A Lost Sales Make-to-Stock System with Batch Demand and Batch Production

This study considers a production setting of a single item, single production resource make-to-stock production system with batch demand, batch production and lost sales. Demand arrives as a Poisson process with a randomly distributed batch size. It is assumed that the batch demand can be partially satisfied and unsatisfied demands are lost. Production time follows an exponential distribution, and each production order contains a single lot that does not exceed the maximum lot size. The decision to be considered in managing such a system is the production control decision, which determines when to start production and how much to produce in a batch. This study contributes to the technical literature on controlling make-to-stock systems by addressing a single production resource simultaneously with batch demand and batch production. The system is formulated with the dynamic programming and the model is solved using the value iteration algorithm. In the light of the results obtained by using this algorithm, it has been shown by numerical studies that the optimal production policy is a dynamic policy.