Stochastic optimal control for staffing and backlog policies in a two-stage customized service supply chain

Motivated by an oilfield services industry case study, we investigate the dynamic behavior of customized service supply chains by developing a two-stage serial staffing model. Each stage holds no finished goods inventory, but rather only backlogs that can be managed by adjusting staffing levels. We develop optimal control policies to balance backlog costs against hiring and firing personnel costs – assuming shared backlog information – under both centralized and decentralized control. We examine when there is sufficient economic incentive for two completely decentralized stages to begin: (1) to share backlog information without centralizing control, or (2) to completely centralize control. These switching points are determined by the relative service and personnel costs of the two stages. From these results, we show that decentralizing control in many cases does not materially worsen performance, so long as information is shared. Moreover, in some cases, even sharing information is of only marginal benefit.