Subcontracting with availability guarantees: production control and capacity decisions

Abstract

We present a simplified model of a system with a producer, a subcontractor and a random demand. The demand level alternates between a high level and a low level with exponential switching times. The producer does not have enough capacity to meet the high demand. Therefore, it either produces to stock in advance or uses a subcontractor to receive additional capacity when it needs. The subcontractor serves a number of manufacturers and guarantees a long-term availability that is defined as the long-term probability that the subcontractor will be available when it is requested, to each manufacturer. Therefore, a manufacturer may not receive the requested capacity from the subcontractor immediately and waits until the subcontractor becomes available. The times that the subcontractor is available and not available are also exponential random variables. The producer uses a threshold-type policy that depends on the state of the inventory/backlogto decide how much to produce and how much to request from the subcontractor. This system is modeled analytically based on a stochastic flow rate control problem with continuous flow and discrete states in a Markovian setting. A numerical analysis of the model is used to analyze the effects of guaranteed availability on the manufacturer’s and subcontractor’s performances. Extensions to the producer’s and subcontractor’s capacity decisions and the subcontractor’s pricing decisions are also discussed.