Threshold-Type Control of Supply Chain Systems with Backordering Decisions
This chapter develops and evaluates threshold-type control policies for the supply chains with backordering decisions presented in Chap. 4. For the joint raw material ordering, production, and backordering control problem, a linear switching threshold policy is presented to approximate the optimal policy. Its effectiveness is examined through numerical examples. For the failure-prone manufacturing supply chain without raw material ordering activity, the analytical results of the discounted cost case are extended to the long-run average cost case, for example, the optimality of a three-parameter threshold control policy. More importantly, the explicit form of the stationary distribution under such threshold policy is derived, which is then used to calculate steady-state performance measures and seek the optimal threshold values. An interesting finding is that the completely backordering policy may be optimal for the discounted cost case but will never be optimal for the average cost case.