Large retailers' operations have changed substantially in the last couple of decades, evolving from single stores replenishing their stock directly from suppliers, to large distribution systems where goods are centrally ordered and then allocated and delivered to each individual store. Tremendous progress in information systems' technology has enabled leading retailers to exploit economies of scale to the fullest by implementing centralized control over their distribution systems.; This dissertation studies the problem of replenishing inventory in a centrally controlled, multi-facility distribution system with constant traveling times and serving external, stochastic demand. We formulate an inventory model for this problem which is a natural extension of the classical single-facility inventory models for both continuous and periodic review. Our contribution consists of establishing two bounds for the cost incurred by such system, and also finding a heuristic policy for a two-stage serial system. This policy is 93%-effective within the class of weakly nested policies---a class to be defined later in this work---and is used to extrapolate recommendations relevant to practitioners.; The lower bounds are obtained by decomposing the distribution system into single-facility sub-problems, a strategy based on the use of inputed penalty costs, and which substantially reduces computational complexity and permits the application of known single-stage techniques. New extensions of the concepts of 'echelon inventory position' and 'nested policy' are also proposed.
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