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Abstract. We develop a new framework for location of competitive facilities by introducing non-constant expenditure functions into spatial interaction location models. This framework allows us to capture two key effects - market expansion and cannibalization - within the same model.
We develop algorithmic approaches for finding optimal or near-optimal solutions for several models that arise from choosing a specific form of the expenditure functions.
Keywords: competitive facility location models, integer programming, greedy heuristics, worst-case bounds
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1. Introduction
Consider the problem of locating a set of m retail or service facilities controlled by the same entity ("Company"). These facilities will compete for customer demand with each other, as well as with any pre-existing facilities in the same area (both, the ones belonging to the Company, and the ones owned by competitors). We would like to find locations that maximize the total demand at all (new and existing) facilities controlled by the Company.
There are two key effects that need to be captured:
* cannibalization and
* market expansion.
"Cannibalization" occurs when new facilities capture some of the demand from pre-existing facilities. While capturing consumer demand from competing facilities may be beneficial, cannibalizing demand from other facilities owned by the Company does not increase the objective function (i.e., total volume of business at Company's facilities), in fact it may undermine the profitability of existing outlets. This effect is particularly acute in the "monopolistic case": when the Company owns both new and pre-existing facilities.
"Market expansion" occurs when the total available consumer demand in the area increases as a result of opening new facilities (i.e., when consumer expenditures on the products or services offered by the facilities increase). This increase may happen for a variety of reasons: opening new outlets may increase the overall utility (convenience) of the product offered to some customers. The marketing expenditures by the new facilities will increase the overall "marketing presence" of the product offered at the facilities, leading to increased consumer demand. In addition, some of the customers who did not previously patronize any of the facilities (perhaps because none were close enough to their...