Magnitude based service level constraints during a fiscal period: The exponential distribution

The purpose of this paper is to focus on service level constraints, defined over a fiscal period, which measure the actual rather than the expected shortage (magnitude perspective). The paper reviews the derivation of such constraints and integrates them into inventory models leading to a chance constrained optimization problem. For the demand during the lead time being exponential, a solution procedure is presented which allows the decision maker to determine the optimal inventory parameters with the same ease as in the traditional lead time case. The formulation and solution procedure is illustrated by sample calculations highlighting the managerial implications.