Joint Optimization of a Bilevel Logistics Network and an Arc Interdiction Location-routing Problem

Abstract

There is a high interest in optimization of transportation and logistics networks due to its high impact on the economic performance of supply chain networks. This paper presents a bilevel mixed-integer programming model as well as a solution method to manage distribution process in a logistic network, where two decision makers, called distributor and interdictor, make efforts to achieve their contradictory targets. This problem, known as arc interdiction location-routing problem (AI-LRP), is in fact a new, extended version of the classical LRP. The distributor strives to deliver goods to customers with minimal risk and cost, while the interdictor, by contrast, endeavors to disrupt products flow through a few critical arcs. AI-LRP has wide applications in reality, including distribution of particular goods like money, precious metals, hazardous materials, and prisoners that may need security measures. The interplay between two decision makers is formulated as a bilevel model. To solve the model, a novel genetic algorithm (NGA) is devised in which the density ordered heuristic of the knapsack problem is applied to generate an initial population of solutions. Computational results illustrate that NGA outperforms a commercial solver in terms of computational time and quality of solutions.