Markdown optimization at multiple stores

Abstract

This article studies a markdown optimization problem commonly faced by many large retailers that involves joint decisions on inventory allocation and markdown pricing 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. 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. It is shown 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. Thus, attention is focused on heuristic solution approaches. The stochastic demand is modeled using discrete demand scenarios based on the retailer’s latest knowledge about the demand distributions. This enables possible demand correlations to be modeled across different time periods. The problem involved at the beginning of each period is formulated as a mixed-integer program with demand scenarios and it is solved using a Lagrangian relaxation – based decomposition approach. The approach is implimented on a rolling horizon basis and it is compared with several commonly used benchmark approaches in practice. An extensive set of computational experiments is perfomed under various practical situations, and it is demonstrated that the proposed approach significantly outperforms the benchmark approaches. A number of managerial insights are derived about the impact of business rules and price sensitivity of individual stores on the total expected revenue and on the optimal inventory allocation and pricing decisions.

Keywords:

• Markdown pricing
• inventory allocation
• multiple stores
• business rules
• Lagrangian relaxation
• heuristics

Additional information

Notes on contributors

Ming Chen

Ming Chen is an Assistant Professor of Operations and Supply Chain Management at the College of Business Administration, California State University Long Beach. His research interests include revenue management and dynamic pricing, optimization, simulation, and resource allocation.

Zhi-Long Chen

Zhi-Long Chen is a Professor of Operations Management at the Robert H. Smith School of Business, University of Maryland. His research interests include supply chain scheduling, production and distribution operations, dynamic pricing, and optimization.

Guruprasad Pundoor

Guru Pundoor works as a scientist at Walmart eCommerce, San Bruno, California. He holds a Ph.D. in Management Science from the Robert H. Smith School of Business, University of Maryland. After his Ph.D., he worked in the business development team at FedEx for a couple of years. He then moved to ILOG (later acquired by IBM) where he worked on several supply chain optimization engagements for multiple clients. His interests are in the area of supply chain strategy.

Suresh Acharya

Suresh Acharya is Vice President of Optimization and Data Science at JDA Software. His areas of interest include retail planning and pricing, supply chain management, and revenue management.

John Yi

John Yi is an Associate Professor of Decision and System Sciences at the Haub School of Business, Saint Joseph’s University. His research interests include resource optimization, predictive analytics, and expert systems.