Optimal position of supply chain delivery window with risk-averse suppliers: A CVaR optimization approach

Abstract The study introduces the concept of risk-averse optimal position of the delivery window (RA-OPDW) into a cost-based delivery performance model. The penalty costs for early and late deliveries have attracted much attention in the background of supply delivery performance. However, minimizing the expected penalty has a critical disadvantage that it ignores the risk-averse attitude of decision-makers. Thereby, a Conditional Value-at-Risk (CVaR) measure of the penalty on untimely delivery is proposed to incorporate the risk-aversion degree of a decision-maker. Then the closed-form expression of optimal position minimizing the CVaR is derived under the condition that the risk-aversion degree is high. The influence of the risk-aversion degree, the delivery window width, the ratio of the unit penalty on late delivery to the unit penalty on early delivery are explored. Besides, a hybrid model that trades off the minimization of CVaR and the expected penalty is investigated. The conditions for the optimal position in the hybrid model is also deduced. Moreover, the minimization of CVaR and the expected penalty are just two special cases of the hybrid model. Finally, a numerical case is executed to compare the optimal position with minimum CVaR and the one minimizing the expected penalty and to illustrate the influence of several parameters on the optimal position.