The leader multipurpose shopping location problem

Abstract

This paper extends the follower’s retail store location problem of Marianov et al. (2018) to include the leader’s decisions. The leader locates its stores knowing that a follower will enter the market later offering a different product. Both maximize their markets given that customers can purchase none, one or two non-essential products on the same trip. The paper determines the best locations for first and second entrants through exact and approximated procedures. It turns out that, by locating with foresight, a first entrant can increase the total business in an area for himself and subsequent entrants. We solve the binary programming bi-level resulting problem for small instances by adapting an ad-hoc procedure. Furthermore, a new bi-level reactive GRASP procedure finds solutions for instances of up to 100 nodes in under 3,600 s of CPU time.