Lagrangian Heuristics for Large-Scale Dynamic Facility Location with Generalized Modular Capacities

Purpose Previously use of drones as a relief distribution vehicle was studied in several studies where required number of drones and the best locations for the relief centers were investigated. The maximum travel distance of drones without a need to recharge is limited by their endurance. Recharge stations can be used to extend the coverage area of the drones. The purpose of this paper is to find the best topology for both relief centers and recharge stations to cover a large-scale area with minimum and feasible incurred costs and waiting times. Design/methodology/approach A multi-level facility location problem (FLP) is utilized to find the optimum number of relief centers and refuel stations and their locations. It is supposed that the demand occurs according to Poisson distribution. The allocation of the demand is based on nearest neighborhood method. A hybrid genetic algorithm is proposed to solve the model. The performance of the algorithm is examined through a case study. Findings The proposed method delivers increased efficiency and responsiveness of the humanitarian relief system. The coverage area of the drones is extended by refuel stations, total costs of the system are reduced and the time to respond an emergency, which is an important factor in survival rate, is significantly decreased. Originality/value This study proposes a multi-level FLP to simultaneously account for recharge stations, relief centers and the number of required drones to cover all the demand for relief in a post-disaster period.

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A Method for Large-Scale Integer Goal Programming with an Application to a Facility Location/Allocation Problem

Lecture Notes in Economics and Mathematical Systems - Organizations: Multiple Agents with Multiple Criteria ◽

10.1007/978-3-642-45527-8_38 ◽

1981 ◽

pp. 490-498 ◽

Cited By ~ 2

Author(s):

S. H. Zanakis

Keyword(s):

Facility Location ◽

Goal Programming ◽

Large Scale ◽

Allocation Problem ◽

Location Allocation ◽

Location Allocation Problem

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A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games

INFORMS Journal on Computing ◽

10.1287/ijoc.2021.1085 ◽

2021 ◽

Author(s):

Claudio Contardo ◽

Jorge A. Sefair

Keyword(s):

Exact Solution ◽

Approximation Algorithm ◽

Facility Location ◽

Shortest Path ◽

Large Scale ◽

Optimization Problem ◽

Optimal Solution ◽

Solution Space ◽

Decision Variables ◽

Algorithmic Framework

We present a progressive approximation algorithm for the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. The follower must solve an optimization problem that has been previously perturbed by means of a series of attacking actions led by the attacker. These attacking actions aim at augmenting the cost of the decision variables of the follower’s optimization problem. The objective, from the attacker’s viewpoint, is that of choosing an attacking strategy that reduces as much as possible the quality of the optimal solution attainable by the follower. The progressive approximation mechanism consists of the iterative solution of an interdiction problem in which the attacker actions are restricted to a subset of the whole solution space and a pricing subproblem invoked with the objective of proving the optimality of the attacking strategy. This scheme is especially useful when the optimal solutions to the follower’s subproblem intersect with the decision space of the attacker only in a small number of decision variables. In such cases, the progressive approximation method can solve interdiction games otherwise intractable for classical methods. We illustrate the efficiency of our approach on the shortest path, 0-1 knapsack and facility location interdiction games. Summary of Contribution: In this article, we present a progressive approximation algorithm for the exact solution of several classes of interdiction games in which two noncooperative players (namely an attacker and a follower) interact sequentially. We exploit the discrete nature of this interdiction game to design an effective algorithmic framework that improves the performance of general-purpose solvers. Our algorithm combines elements from mathematical programming and computer science, including a metaheuristic algorithm, a binary search procedure, a cutting-planes algorithm, and supervalid inequalities. Although we illustrate our results on three specific problems (shortest path, 0-1 knapsack, and facility location), our algorithmic framework can be extended to a broader class of interdiction problems.

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