Flexible hiring in a make to order system with parallel processing units

In this paper, we study a make-to-order production system with parallel, identical processing units. Each order needs to be satisfied on a single processing unit that is run by a crew. The inter-arrival time and the service time for each order are random variables. The system operates under a lead time performance constraint, which demands the completion of each order within a pre-determined lead time with a certain probability. The minimum number of processing units needed to satisfy this constraint is determined at the tactical level. Our research focuses on the cost savings that can be realized with the use of flexible crews via contractual hiring agreements with an External Labor Supply Agency (ELSA). The ELSA can periodically provide an agreed number of crews. The cost incurred for a flexible crew is higher than that for a permanent crew, and is decreasing in the period length. We model and analyze this system using the transient behavior analysis of multi-server queues and propose several empirically testable functions for the cost of flexible crews. In our computational study, we demonstrate possible cost savings of 2-level, threshold type hiring policies, relative to the fixed capacity system, under 9 scenarios with three demand-to-processing rate ratios and three lead time performance constraints, each of which reflects a different level of ambition. We observe that the maximum savings occur when the cost of a flexible crew is same as that of a permanent crew, and range from 29.38% to 50.56%. However, as the flexible crews become more expensive, the system may choose to employ permanent crews only. We observe that cost savings consist of two parts: savings due to the cancellation of the sclerosis of capacity discreteness, and savings due to the use of workload information in hiring actions. The latter part is higher for more ambitious lead time performance constraints, and for higher mean processing times. Finally, when there is an additional cost for transacting an agreement with the ELSA, we observe that the capacity flexibility option loses its charm, especially if the transaction cost is higher than the cost of a permanent crew.