Optimization under supplier portfolio risk considering breach of contract and market risks

Abstract

We consider a two-period sourcing and production problem. First, a firm (OEM) sources from multiple suppliers who have limited capacity and correlated disruption risk. After the supply is realized, the firm also has access to the spot market for the extra material needed for its production. The firm must decide (1) which suppliers to source from, (2) how much to source from them, and (3) how much to produce and how much to source from the spot market. We formulate this as a stochastic optimization problem to study the tradeoff the firm faces between costs and default risk. In order to incorporate the correlation of the supplier’s default risk, we use the t-copula dependence structure. A contract default is a rare event. Thus, in a Monte Carlo simulation, there is considerable variance around the optimal sourcing quantity. This variance leads to complexity in computing the optimal decision. We find that a diligent combination of importance sampling and conditional Monte Carlo schemes effectively reduces the variance in simulation estimates for the first-order conditions in the stochastic optimization problem. This paper shows that, for a supply chain with correlated default risks, the optimal sourcing problem can be solved by using importance sampling and a conditional Monte Carlo simulation.