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This paper formulates and analyzes a model to integrate inventory management and promotion decisions in a multi-product environment. The model assumes that actual demands for the items depend on both item availability and the level of promotion used for the item. A notable feature of the model is that customer demand is partially backordered, where the fraction of demand backordered depends on how long a customer has to wait for delivery. The firm is assumed to have a limited promotion budget. The effect of a promotion is modeled through an increase in the demand rate of the item being promoted. We formulate a general, non-stationary, finite horizon version of the problem. However this problem is very difficult to solve optimally. In order to develop insights into the nature of the solution we formulate a stationary version of the general problem with the additional restriction that only one item can be promoted at a time. An efficient solution approach is developed for this stationary version, and limited numerical results are provided. These numerical results indicate that a coordinated approach to promotions and logistics decisions can lead to significantly higher profit for the firm.