An inventory model for deteriorating items with shortages and time-varying demand

- This article studies an inventory system for deterioration items with time-varying demand.
- Shortages are backlogged and the demand rate follows a power pattern.
- The objective consists of the minimization of the total cost per inventory cycle.
- The optimal scheduling period, the economic lot size, the optimal reorder point are obtained.
- We analyze changes in the deterioration rate on the optimal inventory policy.

A deterministic inventory system for items with a constant deterioration rate is studied. Demand varies in time and it is assumed that it follows a power pattern. Shortages are allowed and backlogged. The ordering cost, the holding cost, the backlogging cost, the deteriorating cost, and the purchasing cost are considered in the inventory management. An approach is proposed to minimize the total cost per inventory cycle. This cost depends on two decision variables: the time at which the inventory level falls to zero and the length of the scheduling period. Numerical examples illustrate the theoretical results.