A simulation-optimization approach for the stochastic discrete cost multicommodity flow problem

• Published in: Engineering optimization Vol. 52; no. 3; pp. 507 - 526
• Main Authors: Mejri, Imen, Layeb, Safa Bhar, Haouari, Mohamed, Mansour, Farah Zeghal
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03-03-2020; Taylor & Francis Ltd
• Subjects: Algorithms; Computer simulation; Lower bounds; Monte Carlo simulation; Network topologies; Networks; Optimization; sample average approximation; simulation-optimization approach; stochastic programming
• ISSN: 0305-215X; 1029-0273
• DOI: 10.1080/0305215X.2019.1603299

This article addresses a variant of the Discrete Cost Multicommodity Flow (DCMF) problem with random demands, where a penalty is incurred for each unrouted demand. The problem requires finding a network topology that minimizes the sum of the fixed installation facility costs and the expected penalties of unmet multicommodity demands. A two-stage stochastic programming with recourse model is proposed. A simulation-optimization approach is developed to solve this challenging problem approximately. To be precise, the first-stage problem requires solving a specific multi-facility network design problem using an exact enhanced cut-generation procedure coupled with a column generation algorithm. The second-stage problem aims at computing the expected penalty using a Monte Carlo simulation procedure together with a hedging strategy. To assess the empirical performance of the proposed approach, a Sample Average Approximation (SAA) procedure is developed to derive valid lower bounds. Results of extensive computational experiments attest to the efficacy of the proposed approach.