Optimizing Supplier Selection with Disruptions by Chance-Constrained Programming

This work develops a new chance-constrained programming model for supplier selection problem, in which suppliers are assigned sequentially so that the buyer may have already one backup when its primary supplier suffers a default due to disruptive risks. In the proposed optimization problem, costs, quality and lead times are characterized by random variables. The objective of the proposed model is to maximize the probability of the total costs no more than a prescribed maximum allowable value. Two probability constraints are used to guarantee that the probabilities about the total quality and total lead times can satisfy the known service levels, while other constraints are utilized to ensure our allocation scheme. By assuming multivariate normal distributions, we can transform the probability objective and probabilistic constraint functions into their equivalent fractional forms, so we can solve the deterministic fractional programming by conventional optimization method. Finally, some numerical experiments have been performed to illustrate the effectiveness of the proposed solution strategy.