Stochastic supply chain network design under the mean-CVaR criterion

Abstract

In the highly competitive market of the 21stcentury, organizations face the persistent challenge to improve supply chain efficiency, allowing products to move more quickly at lower cost. Unfortunately, some ostensible improvements also increase the supply chain’s vulnerability to uncertainties (e.g., uncertain customer demand and capacity), resulting in higher risk. Hence, there is a growing realization that the impact of risk to supply chains should be analyzed. Conditional Value at Risk (CVaR) is one of the newest method utilized to measure such risk.

This study develops a set of mathematical models to facilitate the analysis of the operating characteristics of a supply chain when its demand and capacity are uncertain involving three supply chain network design problems. The objective is to minimize the expected operating cost and its corresponding CVaR. The first problem focuses on facility location and distribution planning. The second problem extends the first one by incorporating procurement and manufacturing decisions on the basis of a time-expanded network. In order to describe the situation where uncertainties are realized over time, the third problem extends the second one to a multi-stage (more than two stage).For each problem, both a basic model and a sample-based model are formulated. The basic model can be approximated accurately by the sample-based model of an adequate sample size.

The first sample-based model can be first reformulated to a set-covering problem, then decomposed into a master problem and a number of column generation pricing-problems. Then, a hybrid algorithm based upon Multi-population Particle Swarm Optimization and Tabu Search (MPSO-TS) is proposed to solve the pricing-problems. The computation time of MPSO-TS rises proportionately with increases in sample size. Therefore, a tailor-made simulation framework based on Sample Average Approximation (SAA) integrating the MPSO-TS aided column generation algorithm is constructed to solve the basic model (also referred to the corresponding sample-based model of an adequate sample size). The effectiveness and robustness of the proposed methodologies are tested on a set of randomly generated problems.

In the second problem, the sample-based model can be decomposed into a master problem and a sub-problem based on the Benders Decomposition (BD) scheme. To improve the convergence behavior of the standard BD algorithm, three accelerating strategies are utilized: adding logistical constraints, cutting disaggregation, and applying local branching (LB) strategy. Similar to the first problem, a tailor-made simulation framework based on SAA integrating with the accelerated BD algorithm is constructed to solve the basic model. Results obtained from the experiments using randomly generated test problems show the effectiveness and efficiency of the proposed methodologies. Since the structure of the third sample-based model indicates that no exact solutions can be achieved, a corresponding model is developed under the mean criterion. Two simulation methods relying on a rolling horizon approach are proposed by using the accelerated BD algorithm to solve both these models. A lower bound analysis is also proposed to assist in the performance evaluation process. The superior effectiveness of these methodologies is validated by a set of randomly generated test problems.