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Designing a multi-objective mathematical model of a perishable supply chain (PSC) in a state of uncertainty

Fatemeh Fallah (Qazvin Islamic Azad University, Qazvin, Iran)
Parham Azimi (Qazvin Islamic Azad University, Qazvin, Iran)
Mani Sharifi (Department of Industrial Engineering, Ryerson University, Toronto, Canada)

Journal of Modelling in Management

ISSN: 1746-5664

Article publication date: 22 December 2022




The pharmaceutical industry is one of the most essential areas of health in any country. It is defined as a system of processes, operations and organizations involved in discovering, developing and producing drugs. The supply chain in the pharmaceutical field is one of the most important strategic issues in the pharmaceutical and health-care industries. The purpose of this study is to reduce the total cost of the supply chain network and reduce the amount of distribution scheduling.


In this study, the authors designed a drug supply chain network with uncertainty-related corruption. The optimal number and location of potential facilities, the optimal allocation of flow between facilities, the optimal routing of vehicles and the optimal amount of inventory in production and distribution center warehouses were determined to achieve these two objective functions.


In evaluating the small sample size problem, it was found that the comprehensive benchmarking method was more efficient than the other methods in obtaining the mean index of the first objective function. The utility function method has also proved its efficiency in obtaining the mean of the second objective function indices, the spacing index and the computational time. Because of the inefficiency of GAMS software in resolving size issues, the modified NSGA II and MOPSO algorithms with modified priority-based encryption have been used. First, using the Taguchi method, the initial parameters of the metaheuristic algorithms are adjusted, and then, 15 sample problems are designed in larger sizes. To avoid generating random data, five problems were equally designed, and the averages of objective functions and metrics of met heuristic algorithms (number of efficient solutions, maximum expansion index, spacing index and computational time) were analyzed as the basis of evaluation and comparison. Therefore, using all the indicators and results of the NSGA II algorithm is recommended.


In this research, a biobjective modeling approach is proposed to minimize the total costs of the supply chain network (construction costs, storage costs and product transportation costs between centers) and advertising costs and to minimize distribution and transportation scheduling across each level of the supply chain network.



Fallah, F., Azimi, P. and Sharifi, M. (2022), "Designing a multi-objective mathematical model of a perishable supply chain (PSC) in a state of uncertainty", Journal of Modelling in Management, Vol. ahead-of-print No. ahead-of-print.



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