In this thesis, we consider determining the economic lot sizes for a finite production rate assembly system with n facilities. Costs at each facility consist of a stationary positive echelon holding cost, and a fixed set up cost. The goal is to determine the production lot size at each facility in order to minimize the long-run total average cost of the system. Power-of-two policies, in which the lot size at each facility is a power of two times some base lot size, are considered. A 94%-effective power-of-two policy is determined from the optimal solution to a continuous relaxation problem by an O(n) algorithm, while a 98%-effective power-of-two policy is found using an O(n log n) algorithm. Near optimal solutions to the continuous relaxation problem are found by a subgradient optimization procedure and a cyclic coordinate descent method. Computational results suggest both methods are efficient for very large systems.
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