A Me-based rough approximation approach for multi-period and multi-product fashion assortment planning problem with substitution

Assortment planning is the process conducted by fashion retailers to determine the variety and quantity of products to sell at each sales period. As it has a great impact on the financial performance for retail stores, retailers take it as the crucial activity and the nucleus for an intelligent inventory control system. In this paper, we consider the assortment planning with substitution (a substitute product when the original choice is unavailable) under a fuzzy environment and then a fuzzy optimization model is built to obtain maximum benefits for retailers. For the fuzzy variables in the objective functions, we propose a fuzzy measure which can represent any attitudes between extremely optimistic and pessimistic to handle objective functions and get their expected value. For the constraints, a similarity relationship based on the fuzzy measure is defined, and the feasible region is addressed by the rough approximation based on this similarity relationship. Then, the lower approximation model (LAM) and the upper approximation model (UAM), which can avoid losing much information in the modeling process, are generated. To solve the model, a hybrid genetic algorithm with rough simulation is proposed. Finally, an application is used to demonstrate the practicality and effectiveness of the model and solution algorithm.