Optimizing a single-product production-inventory system under constant absolute risk aversion

This paper considers a single-product production-inventory system managed by a base-stock policy where the factory inventory manager with cost concerns over a short time horizon can be modeled with the constant absolute risk aversion (CARA) utility function. We consider both backordering cost and stockout cost scenarios and investigate the roles of capacity utilization level and CARA coefficient on the optimal base-stock level. We derive closed-form solutions for the optimal inventory decisions, present related numerical experiments, and discuss their managerial implications. It is discovered that both scenarios share certain common structure in their optimal inventory decisions. Specifically, in the backordering cost scenario, if the backordering cost is high or the holding cost is low, the optimal base-stock level is high. In the stockout cost scenario, if the stockout cost is high or the holding cost is low, the optimal base-stock level is high. For both scenarios, inventory levels are high with tight capacity, and optimal base-stock level generally increases if the manager becomes more risk averse.