Efficient optimization techniques for the allocation of warehouse space in a hierarchy of inventory systems

Abstract

The well known methods for calculating the procurement quantity and procurement level in a deterministic inventory situation are extended to include situations in which warehouse space available is significantly less than required to handle the unconstrained optimal case. The degree of severity of warehouse space shortage is found to limit application of published methods which are predicated on the assignment of finite space to each inventory item using Lagrangian multipliers. The principle that total cost increase rate, or the slope of the total cost versus space available function (Lagrangian multiplier) must be identical for each item in the constrained case is shown to be inapplicable when the shortage of warehouse space is severe. Severe space shortage will cause optimal procurement policies which exclude those items which have the lowest stockout penalty from being stocked at all. Priority of space allocation is given to those items which have the greatest value per unit of cubic space occupied in terms of stockout penalty. Treatment of the single-item single-source (SISS) case is given by closed solution rather than through normal iterative procedures which make use of the Lagrangian multiplier in determining optimal procurement and inventory policy. The SISS solution procedure is extended to the single-item multiple-source (SIMS) case. In the multiple-item single-source (MISS) case, all items are ranked in descending order of shortage cost per unit of warehouse space occupied by each item. Allocation of space is made for each item in succession until all of the available space has been allocated. In the event of severe space shortage, many of the items which have low stockout penalty per unit space occupied will be allocated zero space and will be handled under appropriate procurement and inventory procedures. In the multiple-item multiple-source (MIMS) case, all items are ranked in descending order of shortage cost per unit of warehouse space occupied by each item. Allocation of space proceeds as in the MISS case until all of the available warehouse space has been allocated. Then the least-cost source is selected for each item. Having eliminated source as a consideration, the MIMS case is now treated as a MISS problem and is handled accordingly. It is shown that these procedures select the minimum cost warehouse space allocation for the NIMS problem. This selection is verified by handling the same problem using enumeration and dynamic programming methods.