Location of retail facilities under conditions of uncertainty

Abstract

Models for the optimal location of retail facilities are typically premised on current market conditions. In this paper we incorporate future market conditions into the model for the location of a retail facility. Future market conditions are analyzed as a set of possible scenarios. We analyze the problem of finding the best location for a new retail facility such that the market share captured at that location is as close to the maximum as possible regardless of the future scenario. The objective is the minimax regret which is widely used in decision analysis. To illustrate the models an example problem is analyzed and solved in detail.

A review of competitive facility location in the plane

“…Drezner [21] found the location of a new facility when future market conditions are unclear using the minimax regret objective. There are several defined scenarios concerning future market conditions:…”

Modeling Competitive Facility Location Problems: New Approaches and Results

“…In this section we survey two models for locating a new facility under conditions of uncertainty: the minimax regret objective (Drezner [25]) and the leader-follower, also called the Stackelberg equilibrium model (Stackelberg [82], Drezner and Drezner [32], Plastria and Vanhaverbeke [77]). …”

“…Minimax Regret Objective. Drezner [25] incorporated future market conditions into the gravity model for the retail facility location. Future market conditions were analyzed as a set of possible scenarios.…”

“…Drezner [25] applied the multistart heuristic approach to find M * k and minimize R(X) for the location of one facility in the plane. An example problem is solved for Orange County, California.…”

“…If all competing facilities are far away, then p is close to 1 and only a small portion of the buying power will be spent at any facility. If several facilities are relatively close, then almost all of the buying power will be spent because the product of the 1 − e −λj d(Pi, Qj ) terms will include several small values that yield a small p in (25).…”