi objective Optimization
http://www.jise.ir/article_54750.html
http://www.jise.ir/article_54750_758d3f7dd777f21502e080f774cf671a.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
08
Self-Starting Control Chart and Post Signal Diagnostics for Monitoring Project Earned Value Management Indices
85
100
EN
Fatemeh
Sogandi
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
f.sogandi1990@gmail.com
S.Meysam
Mousavi
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
mousavi.sme@gmail.com
Amirhossein
Amiri
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
amirhossein.amiri@gmail.com
Earned value management (EVM) is a well-known approach in a project control system which uses some indices to track schedule and cost performance of a project. In this paper, a new statistical framework based on self-starting monitoring and change point estimation is proposed to monitor correlated EVM indices which are usually auto-correlated over time and non-normally distributed. Also, a new change point estimator is developed to find the real time of change in the indices mean. Furthermore, a new diagnosing method is presented to recognize the deviated mean index. The performance of the proposed methods is evaluated through simulation studies and an illustrative example.
Correlated EVM indices,self-starting monitoring,auto-correlated non-normal indices,Change point,diagnosing method,projects
http://www.jise.ir/article_54916.html
http://www.jise.ir/article_54916_429a50b2fedc3f17b6e3ac07bceca1e7.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
09
Equitable multi objective model for public facility location using RLTP technique
101
113
EN
Ali
Bozorgi-Amiri
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
alibozorgi@ut.ac.ir
Ariyan
Hosseinzadeh
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
hosseinzadeh.a@ut.ac.ir
In the present research, a multi-objective model is proposed, which considers equity among the citizens in addition to the cost criterion. Then, the model will be solved using Reservation Level Tchebycheff Procedure (RLTP), which is one of the interactive multi-objective decision-making techniques. Subsequently, the obtained results will be compared with those of the single-objective models to determine the effect of considering and not considering the equity criterion on public facilities location. Results of the present study show that the basic models of public facilities location do not consider the equity criterion; thus, in order to protect citizens’ rights, it is necessary for decision-makers of the urban management and planning to consider the objective of equity, along with other objectives of the project, as a multi-objective model in public facilities location problems. The proposed multi-objective model has also desirable and acceptable performance, which can be used in the public facilities location problems.
Citizenship equity,urban management and planning,public facilities location,reservation level Tchebycheff procedure (RLTP)
http://www.jise.ir/article_54917.html
http://www.jise.ir/article_54917_4b944191feb0494d2e0f38061209dc37.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
04
09
Simultaneous reduction of emissions (CO2 and CO) and optimization of production routing problem in a closed-loop supply chain
114
133
EN
Yasser
Emamian
Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran
yasser.emamian@gmail.com
Isa
Nakhai
Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran
nakhai.isa@gmail.com
Alireza
Eydi
Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran
alireza.eydi@uok.ac.ir
Environmental pollution and emissions, along with the increasing production and distribution of goods, have placed the future of humanity at stake. Today, measures such as the extensive reduction in emissions, especially of CO<sub>2</sub> and CO, have been emphasized by most researchers as a solution to the problem of environmental protection. This paper sought to explore production routing problem in closed-loop supply chains in order to find a solution to reduce CO<sub>2</sub> and CO emissions using the robust optimization technique in the process of product distribution. The uncertainty in some parameters, such as real-world demand, along with heterogeneous goals, compelled us to develop a fuzzy robust multi-objective model. Given the high complexity of the problem, metaheuristic methods were proposed for solving the model. To this end, the bee optimization method was developed. Some typical problems were solved to evaluate the solutions. In addition, in order to prove the algorithm’s efficiency, the results were compared with those of the genetic algorithm in terms of quality, dispersion, uniformity, and runtime. The dispersion index values showed that the bee colony algorithm produces more workable solutions for the exploration and extraction of the feasible region. The uniformity index values and the runtime results also indicated that the genetic algorithm provides shorter runtimes and searches the solution space in a more uniform manner, as compared with the bee colony algorithm.
emissions,production routing,Closed-loop supply chain,robust optimization
http://www.jise.ir/article_57039.html
http://www.jise.ir/article_57039_02d92875d80f2d592d5f3f5c358be595.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
10
Minimizing the maximum tardiness and makespan criteria in a job shop scheduling problem with sequence dependent setup times
134
150
EN
Mehdi
Heydari
School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
mheydari@iust.ac.ir
Adel
Aazami
0000-0003-2031-2602
School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
a_aazami@ind.iust.ac.ir
The job shop scheduling problem (JSP) is one of the most difficult problems in traditional scheduling because any job consists of a set operations and also any operation processes by a machine. Whereas the operation is placed in the machine, it is essential to be considering setup times that the times strongly depend on the various sequencing of jobs on the machines. This research is developed a two-objective model to solve JSP with sequence-dependent setup times (SDST). Considering SDST and optimizing of the both objectives simultaneously (makespan and maximum tardiness) bring us closer to natural-world problems. The ε-constraint method is applied to solve the mentioned two-objective model. A set of numerical data is generated and tested to validate the model’s efficiency and flexibility. The developed model can efficiently use for solving JSPs in the real world, especially for manufacturing companies with having setup and delivery time’s constraints.
