Periodic capacity management under a lead‐time performance constraint

In this paper, we study a production system that operates under a lead‐time performance constraint which guarantees the completion of an order before a pre‐determined lead‐time with a certain probability. The demand arrival times and the service requirements for the orders are random. To reduce the capacity‐related operational costs, the production system under study has the option to use flexible capacity. We focus on periodic capacity policies and model the production system as a queuing system that can change its capacity periodically and choose to operate in one of the two levels: a permanent capacity level and a permanent plus contingent capacity level. Contingent capacity is supplied if needed at the start of a period, and is available during that period, at a cost rate that is decreasing in period length in different functional forms. Next, we propose a search algorithm that finds the capacity levels and the switching point that minimizes the capacity‐related costs for a given period length. The behaviour of the capacity‐related costs changes drastically under different period lengths and cost structures. In our computational study, we observe that the periodic capacity flexibility can reduce the capacity‐related operational costs significantly (up to 35%). However, in order to achieve these savings, the period length must be chosen carefully depending on ambition level and capacity‐related costs. We also observe that the percentage savings are higher for more ambitious lead‐time performance constraints. Moreover, we observe that the use of contingent capacity makes the total system costs more insensitive to the lead‐time performance requirements.