A Benders-Decomposition and Meta-Heuristic Algorithm for a Bi- Objective Stochastic Reliable Capacitated Facility Location Problem Not Dealing with Benders Feasibility-Cut Stage

Document Type: Original Manuscript


1 Department of engineering,University of Applied Science andTechnology,Tehran, Iran

2 Department of Industrial Engineering, University of PayameNoor,Tehran,Iran



This paper addresses a bi-objective two-stage stochastic mixed-integer linear programming model for a stochastic reliable capacitated facility location in which the optimum numbers, locations and as well as shipment quantity of the product between the network nodes for all scenarios should be determined. Unlike most of previous relevant works, multiple levels of capacities available to the manufacturers in different scenarios are permitted in this study. The proposed objectives of the model include: the minimization of expected sum of installation, production, transportation under uncertainty of parameters, such as transportation and production and disruption of facilities, as well as minimizing expected standard deviation of network costs for whole scenarios. Since one of the most important reasons for researchers' reluctance to apply Benders-decomposition algorithm in facility-location concept is the time-consuming nature of its feasibility-cut stage, one of the most outstanding innovation in this paper is to add a strengthening redundant constraint to the proposed model in order to eliminate the mechanism related to feasibility cuts in master problem. to the best of our knowledge, it is the first time that this technique, not being involved in keeping master-problem feasibility, is used to solve a reliable capacitated facility location problem. In this approach, in terms of time-consuming the Benders algorithm is able to powerfully compete with metaheuristic algorithms, but with an exact solution. To prove advantage of this algorithm satisfying both ultimate solution optimality and appropriate running time compared to metaheuristic algorithms at the same time, one metaheuristic algorithm, namely Imperialist Competitive Algorithm (ICA), is presented. Usefulness and practicality of the proposed model and solution method demonstrated through a case example in different class with variable size.

Graphical Abstract

A Benders-Decomposition and Meta-Heuristic Algorithm for a Bi- Objective Stochastic Reliable Capacitated Facility Location Problem Not Dealing with Benders Feasibility-Cut Stage


  • Multiple levels of capacities available to the manufacturers in different scenarios, unlike most of previous relevant works.
  • A modified version of Benders decomposition to generate exact optimal solutions
  • Solving a reliable capacitated facility location problem, not being involved in keeping master-problem feasibility.
  • adding a strengthening redundant constraint to master problem in order to eliminate the mechanism related to feasibility cuts in master problem, which is known as a challenging issue and time-consuming stage in this field


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