Scenario-Based Modeling of Interdependent Demand and Supply Uncertainties

Abstract

This paper develops a scenario generation framework for modeling demand and supply uncertainties. This framework is applied to a decision problem at an illustrative manufacturing company facing risks caused by uncertainties in end product demand and component availability. In particular, we focus on the impact of interdependent demand and supply uncertainty. To evaluate analytically the impact of interdependence between these two uncertainties, we analyze a simple newsvendor model with a bivariate normal distribution for demand and supply yield. Then, in more complex settings, we use scenarios based on copula functions, which can account for both linear and nonlinear dependences. These scenarios are used in conjunction with stochastic programming models to evaluate sourcing costs and risks under various conditions. In particular, we study a decision problem faced by a manufacturer which uses capacity reservation contracts in the presence of an unreliable supplier and uncertain product demand. Our results indicate that worst-case risks grow significantly when the dependences in uncertainties about demand and supply yield are stronger. We also highlight differences caused by linear and tail-dependent dependence structures. Based on the results, we argue that using the proposed framework to model uncertainties and their interdependences allows managers to better manage risks.