Production Control of a Make-to-Stock System with Non-identical Parallel Production Lines and Lost Sales

A production-inventory control problem of a single-item make-to-stock system with non-identical production lines is studied. The item is demanded by customers arriving according to the Poisson process. Unmet demands of incoming customers are lost and lost sales cost occurs. The mentioned production system has multiple and parallel production lines, but these lines are not the same. Hence, some production lines run faster while others run slower. Moreover, each production line is capable to produce the item, and item processing times have an Exponential distribution with different rates. To ease modelling, it is assumed that there are two different production line groups processing the item at different rates. The decision to be taken into account in the management of such a system is the production control decision. It determines when to start production in which production line group. This study contributes to the technical literature on controlling make-to-stock systems by addressing non-identical production lines. A formulation based on dynamic programming is presented and the model is solved with the value iteration algorithm. An extensive numerical study is presented to understand the nature of the production policy. It is shown that the optimal policy is state-dependent according to the numerical results.