Supply Chain Network Design under Demand Uncertainty and Supply Disruptions: A Distributionally Robust Optimization Approach

Ruozhen Qiu,Yizhi Wang

doi:10.1155/2016/3848520

Abstract

We develop a robust optimization model for designing a three-echelon supply chain network that consists of manufacturers, distribution centers, and retailers under both demand uncertainty and supply disruptions. The market demands are assumed to be random variables with known distribution and the supply disruptions caused by some of the facilities faults or connection links interruptions are formulated by several scenarios with unknown occurrence probabilities. In particular, we assume the probabilities that the disruption scenarios happen belong to the two predefined uncertainty sets, named box and ellipsoid uncertainty sets, respectively. Through mathematical deductions, the proposed robust SCN design models can be transformed into the tractable linear program for box uncertainty and into second-order cone program for ellipsoid uncertainty. We further offer propositions with proof to show the equivalence of the transformed problems with the original ones. The applications of the proposed models together with solution approaches are investigated in a real case to design a tea supply chain network and validate their effectiveness. Numerical results obtained from model implementation and sensitivity analysis arrive at important practical insights.

Highlights

Designing and managing a supply chain network have become crucial due to the increasing market competition, variable customer demands, and the fast development of the economic and technological globalization
We focus on the Supply chain network (SCN) design of a threeechelon supply chain under both the demand uncertainty and supply disruptions
The optimal profit of the whole supply chain in the real scenario may differ from the objective function value derived from the proposed mathematical model; we introduce the solution robustness defined in Mulvey et al [13] to reduce the deviation and make the SCN design model more robust: max

Summary

Introduction

Designing and managing a supply chain network have become crucial due to the increasing market competition, variable customer demands, and the fast development of the economic and technological globalization. Using the robust optimization approach proposed by Mulvey et al [13], Babazadeh and Razmi [14] develop an efficient mixed-integer linear programming to handle both operational and disruption risks of the agile supply chain network. According to Klibi et al [6], stochastic programming techniques usually require the perfect information of probability distributions of random variables, such as the likelihood of an interruption occurrence and its magnitude of impact Such historical data, especially for those rare events, is limited or nonexistent making it difficult or impossible to estimate the actual distribution of uncertain parameters [20]. Hasani and Khosrojerdi [30] develop a mixed-integer, nonlinear model and consider six flexible and resilience strategies simultaneously in designing robust global supply chain networks under disruptions and uncertainties They present an efficient parallel Taguchi-based memetic algorithm to solve the proposed model. We summarize the paper and discuss future research directions

Problem Description

Mathematical Formulations

Robust SCN Design Model under Uncertain Supply Disruption Probability

Case Study and Numerical Results

Conclusions