Determining the Optimal Location of Vehicle Inspection Facilities Under Uncertainty via New Optimization Approaches

Abstract

This study addresses the problem of optimally locating vehicle inspection facilities under uncertain customer demand and varying velocity considering regional constraints. The objective is to simultaneously minimize the transportation time of all customers and their transportation cost, while ensuring consumers to reach their desired destinations within their expected time and cost. We study two variants of the problem: vehicle inspection location with complete probability distributions of customer demand and vehicle velocity, and that with partial information of customer demand and vehicle velocity, i.e., only the supports and means of the stochastic variables are known. For the former problem, an expected value model and a chance-constrained program are first formulated. Then based on explored problem properties, the expected value program is equivalently reformulated as a deterministic non-linear program. To efficiently deal with the chance-constrained program, a sample average approximation (SAA)-based approach is proposed. For the latter one, we develop a new distribution-free model. Computational results for benchmark examples demonstrate that: i) for the former, the proposed deterministic program reformulation-based approach and SAA algorithm outperform the state-of-the-art approaches; ii) for the latter, the proposed distribution-free model can effectively deal with the problem with partial demand and velocity information.