Managing customer waiting times in an inventory system using Conditional Value-at-Risk measure

In today’s fast-paced world, delays or prolonged customer waiting times pose a threat to the firm’s profitability. This study utilizes the mean-CVaR metric to incorporate the risk associated with prolonged customer waiting times into the optimal trade-off decisions. For this purpose, we consider a single inventory system that faces Poisson demand and utilizes a base-stock policy to replenish its inventory, which takes a fixed amount of time. The firm implements a preorder strategy, encouraging customers to place their orders a fixed amount of time in advance of their actual needs, a period referred to as the commitment lead time. The firm rewards customers with a bonus termed the commitment cost, which increases with the length of the commitment lead time. We aim to determine the optimal control policy, including the optimal base-stock level and optimal commitment lead time, that minimizes the long-run average cost. The cost includes inventory holding, commitment, and customer waiting costs, with the latter adjusted for the firm’s degree of risk aversion. The optimal policy depends on the interdependence of the decisions, with the optimal commitment lead time following a “bang-bang” pattern, and the corresponding optimal base-stock level taking an “all-or-nothing” form. For linear commitment costs with a cost factor per time unit, we identify a threshold that increases with the firm’s risk aversion degree. Firms with greater risk aversion typically favor the buy-to-order strategy, while those with lower risk aversion may opt for either buy-to-stock or buy-to-order depending on their assessment of waiting costs.