A linear programming formulation for an inventory management decision with a service constraint

Abstract

Inventory systems with uncertainty go hand in hand with the determination of a safety stock level. The decision on the safety stock level is based on a performance measure, for example, the expected shortage per replenishment period of the probability distribution during lead time, which might not be available. In case of incomplete information regarding the lead-time distribution of demand, no single figure for the safety stock can be determined in order to satisfy a performance measure. However, an optimisation model may be formulated in order to determine a safety stock level which guarantees the performance measure under the worst case of lead-time demand, of which the distribution is known in an incomplete way. It is shown that this optimisation problem can be formulated as a linear programming problem.