A column generation heuristic for congested facility location problem with clearing functions

2013 ◽  
Vol 64 (12) ◽  
pp. 1780-1789 ◽  
Author(s):  
S Kim
Keyword(s):  
Facility Location ◽  
Column Generation ◽  
Location Problem ◽  
Facility Location Problem ◽  
Clearing Functions

A Note on “The Facility Location Problem with Limited Distances”

2020 ◽  
Vol 54 (6) ◽  
pp. 1439-1445
Author(s):  
Prahalad Venkateshan
Keyword(s):  
Facility Location ◽  
Column Generation ◽  
Location Problem ◽  
Facility Location Problem ◽  
Sum Of Squares ◽  
Generation Algorithm ◽  
Math Programming ◽  
Modified Algorithm

In this paper, it is shown that the polynomially bounded enumerative procedure to solve the facility location problem with limited distances, originally described by Drezner, Mehrez, and Wesolowsky [Drezner Z, Mehrez A, Wesolowsky GO (1991) The facility location problem with limited distances. Transportation Sci. 25(3):183–187.], and subsequently corrected by Aloise, Hansen, and Liberti [Aloise D, Hansen P, Liberti L (2012) An improved column generation algorithm for minimum sum-of-squares clustering. Math. Programming 131(1–2):195–220.], can still fail to optimally solve the problem. Conditions under which the procedures succeed are identified. A new modified algorithm is presented that solves the facility location problem with limited distances. It is further shown that the proposed correction is complete in that it does not require further corrections.

The Value of Randomized Solutions in Mixed-Integer Distributionally Robust Optimization Problems

2021 ◽  
Author(s):  
Erick Delage ◽  
Ahmed Saif
Keyword(s):  
Robust Optimization ◽  
Facility Location ◽  
Column Generation ◽  
Location Problem ◽  
Optimization Problems ◽  
Facility Location Problem ◽  
Mixed Integer ◽  
Distributionally Robust Optimization ◽  
Continuous Relaxation ◽  
Distributionally Robust

Randomized decision making refers to the process of making decisions randomly according to the outcome of an independent randomization device, such as a dice roll or a coin flip. The concept is unconventional, and somehow counterintuitive, in the domain of mathematical programming, in which deterministic decisions are usually sought even when the problem parameters are uncertain. However, it has recently been shown that using a randomized, rather than a deterministic, strategy in nonconvex distributionally robust optimization (DRO) problems can lead to improvements in their objective values. It is still unknown, though, what is the magnitude of improvement that can be attained through randomization or how to numerically find the optimal randomized strategy. In this paper, we study the value of randomization in mixed-integer DRO problems and show that it is bounded by the improvement achievable through its continuous relaxation. Furthermore, we identify conditions under which the bound is tight. We then develop algorithmic procedures, based on column generation, for solving both single- and two-stage linear DRO problems with randomization that can be used with both moment-based and Wasserstein ambiguity sets. Finally, we apply the proposed algorithm to solve three classical discrete DRO problems: the assignment problem, the uncapacitated facility location problem, and the capacitated facility location problem and report numerical results that show the quality of our bounds, the computational efficiency of the proposed solution method, and the magnitude of performance improvement achieved by randomized decisions. Summary of Contribution: In this paper, we present both theoretical results and algorithmic tools to identify optimal randomized strategies for discrete distributionally robust optimization (DRO) problems and evaluate the performance improvements that can be achieved when using them rather than classical deterministic strategies. On the theory side, we provide improvement bounds based on continuous relaxation and identify the conditions under which these bound are tight. On the algorithmic side, we propose a finitely convergent, two-layer, column-generation algorithm that iterates between identifying feasible solutions and finding extreme realizations of the uncertain parameter. The proposed algorithm was implemented to solve distributionally robust stochastic versions of three classical optimization problems and extensive numerical results are reported. The paper extends a previous, purely theoretical work of the first author on the idea of randomized strategies in nonconvex DRO problems by providing useful bounds and algorithms to solve this kind of problems.

scholarly journals The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches

Top ◽  
2009 ◽  
Vol 18 (1) ◽  
pp. 43-61 ◽  
Author(s):  
Maria Albareda-Sambola ◽  
Elena Fernández ◽  
Yolanda Hinojosa ◽  
Justo Puerto
Keyword(s):  
Facility Location ◽  
Column Generation ◽  
Location Problem ◽  
Facility Location Problem ◽  
Single Period ◽  
Lagrangean Heuristic

scholarly journals Dispersing Obnoxious Facilities on a Graph

Algorithmica ◽  
2021 ◽  
Author(s):  
Alexander Grigoriev ◽  
Tim A. Hartmann ◽  
Stefan Lendl ◽  
Gerhard J. Woeginger
Keyword(s):  
Facility Location ◽  
Location Problem ◽  
Unit Length ◽  
Facility Location Problem ◽  
Np Hard ◽  
Obnoxious Facilities ◽  
Rational Parameter ◽  
Polynomially Solvable

AbstractWe study a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many facilities as possible subject to the condition that any two facilities have at least distance $$\delta$$ δ from each other. We investigate the complexity of this problem in terms of the rational parameter $$\delta$$ δ . The problem is polynomially solvable, if the numerator of $$\delta$$ δ is 1 or 2, while all other cases turn out to be NP-hard.

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