On the use of bounds on the stop-loss premium for an inventory management decision problem

Abstract

A specific integral, which is used in insurance mathematics for the determination of a stop-loss premium, corresponds to the definition of a performance characteristic of an inventory management decision problem. It is investigated whether the operational management problem might benefit from specific results obtained in the actuarial world. In the case little information is available on the demand distribution during the lead-time, which is relevant in inventory decision-making, interesting results might be used from the actuarial problem where limited information (e.g., only a few moments of the claim size distribution) is known. With a limited transformation of the actuarial results, upper and lower bounds may be determined for the safety stock in the inventory management problem. Also a numerical approximation using linear programming is shown to be equivalent to the problem under study.