Optimality of Myopic Policies for Dynamic Lot-Sizing Problems in Serial Production Lines with Random Yields and Autoregressive Demand
- Matthew Sobel
- Volodymyr Babich
Operations Research, vol. 60, pp. 1537-1550, December 2012
We study lot-size policies in a serial, multi-stage, manufacturing/inventory system subject to two key generalizations: (1) yields at each production stage are random and (2) the demand process is autoregressive. Previous research showed that the optimal policies in models with random yields (even in one-installation models) do not have the familiar order-up-to structure and are not myopic. Thus, dynamic programming algorithms are needed to compute the optimal polices and one runs into the ``curse of dimensionality,'' which is exacerbated in our model by the need to expand the state space to accommodate the autoregressive demand feature. We prove that, for our more complex model, the order-up-to policy is optimal and, more importantly, the optimal policy is myopic. Thus, the computational burden of dynamic programming algorithms is avoided. Our results depend on two assumptions concerning the stochastic yield: the expected yield at a work station is proportional to the lot size, and the distribution of the deviation of the yield from its mean does not depend on the lot size. To derive the optimal policies we introduce the concept of echelon-like variables, which is a generalization of the echelon variables in Clark and Scarf (1960). Furthermore, we show that the same policy is optimal for the models with the infinite-horizon discounted cost, infinite-horizon long-run average cost, and the finite-horizon discounted cost criteria (the latter holds with the appropriate choice of the salvage value function).