This paper studies Multi-Depot Rural Postman Problems on an undirected graph. These problems extend the well-known Undirected Rural Postman Problem to the case where there are several depots instead of just one. Linear integer programming formulations that only use binary variables are proposed for the problem that minimizes the overall routing costs and for the model that minimizes the length of the longest route. An exact branch-and-cut algorithm is presented for each considered model, where violated constraints of both types are separated in polynomial time. Despite the difficulty of the problems, the numerical results from a series of computational experiments with various types of instances illustrate a quite good behavior of the algorithms. When the overall routing costs are minimized, over 43% of the instances were optimally solved at the root node, and 95% were solved at termination, most of them with a small additional computational effort. When the length of the longest route is minimized, over 25% of the instances were optimally solved at the root node, and 99% were solved at termination.
This paper considers the Multi-Depot Rural Postman Problem, an extension of the classical Rural Postman Problem in which there are several depots instead of only one. The aim is to construct a minimum cost set of routes traversing each required edge of the graph, where each route starts and ends at the same depot. The paper makes the following scientific contributions: i) it presents optimality conditions and a worst-case analysis for the problem; ii) it proposes a compact integer linear programming formulation containing only binary variables, as well as a polyhedral analysis; iii) it develops a branch-and-cut algorithm that includes several new exact and heuristic separation procedures. Instances involving up to four depots, 744 vertices, and 1315 edges are solved to optimality. These instances contain up to 140 required components and 1000 required edges.
We study a multi‐country disaster preparedness partnership involving the joint prepositioning of emergency relief items. Our focus is the Caribbean region, which faces increasing disaster threats due to weather‐related events and has committed to share its resources for regional integration. We collaborate with the inter‐governmental Caribbean Disaster and Emergency Management Agency (CDEMA), which is interested in creating a methodology to equitably (fairly) allocate the costs necessary to operationalize this commitment. We present alternative cost allocation methods among the partner countries by considering their risk level and their ability to pay. Specifically, we adapt some techniques such as the Shapley value, the equal profit method, and the alternative cost avoided method, and we also propose a new insurance‐based allocation scheme to determine the country contributions. This mechanism, which is formulated as a linear programming model, sets country premiums by considering the expected value and the standard deviation of country demands and their gross national income. We discuss the structural properties of these methods and numerically evaluate their performance in achieving an equitable allocation scheme with respect to three equity indicators based on the Gini coefficient. Our proposed cost‐sharing mechanism not only achieves superior solutions compared with other methodologies with respect to the proposed equity metrics, but is also computationally efficient. We numerically illustrate how it can be used to obtain alternative cost allocation plans by giving different weights to disaster risk and economic standing parameters, and we analyze the benefits and fairness of the partnership in a transparent way.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.