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

Amir Hossein Sadeghi, Ziyuan Sun, Amirreza Sahebi-Fakhrabad, Hamid Arzani and Robert Handfield ()
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Amir Hossein Sadeghi: Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27606, USA
Ziyuan Sun: Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QC H3G 1M8, Canada
Amirreza Sahebi-Fakhrabad: Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27606, USA
Hamid Arzani: Rotman School of Management, University of Toronto, Toronto, ON M5T 1P5, Canada
Robert Handfield: Department of Business Management Poole College of Management, North Carolina State University, Raleigh, NC 27695, USA

Logistics, 2023, vol. 7, issue 1, 1-24

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

Keywords: p-median problem; supply chain network design; dynamic allocation; robust optimization; lagrangian relaxation (search for similar items in EconPapers)
JEL-codes: L8 L80 L81 L86 L87 L9 L90 L91 L92 L93 L98 L99 M1 M10 M11 M16 M19 R4 R40 R41 R49 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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