Robust solution and risk measures for a supply chain planning problem under uncertainty

Abstract

We consider a strategic supply chain planning problem formulated as a two-stageStochastic Integer Programming (SIP) model. The strategic decisions include sitelocations, choices of production, packing and distribution lines, and the capacityincrement or decrement policies. The SIP model provides a practical representationof real world discrete resource allocation problems in the presence of future uncertaintieswhich arise due to changes in the business and economic environment. Suchmodels that consider the future scenarios (along with their respective probabilities)not only identify optimal plans for each scenario, but also determine a hedgedstrategy for all the scenarios. We,(1) exploit the natural decomposable structure of the SIP problem through Benders’decomposition,(2) approximate the probability distribution of the random variables using theGeneralised Lambda distribution, and(3) through simulations, calculate the performance statistics and the risk measuresfor the two models, namely the expected-value and the here-and-now.Key words: Supply Chain planning, Stochastic integer Programming, Benders’decomposition, Generalised Lambda distribution, simulation, Genetic algorithm