We study a markdown optimization problem commonly faced by many large retailers that involves joint decisions of inventory allocation and markdown pricing of a single product at multiple stores subject to various business rules. At the beginning of the markdown planning horizon, there is a certain amount of inventory of a product at a warehouse that needs to be allocated to many retail stores served by the warehouse over the planning horizon. In the same time, a markdown pricing scheme needs to be determined for each store over the planning horizon. A number of business rules for inventory allocation and markdown prices at the stores must be satisfied. The retailer does not have a complete knowledge about the probability distribution of the demand at a given store in a given time period. The retailer's knowledge about the demand distributions improves over time as new information becomes available over time. Hence, the retailer employs a rolling horizon approach where the problem is re-solved at the beginning of each period by incorporating the latest demand information. We show that the problem involved at the beginning of each period is NP-hard even if the demand functions are deterministic and there is only a single store or a single time period. We thus focus on heuristic solution approaches.
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