Sebastián Dávila (USACH & Universidad de Chile)
Associate Researcher, University of Santiago, Chile | PhD Candidate, Doctorado en Sistemas de Ingeniería, Universidad de Chile, ChileThu May 2nd, 12:00-13:00
Postgrado B room, 2nd floor North building, Industrial Engineering Department, USACH
Title: Bilevel Programming Model for a Multi-Product Location Problem
Abstract: A retail firm has several malls with a known location. A particular product, e.g., food processor, comes in types, which differ by shapes, brands and features. Each mall has a limited capacity of products to be sold at that location, so the firm has to choose what products to sell at what mall. Furthermore, the firm can apply discrete levels of discount on the products, e.g., 5% and 10% over the price. The objective of the firm is to find what products to sell at which mall, with what level of discount, so that its profit is maximized.
Consumers are located in points of the region. Each consumer or group of consumers has a different set of acceptable products, and will purchase one of these, or none if it is not convenient for her. Consumers maximize their utility.
The agents (firm and consumers) play a von Stackelberg game, in which the firm is the leader and the customers the follower. Once the firm decides the products to sell at each mall and the possible discounts, consumers purchase (or not) one of their acceptable products wherever their utility is maximized.
We model the problem using first a bilevel formulation, and we further replace the follower problem by the primal constraints and optimality restrictions, to obtain a compact formulation. We also present a strong and a weak formulation.
Computational experiments are shown, using known instances from the literature.