Job shop scheduling,sequence-dependent setup times,makespan criterion,maximum tardiness criterion,mixed integer nonlinear programming
http://www.jise.ir/article_57040.html
http://www.jise.ir/article_57040_59ef11a3c39c282089bba7bd9aa316bd.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
10
An algorithm for integrated worker assignment, mixed-model two-sided assembly line balancing and bottleneck analysis
151
174
EN
Parvaneh
Samouei
Department of industrial Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran
samouei_parvaneh@yahoo.com
Parviz
Fattahi
Department of Industrial Engineering, Alzahra University, Tehran, Iran
p.fattahi@alzahra.ac.ir
This paper addresses a multi-objective mixed-model two-sided assembly line balancing and worker assignment with bottleneck analysis when the task times are dependent on the worker’s skill. This problem is known as NP-hard class, thus, a hybrid cyclic-hierarchical algorithm is presented for solving it. The algorithm is based on Particle Swarm Optimization (PSO) and Theory of Constraints (TOC) and consists of two stages. In stage one, simultaneous balancing and worker assignment are studied. In stage two, bottleneck analysis and product-mix determination are carried out. In addition, a bi-level mathematical model is presented to describe the problem.<br /> The following objective functions are verified in this paper: (1) minimizing the number of mated-stations (2), minimizing the number of stations (3) minimizing the human costs (4) minimizing the weighted smoothness index and (5) maximizing the total profit. In addition to the proposed algorithm, another algorithm, which is based on the simulated annealing and the theory of constraints, is developed to compare the performance of the proposed algorithm in terms of the running time and the solution quality over the different benchmarked test problems. Moreover, several lower bounds are developed for the number of the stations and the number of the mated-stations. The results show and support the efficiency of the proposed approaches.
Two-sided assembly line balancing problem (TSALBP),worker assignment,mixed-model,particle swarm optimization algorithm (PSO),simulated annealing algorithm (SA),theory of constraints
http://www.jise.ir/article_57658.html
http://www.jise.ir/article_57658_8c2660e46811901cb3c07dbcd53417b8.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
10
An integrated heuristic method based on piecewise regression and cluster analysis for fluctuation data (A case study on health-care: Psoriasis patients)
175
189
EN
Farnoosh
Bagheri
Department of Industrial Engineering, University of Science and Culture, Tehran, Iran
bagheri@usc.ac.ir
mahsa
laari
Department of Industrial Engineering, University of Science and Culture, Tehran, Iran
mahsa.laari@yahoo.com
Reza
Kamranrad
Department of Industrial Engineering, University of Science and Culture, Tehran, Iran
rezakamranrad@gmail.com
Majid
Jalili
Department of Industrial Engineering, Material and Energy Research Center, Karaj, Iran
jalili7@yahoo.com
Trend forecasting and proper understanding of the future changes is necessary for planning in health-care area.One of the problems of analytic methods is determination of the number and location of the breakpoints, especially for fluctuation data. In this area, few researches are published when number and location of the nodes are not specified.In this paper, a clustering-based method is developed to obtain the number and the location of breakpoints. We propose an appropriate piecewise regressionmodel to analyze the fluctuation data and predict trends of them.Theefficiency of proposed integrated approach is evaluated by using a simulated and real example, and results are compared with results of Mars algorithm. Comparison shows that proposed approach has less sum of square error (SSE) criterion than Mars algorithm with equall number of nods.
Piecewise regression,node,Clustering,Mars algorithm,health-care systems
http://www.jise.ir/article_59612.html
http://www.jise.ir/article_59612_4b192da3e9a86efbd7fa37fce6b4d284.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
11
A credit period contract towards coordination of pharmaceutical supply chain:The case of inventory-level-dependent demand
190
206
EN
Mahdi
Ebrahimzadeh-Afruzi
School of Industrial Engineering, Iran University of Science and Technology
m_ebrahimzade94@ind.iust.ac.ir
Alireza
Aliahmadi
School of Industrial Engineering, Iran University of Science and Technology
pe@iust.ac.ir
This paper considers a two stages pharmaceutical supply chain (PSC) consisting of a pharmaceutical manufacturer (pharma-manufacturer) that supplies one type of pharmaceutical product to a pharma-retailer. The customer demand rate for the pharmaceutical product is dependent on the pharma-retailer’s current-inventory level. The pharma-retailer determines the order quantity ( ) value as decision variable and the pharma-manufacturer uses EPQ system that usually the economic order quantity value of retailer is less than the optimal production quantity value of manufacturer. First, the problem is investigated in decentralized decision-making and accordingly, a coordination incentive based on credit payment period policy to coordinate the mentioned PSC in two structures is proposed: independent optimization and centralized model with credit policy. Moreover, numerical examples and sensitivity analysis are considered to illustrate the results of the presented coordination structures toward decentralized model.
