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.
Highlights
The facility location problem addresses facility locations intended to serve a set of given demands.In reality, facility location is often a long-term decision and is vital in building a logistics network, so firms must consider the uncertainties in its life-span in the initial design
This study presents robust p-center facility location models based on three types of cost uncertainty: box uncertainty, ellipsoid uncertainty and, cardinality-constrained uncertainty
We apply three classic robust optimization (RO) modeling techniques to formulate a multiple allocation p-center facility location problem. Previous works in this area all focus on minimizing the total cost or maximizing profit
Summary
The facility location problem addresses facility locations intended to serve a set of given demands. Uncertainties can be even more drastic in emergency circumstances, in which firms need to serve demand quickly and fairly. In such cases, decision-makers have to solve location problems under uncertain input data. Facility locations under uncertainty received decades of research attention, with different approaches to embedding uncertain information in location models. These modeling techniques are classified mainly as robust approaches and stochastic approaches, depending on whether decision makers can acquire probabilistic information.
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