Ngan Ha Duong, Tien Thanh Dam, Thuy Anh Ta, Tien Mai
arXiv 15 May 2022 · Mathematics — Optimization · 2 citations (OpenAlex)
arXiv:2205.07345 · PDF · DOI · OpenAlex · Extracted main text
We study a joint facility location and cost planning problem in a competitive market under random utility maximization (RUM) models. The objective is to locate new facilities and make decisions on the costs (or budgets) to spend on the new facilities, aiming to maximize an expected captured customer demand, assuming that customers choose a facility among all available facilities according to a RUM model. We examine two RUM frameworks in the discrete choice literature, namely, the additive and multiplicative RUM. While the former has been widely used in facility location problems, we are the first to explore the latter in the context. We numerically show that the two RUM frameworks can well approximate each other in the context of the cost optimization problem. In addition, we show that, under the additive RUM framework, the resultant cost optimization problem becomes highly non-convex and may have several local optima. In contrast, the use of the multiplicative RUM brings several advantages to the competitive facility location problem. For instance, the cost optimization problem under the multiplicative RUM can be solved efficiently by a general convex optimization solver or can be reformulated as a conic quadratic program and handled by a conic solver available in some off-the-shelf solvers such as CPLEX or GUROBI. Furthermore, we consider a joint location and cost optimization problem under the multiplicative RUM and propose three approaches to solve the problem, namely, an equivalent conic reformulation, a multi-cut outer-approximation algorithm, and a local search heuristic. We provide numerical experiments based on synthetic instances of various sizes to evaluate the performances of the proposed algorithms in solving the cost optimization, and the joint location and cost optimization problems.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Dam, T. T., Ta, T. A., and Mai, T (2021) Submodularity and local search approaches for maximum capture problems under generalized extreme value models self | 1.000 | 10 | 3 | 100% |
| 2 | Mai, T. and Lodi, A (2020) A multicut outer-approximation approach for competitive facility location under random utilities self | 1.000 | 9 | 4 | 100% |
| 3 | Train, K (2003) Discrete Choice Methods with Simulation | 0.874 | 6 | 2 | 100% |
| 4 | Bonami, P. and Tramontani, A (2015) Recent improvement to misocp in cplex | 0.843 | 3 | 3 | 100% |
| 5 | Fosgerau, M. and Bierlaire, M (2009) Discrete choice models with multiplicative error terms | 0.811 | 4 | 2 | 100% |
| 6 | Benati, S. and Hansen, P (2002) The maximum capture problem with random utilities: Problem formulation and algorithms | 0.737 | 3 | 2 | 100% |
| 7 | Ljubić, I. and Moreno, E (2018) Outer approximation and submodular cuts for maximum capture facility location problems with random utilities | 0.737 | 3 | 2 | 100% |
| 8 | McFadden, D (1978) Modelling the choice of residential location | 0.737 | 3 | 2 | 100% |
| 9 | Bonami, P., Lee, J., Leyffer, S., and Wächter, A (2011) More branch-and-bound experiments in convex nonlinear integer programming | 0.644 | 2 | 2 | 100% |
| 10 | Haase, K. and Müller, S (2014) A comparison of linear reformulations for multinomial logit choice probabilities in facility location models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 51 scored citations.