Submodularity and local search approaches for maximum capture problems under generalized extreme value models

Dam, Tien Thanh; Ta, Thuy Anh; Mai, Tien

doi:10.1016/j.ejor.2021.09.006

Cited by 12 publications

(8 citation statements)

References 22 publications

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“…Second, we show that the joint problem can be also handled exactly by a multicut outer-approximation algorithm (Bonami et al, 2011, Hijazi et al, 2014, Mai and Lodi, 2020. Third, motivated by the fact that some recent studies have shown that a local search heuristic would achieve state-of-the-art performance in the context (Dam et al, 2021), we develop such a local search procedure to solve our joint problem.…”

Section: Contributionsmentioning

confidence: 97%

“…Proposition 3 implies that an optimal solution to (9) would not necessarily reach the maximum capacity M . Moreover, in prior MCP work, Dam et al (2021) and Thuy show that a simple greedy local search based on adding locations to an empty set of locations guarantee (1 − 1/e) approximation solutions. This would be not the case for (9) due to the non-monotonicity.…”

Section: Local Search Heuristicmentioning

confidence: 97%

“…Ljubić and Moreno (2018) propose a branch-and-cut method combining outer-approximation and submodular cuts, and Mai and Lodi (2020) propose a multicut outer-approximation algorithm to efficiently solve large-scale instances. Recently, (Dam et al, 2021) study the MCP under the generalized extreme value (GEV) family of models and propose a local search algorithm with guarantees. To the best of our knowledge, existing works in the context of the MCP only focus on the selection of locations, thus the original optimization problems only involve binary variables.…”

Section: Contributionsmentioning

confidence: 99%

“…, where U c i represents the utility of the competitor. Without loss of generality, we can assume that U c i = 1 (Dam et al, 2021). When the facility planing and cost optimization problems are considered simultaneously, we write the utilities V ij as V ij = a ij x j +b ij , where a ij is a parameter representing the sensitivity of customer i w.r.t.…”

Section: Joint Location and Cost Optimization Mcpmentioning

confidence: 99%

“…The last step is a simple exchanging procedure trying to swap a location in the current choice set with some other locations outside the current choice set of locations to improve the solution found after the second step. We refer the reader to Dam et al (2021) for more details.…”

Section: Local Search Heuristicmentioning

confidence: 99%

See 4 more Smart Citations

Joint Location and Cost Planning in Maximum Capture Facility Location under Multiplicative Random Utility Maximization

Duong¹,

Dam²,

Ta³

et al. 2022

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We study a joint facility location and budget planning problem in a competitive market under random utility maximization (RUM) models. The objective is to locate new facilities and make decisions on the budgets (or costs) 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 show that, under the additive RUM framework, the resulting cost optimization problem becomes highly non-convex and may have several local optimum solutions. In contrast, the use of the multiplicative RUM brings several advantages to the competitive facility location problem. More precisely, we show that 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 optimization tools such as CPLEX or GUROBI. Furthermore, we consider a joint location and cost optimization problem 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 joint location and cost optimization problems.

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Section: Contributionsmentioning

confidence: 97%

Section: Local Search Heuristicmentioning

confidence: 97%