A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem

Abstract

In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.

Research on Collaborative Planning and Symmetric Scheduling for Parallel Shipbuilding Projects in the Open Distributed Manufacturing Environment

“…Some scholars focus on the research of the decision-making model. Du et al apply a robust optimization approach to a p-center facility location problem under uncertainty and use Gurobi to solve the equivalent robust counterpart models [19]. Liu et al considered the problem of providing an efficient privacy protection decision tree evaluation service for resource constrained customers under the Internet of Things, and established a security comparison protocol based on the additive secret sharing technology through the cloud model to achieve efficient decision evaluation [20].…”

“…Considering the distribution and symmetry of the planning and decision-making processes in the shipbuilding projects, an appropriate decision-making method and tool to assist the participants to make better decisions is extremely important. There are many researches on symmetric decision-making theory, including the decision-making model [19][20][21][22][23] and decision-making system modeling [24][25][26][27][28][29]. The purpose of this paper is to provide effective decision-making methods for project participants.…”

Robust Milp Formulations for the Two-Stage Weighted Vertex P-Center Problem

“…Each element of the uncertainty set is called a scenario. The most classical sets are the box, the ellipsoid and the budgeted uncertainty sets (see e.g., Ben-Tal et al (2009); Bertsimas & Sim (2004); Du & Zhou (2018); Paul & Wang (2019)).…”

A Novel Approach for Determination of Reliability of Covering a Node from K Nodes

“…As the basic network location models in [1], the following are listed; Set Covering Location Problem (SCLP), Maximal Covering Location Problem (MCLP), p-center problem, p-dispersion problem, p-median problem, Fixed Charge Location Problem, Hub Location Problem, and The Maximum Location Problem. The robust optimization approach to the p-center location problem has been given in [4]. Adeleke and Olukanni described models which have been adapted to problems relating to waste management: Single Facility Location Problem, Multi-Facility Location Problem, Fixed Costs Capacitated Facility Location Problem, Capacitated p-Median Facility Location Problem, Covering Location Problems (Symmetrical Total Covering and Maximum Covering Location Problem), and Undesirable Facility Location Problem [5].…”