Robust Capacitated Facility Location Problem: Optimization Model and Solution Algorithms

In this article, we propose an extension of the capacitated facility location problem under uncertainty, where uncertainty may appear in the model’s key parameters such as demands and costs. In this model, it is assumed that facilities have hard constraint on the amount of demand they can serve and, as a result, some customers may not be fully satisfied. Unfortunately, traditional models ignore this situation and if facilities do not serve all demands, the model becomes infeasible. Accordingly, we develop the mathematical formulation in order to allow partial satisfaction by introducing penalty costs for unsatisfied demands. In general, this model optimizes location for predefined number of capacitated facilities in such a way that minimizes total expected costs of transportation, construction, and penalty costs of uncovered demands, while relative regret in each scenario must be no greater than a positive number ( 0 p  ). The developed model is NP-hard and very challenging to solve. Therefore, an efficient heuristic solution algorithm based on the variable neighborhood search is developed to solve the problem. The algorithm’s efficiency is compared with the simulated annealing algorithm and CPLEX solver by solving variety of test problems.Computational experiments show that the proposed algorithm is more effective and efficient in terms of CPU time and solutions quality.