426. The follower competitive facility location problem under the nested logit choice rule
Invited abstract in session TB-4: Topics in Competition and Games, cluster Location, Network Design, and Routing.
Tuesday, 10:30-12:00Room: CE-209
Authors (first author is the speaker)
| 1. | Gonzalo Mendez-Vogel
|
| Department of Engineering Sciences, Universidad Andres Bello | |
| 2. | Vladimir Marianov
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| Electrical Engineering, Pontificia Universidad Catolica de Chile | |
| 3. | Armin Lüer-Villagra
|
| Department of Engineering Sciences, Universidad Andres Bello |
Abstract
Recently, more realistic customer choice rules based on the Multinomial Logit have been proposed for the follower competitive facility location problem, together with efficient exact solution methods based on cut generation approaches. We address this problem where a new chain, the entrant, decides to locate some stores in a market where incumbent chains offer substitute products, differing from the entrant's product in secondary features. The entrant's stores are very similar to each other, as are the incumbent chains. For a given customer, purchases made at the stores of one of the chains are correlated, given the similitude between the stores, but the Multinomial Logit rule does not capture this correlation. We propose using a Nested Logit rule - capturing this correlation and, in addition, representing a sequential decision process by the customer, who first chooses the chain and then the store. We prove the concavity of the objective function in the problem and find exact solutions using Branch and Cut over a generalized linear reformulation of the problem and four different cuts: submodular and an improvement of these, outer-approximation, and a set of new cuts. Our results show locations fitting better intuition and practice. Furthermore, our computational times improve in many cases upon the known results for similar problems.
Keywords
- Location Problems
- Facilities Planning and Design
- Programming, Integer
Status: accepted
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