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.

中文翻译：

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具有规避风险供应商的供应链交付窗口的最优位置：一种 CVaR 优化方法

摘要 本研究将风险规避最佳交货窗口位置（RA-OPDW）的概念引入到基于成本的交货绩效模型中。在供应交付绩效大背景下，提早交货和延迟交货的罚款成本备受关注。然而，最小化预期惩罚有一个严重的缺点，它忽略了决策者的风险规避态度。因此，提出了一种条件性风险价值 (CVaR) 措施来衡量不及时交付的惩罚，以纳入决策者的风险规避程度。然后推导出在风险规避程度较高的条件下最小化CVaR的最优仓位的闭式表达式。风险规避程度、交割窗口宽度、探讨了延迟交货的单位罚金与提前交货的单位罚金的比率。此外，研究了一种权衡 CVaR 最小化和预期惩罚的混合模型。还推导出了混合模型中最佳位置的条件。此外，CVaR 的最小化和预期惩罚只是混合模型的两个特例。最后，通过一个数值案例来比较最优位置与最小 CVaR 和最小化预期惩罚的位置，并说明几个参数对最优位置的影响。CVaR 的最小化和预期惩罚只是混合模型的两个特例。最后，通过一个数值案例来比较最优位置与最小 CVaR 和最小化预期惩罚的位置，并说明几个参数对最优位置的影响。CVaR 的最小化和预期惩罚只是混合模型的两个特例。最后，通过一个数值案例来比较最优位置与最小 CVaR 和最小化预期惩罚的位置，并说明几个参数对最优位置的影响。