Procurement of prescribed sizes: A Markovian approach

The paper considers how a total budgeted inventory level should be allocated among the various sizes of an item of clothing. A Markov Process is used to model how an individual changes size over time. The paper allows for (a random number of) individuals entering and leaving the organization, and for uncertainty in the numbr of units required by each member. An optimal allocation procedure is developed which minimizes both expected item shortages and excess inventory. Experiments are conducted comparing the performance of the optimal allocation procedure with that of two simpler procedures requiring less information on the population. In a case study of a municipal police service the paper found the common procedure of allocating in proportion to the existing demand for each size to be very close to optimal.