Pharmaceutical supply chain,inventory-dependent demand,production,credit payment period,Coordination
http://www.jise.ir/article_59680.html
http://www.jise.ir/article_59680_4ee7d0e57baac0f44888875e3b691ca5.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
16
Multi-item inventory model with probabilistic demand function under permissible delay in payment and fuzzy-stochastic budget constraint: A signomial geometric programming method
207
227
EN
Masoud
Rabani
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
mrabani@ut.ac.ir
Leila
Aliabadi
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
leyla.aliabadi@ut.ac.ir
This study proposes a new multi-item inventory model with hybrid cost parameters under a fuzzy-stochastic constraint and permissible delay in payment. The price and marketing expenditure dependent stochastic demand and the demand dependent the unit production cost are considered. Shortages are allowed and partially backordered. The main objective of this paper is to determine selling price, marketing expenditure, credit period, and variables of inventory control simultaneously for maximizing the total profit. To solve the problem, first some transformations are applied to convert the original problem into a multi-objective nonlinear programming problem, of which each objective has signomial terms. Then, the multi-objective nonlinear programming problem is solved by first converting it into a single objective problem and then by using global optimization of signomial geometric programming problems. At the end, several numerical examples and sensitivity analysis are done to test model and solution procedure and also obtain managerial insights.
Signomial geometric programming,delay in payment,fuzzy-stochastic recourse,price and marketing dependent stochastic demand,EOQ
http://www.jise.ir/article_59681.html
http://www.jise.ir/article_59681_42adbf72cce5732557c02e686f886c37.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
17
Developing a fuzzy expert system to predict technology commercialization success
228
250
EN
Jafar
YazdiMoghaddam
Faculty of Industrial Engineering, Yazd University, Yazd, Iran
j.yazdimoghaddam@gmail.com
Mohammad Salleh
Owlia
Faculty of Industrial Engineering, Yazd University, Yazd, Iran
owliams@yazd.ac.ir
Reza
Bandarian
Business Development Department, Research Institute of Petroleum Industry (RIPI), Tehran, Iran
bandarianr@ripi.ir
A majority of efforts in terms of technology commercialization have failed; however, the issue of commercialization and its high importance are agreed upon by policymakers, entrepreneurs and researchers. This shows the high complexity of the commercialization process. One of the main solutions to overcome the commercialization problems is to predict the success of technology commercialization before its implementation. Hence, this study aims to design a fuzzy expert system to predict the technology commercialization success in the early stages of its development and before its implementation. According to the literature review and the fuzzy Delphi method, the technology commercialization success factors (TCSFs) were identified and refined. The final result of the fuzzy Delphi process consists of 32 components categorized in four dimensions: technical specifications, financial and economic specifications, market specifications and rules and regulations. These success dimensions form the inputs of the prediction model in this study. The performance of the model was evaluated by actual samples selected from different fields of technology. The accuracy of the model was estimated to be 73% according to a validation process, indicating the high accuracy of the proposed model in predicting the commercialization success. This model could be used practically by risk-taking investors, technology advocates and innovators to adopt new technology commercialization opportunities.
Technology commercialization,technology commercialization success factors,commercialization success predict,fuzzy expert system
http://www.jise.ir/article_74015.html
http://www.jise.ir/article_74015_094b4a1e30d23cd5ea4fefb5c0707ba3.pdf
Iranian Institute of Industrial Engineering
Journal of Industrial and Systems Engineering
1735-8272
11
2
2018
10
17
A differential evolution algorithm to solve new green VRP model by optimizing fuel consumption considering traffic limitations for collection of expired products
251
269
EN
Mojgan
Karami
School of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran
karamimozhgan@yahoo.com
Vahidreza
Ghezavati
School of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran
vrghezavati@gmail.com
The purpose of this research is to present a new mathematical modeling for a vehicle routing problem considering concurrently the criteria such as distance, weight, traffic considerations, time window limitation, and heterogeneous vehicles in the reverse logistics network for collection of expired products. In addition, we aim to present an efficient solution approach according to differential evolution (DE) procedure to solve such a complicated problem. By using mathematical modeling tools for formulating the environmental sensitivities in vehicle routing problems, the reverse logistics must be managed according to criteria such as cargo weight carried by the vehicle, the vehicle speed and the covered distance by the vehicle. This leads to optimization and reduction of transportation fuel consumption and hence reduction of air pollution and environment concerns. This concept has led to creation and study of the green vehicle routing problems in this paper.Numerical analysis indicates that performance of the proposed DE algorithm can be validated in terms of CPU run time and optimality gap for solving the proposed model. Furthermore, sensitivity analysis show that extending maximum travelling distance by each vehicle, and increasing capacity of vehicles lead to reduction of total cost in the problem.
Green Vehicle Routing Problem,reverse logistics,expired products,transportation system,differential evolutionary algorithm
http://www.jise.ir/article_59682.html
http://www.jise.ir/article_59682_18b5a191775c97b79994878e63506777.pdf