An Approximate Analysis of Dynamic Pricing, Outsourcing, and Scheduling Policies for a Multiclass Make-to-Stock Queue in the Heavy Traffic Regime

A new study by Ata and Barjesteh proposes an effective joint dynamic pricing, outsourcing, and scheduling policy for a multiclass make-to-stock manufacturing system. The authors approximate this control problem with a Brownian control problem. They solve the Brownian problem explicitly by exploiting the solution to a Riccati equation and propose a policy for the manufacturing system based on its solution. The proposed policy is a two-sided barrier policy. Outsourcing and idling processes are used to maintain the workload above the lower and below the upper barriers, respectively. Dynamic prices are used to control the workload process between the two barriers. The authors show using a simulation study that the optimality gap of the proposed policy is small, and their proposed policy outperforms a long list of static pricing policies. Moreover, the gap between their proposed policy and the static pricing policies increases with the server utilization and the outsourcing cost.