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The Dynamic Modified Stochastic p-Median Problem (DMS-p-MP) is an importantproblem in supply chain network design, as it deals with the optimal locationof facilities and the allocation of demand in a dynamic and uncertainenvironment. In this research paper, we propose a mixed-integer linearformulation for the DMS-p-MP, which captures the key features of the problemand allows for efficient solution methods. The DMS-p-MP adds two key featuresto the classical problem: (1) it considers the dynamic nature of the problem,where the demand is uncertain and changes over time, and (2) it allows for themodification of the facility locations over time, subject to a fixed number ofmodifications. The proposed model is using robust optimization in order toaddress the uncertainty of demand by allowing for the optimization of solutionsthat are not overly sensitive to small changes in the data or parameters. Tomanage the computational challenges presented by large-scale DMS-p-MP networks,a Lagrangian relaxation (LR) algorithm is employed. Our computational study ina real-life case study demonstrates the effectiveness of the proposedformulation in solving the DMS p-Median Problem. According to the results, thenumber of opened and closed buildings remains unchanged as the time horizonincreases. This is due to the periodic nature of our demand. This formulationcan be applied to real-world problems, providing decision-makers with aneffective tool to optimize their supply chain network design in a dynamic anduncertain environment.

A Mixed-integer Linear Formulation for Dynamic Modified Stochastic p-Median Problem in a Competitive Supply Chain Network Design