Dynamic Capacity Management with General Upgrading
研究企业如何采购和分配多等级容量来满足随时间到达的多等级客户需求，考虑多步升级规则，提出最优分配策略和启发式算法，数值分析表明该启发式算法快速且利润接近最优。
This paper studies a capacity management problem with upgrading. A firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time. A general upgrading rule is considered, i.e., unmet demand can be satisfied using multistep upgrade. No replenishment is allowed and the firm has to make the allocation decisions without observing future demand. We first characterize the structure of the optimal allocation policy, which consists of parallel allocation and then sequential rationing. Specifically, the firm first uses capacity to satisfy the same-class demand as much as possible, then considers possible upgrading decisions in a sequential manner. We also propose a heuristic based on certainty equivalence control to solve the problem. Numerical analysis shows that the heuristic is fast and delivers close-to-optimal profit for the firm. Finally, we conduct extensive numerical studies to derive insights into the problem. It is found that under the proposed heuristic, the value of using sophisticated multistep upgrading can be quite significant; however, using simple approximations for the initial capacity leads to negligible profit loss, which suggests that the firm’s profit is not sensitive to the initial capacity decision if the optimal upgrading policy is used.