Optimal inventory policies with service-level constraints

In a practical situation it is often difficult to determine the value of the shortage costs for use in inventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q,r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.