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

Background: The Dynamic Modified Stochastic p-Median Problem (DMS-p-MP) is an important problem in supply chain network design, as it deals with the optimal location of facilities and allocation demand a dynamic uncertain environment. Methods: In this research paper, we propose mixed-integer linear formulation for DMS-p-MP, which captures key features allows efficient solution methods. DMS-p-MP adds two to classical problem: (1) considers nature problem, where changes over time, (2) modification facility locations subject fixed number modifications. proposed model uses robust optimization order address uncertainty by allowing solutions that are not overly sensitive small data or parameters. To manage computational challenges presented large-scale networks, Lagrangian relaxation (LR) algorithm employed. Results: Our study real-life case demonstrates effectiveness solving DMS Problem. results show opened closed buildings remains unchanged time horizon increases due periodic our demand. Conclusions: This can be applied real-world problems, providing decision-makers effective tool optimize their design