Assortment Planning for Multiple Quality Levels Using Locational Choice

Assortment planning is the process in which a retailer selects a product line to offer to customers and is a key determinant of a retailer’s profit. We consider the assortment planning problem using a locational choice model for customer product selection and allow for both horizontal and vertical product differentiation. When the distribution of customer preference is unimodal, the optimal solutions for this problem are unknown. We propose two solution philosophies for generating product assortments. First, we introduce a metaheuristic representation for the problem and test the performance of three metaheuristic techniques. We suggest that a tabu search or genetic algorithm may be the best technique for the problem depending on the parameters. Next, we introduce a combined dynamic programming and line search approach for generating optimal solutions. We use this technique to explore the properties of the optimal solution and suggest instances where this technique is preferable to the metaheuristic methods. We then propose a new model which allows for heterogeneous quality preferences among the customer population. This model allows for more realistic customer product selection but also increases the complexity of the problem. We give mathematical properties of optimal solutions to the heterogeneous model and propose a new metaheuristic representation and a genetic algorithm for solving the problem.