On the robust decision-making in a supply chain under disruption risks

This paper considers a robust decision-making problem associated with supplies of parts and deliveries of finished products in a customer driven supply chain under disruption risks. The robustness refers to an equitably efficient performance of a supply chain in average-case as well as in the worst-case, which reflects the decision-makers common requirement to maintain an equally good performance of a supply chain under different conditions. Given a set of customer orders for products, the decision-maker needs to select suppliers of parts required to complete the orders, allocate the demand for parts among the selected suppliers and schedule the orders over the planning horizon, to equitably optimise average and worst-case performance of the supply chain. The supplies are subject to independent random local and regional disruptions. The obtained combinatorial stochastic optimisation problem is formulated as a mixed-integer program with conditional value-at-risk as a risk measure. The ordered weighted averaging aggregation of the expected value and the conditional value-at-risk of the selected optimality criterion is applied to obtain a robust solution. The risk-neutral, risk-averse and robust solutions that optimise, respectively average, worst-case and equitable average and worst-case performance of a supply chain are determined and compared for cost and customer service level objective functions. Numerical examples and computational results, in particular comparison with the mean-risk approach, are presented and some managerial insights are reported.