Influence of positive order fulfillment time in batch production system
In batch production systems with zero fulfillment time, inventory on all items has to be maintained to respond to stochastic customer demand. Meeting a desired service level would require high safety stock levels. Cyclical inventory cost is charged to each make-to-stock (MTS) item. These two types of costs lead to an expensive inventory holding policy. However if customer contracts can be revised with positive fulfillment time, there is an opportunity to reduce both types of inventory costs. The positive order fulfillment time allows the manufacturer to reduce safety stock by scheduling production in response to arriving orders and to reduce cyclical inventory cost by converting some items to make-to-order (MTO). This research considers a formal approach to determine a policy to minimize the inventory cost with desired service level and positive order fulfillment time. Our production system is a single server multi-item system with constant order fulfillment time and homogeneous stochastic processing time, hence, it can be modeled as an M/G/1 queue. In addition, the queue operates on a first-come-first-serve (FCFS) scheduling rule. For this type of system, we derive the conditions under which a pure MTO policy can be applied. We also use a mixed-integer nonlinear programming model to determine a combined MTS/MTO policy when pure MTO is not feasible. In terms of this combined MTO/MTS policy, through numerical study we show the percentage of items that will be MTO is dependent on initial system load and the order fulfilment time. We also find out that we expect to save more, from this combined MTO/MTS, facing a system with a small initial load and a long order fulfillment time. Moreover, an item with small arrival rate, large order size mean and large unit time holding cost is more likely to be MTO. This should result in insights for a manufacturer using combined MTS/MTO policy with positive order fulfillment time.