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We study lot-size policies in a serial, multi-stage, manufacturing/inventory system with two key generalizations, namely (1) random yields at each production stage and (2) an autoregressive demand process. Previous research shows that the optimal policies in models with random yields (even in models with a single installation) lack the familiar order-up-to structure and are not myopic. Thus, dynamic programming algorithms are needed to compute optimal policies and one encounters the “curse of dimensionality;” this is exacerbated here by the need to expand the size and dimension of the state space to accommodate the autoregressive demand feature. Nevertheless, although our model is more complex, we prove that there is an optimal policy with the order-up-to feature and, more importantly, that the optimal policy is myopic. This avoids the computational burden of dynamic programming. Our results depend on two assumptions concerning the stochastic yield, namely that 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. We introduce the concept of echelon-like variables to derive the structure of optimal policies; this is a generalization of the echelon variables in Clark and Scarf (1960). Furthermore, we show that the same kind of policy is optimal for several criteria: infinite-horizon discounted cost, infinite-horizon long-run average cost, and finite-horizon discounted cost (with the appropriate choice of the salvage value function).
In the real world, production systems are affected by external and internal uncertainties. Stochastic demand - an external uncertainty - arises mainly due to forecast errors and unknown behavior of customers in future. Internal uncertainties occur in situations where random yield, random production capacity, or stochastic processing times affect the productivity of a manufacturing system. The resulting stochastic production output is especially present in industries with modern and complex technologies as the semiconductor industry. This thesis provides model formulations and solution methods for capacitated dynamic lot sizing problems with stochastic demand and stochastic production output that can be used by practitioners within Manufacturing Resource Planning Systems (MRP), Capacitated Production Planning Systems (CPPS), and Advanced Planning Systems (APS). In all models, backordered demand is controlled with service levels. Numerical studies compare the solution methods and give managerial implications in presence of stochastic production output. This book addresses practitioners, consultants, and developers as well as students, lecturers, and researchers with focus on lot sizing, production planning, and supply chain management.
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