Incorporating uncertainty into a multicriteria supplier selection problem

Current business trends towards longer and leaner supply chains increase risks in the whole chain. The supplier selection decision has become an important strategic level decision. We develop a two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model to incorporate uncertainty of demand and supplier capacity. We use a probabilistic distribution of supplier capacity to represent issues of timely delivered supplies due to long transportation routes and production disruption at the suppliers. The demand distribution represents uncertainty in future demand. Both models include several objectives and determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. The developed models aim to balance the benefit from a small number of suppliers with the risk of not being able to meet demand. A deterministic mixed integer programming (MIP) model is also formulated for comparison purposes. Both the SP model and the CCP model improve on the MIP model in terms of providing a robust selection of suppliers and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the probabilistic models. It is also found from the experimental results that the CCP model gives the decision maker a more complete picture of tradeoffs between alternative solutions in less computational time as compared to the SP model. However, the CCP model assumes a probability distribution for the random demand and supplier capacity whereas the SP model is scenario-based. In order to describe the tradeoffs between costs and risks under alternative Pareto-optimal supplier selection solutions in an analytical form, we develop multiparametric programming techniques to more completely analyze the multiple selection criteria and probabilistic constraints on demand and supplier capacity in the CCP model.