The equity constrained shortest path problem

doi:10.1016/0305-0548(90)90006-S

Computers & Operations Research

Volume 17, Issue 3, 1990, Pages 297-307

https://doi.org/10.1016/0305-0548(90)90006-S Get rights and content

Abstract

This paper examines the problem of finding the shortest path on a network subject to “equity” constraints. A Lagrangean dual bounding approach is utilized, which relaxes the “complicating constraints” of the problem. After solving the Lagrangean dual, the duality gap is closed by finding the t shortest paths with respect to the Lagrangean function. Both looping and loopless paths are considered. A quick-and-dirty heuristic procedure is also suggested. We report a sampling of our computational experiences with the model.

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A routing and scheduling approach to rail transportation of hazardous materials with demand due dates
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This paper investigates the routing and scheduling of rail shipments of hazardous materials (hazmat) in the presence of due dates. In particular, we consider the problem of minimizing the weighted sum of earliness and tardiness for each demand plus the holding cost at each yard, while forcing a risk threshold on each service leg at any time instant. The Federal Railroad Administration (FRA) accident records, between 1999 and 2013, were analyzed to establish that train speed was the most significant factor in derailment. A mixed-integer programming model and a heuristic-based solution method are proposed for preparing the shipment plan. Finally, the analytical framework is used to study and analyze a number of realistic-sized problem instances generated using the infrastructure of a Class I railroad operator.
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We design routes for transportation of hazardous materials (HAZMAT) in urban areas, with multiple origin-destination pairs. First, we introduce the maxisum HAZMAT routing problem, which maximizes the sum of the population-weighted distances from vulnerable centers to their closest point on the routes. Secondly, the maximin-maxisum HAZMAT routing problem trades-off maxisum versus the population-weighted distance from the route to its closest center. We propose efficient IP formulations for both NP-Hard problems, as well as a polynomial heuristic that reaches gaps below 0.54% in a few seconds on the real case in the city of Santiago, Chile.
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Citation Excerpt :
Marianov and ReVelle (1998) propose stipulating an upper bound on the total risk associated with each link. Gopalan, Batta, and Karwan (1990a) consider a route defined by an origin–destination pair to be equitable if the difference between the risk levels imposed on any pair of zones in the neighbourhood of the route stays below a preset threshold. They calculate the risk associated with a link in the route as the sum of the risks imposed on the various zones in the link’s neighbourhood, an approach that could double-count part of the population.
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Several models have been proposed for addressing equity in the context of hazmat transport. Gopalan et al. [16] develop a model for a single hazmat trip in which the objective is to minimize risk subject to a set of constraints that ensure that the difference in risk borne by population zones is less than a set threshold (equity specification). This model was later generalized by Gopalan et al. [17] to the case of multiple hazmat trips of a single O–D pair.
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^∗: Ram Gopalan is a PhD candidate at the Operations Research Center at M.I.T. He has an MS degree from the Department of Industrial Engineering at SUNY at Buffalo, and a B. Tech. degree from the Department of Mechanical Engineering at I.I.T. Madras, India. His interests include the applications of operations research to problems in urban systems and production systems. This article is based upon his MS thesis, which he completed under the joint supervision of Professors Batta and Karwan.

^†: Rajan Batta is an Assistant Professor in the Department of Industrial Engineering at SUNY at Buffalo. He has a PhD in operations research from M.I.T., and a B. Tech. degree in mechanical engineering from I.I.T. Delhi, India. His interests include the applications of operations research to problems in urban systems and production systems. He has published extensively on these topics.

^§: Mark H. Karwan is Professor and Chairman of the Department of Industrial Engineering at SUNY at Buffalo. He has a PhD from the Department of Industrial and Systems Engineering at Georgia Tech., and BES and MSE degrees from the Mathematical Sciences Department at Johns Hopkins. His interests include multiple criteria decision making and mathematical programming and its applications in a variety of problem areas. He has published extensively on these topics.

View full text

The equity constrained shortest path problem

Abstract

Transport. Res.

Accident Anal. Prevent.

Siting and the politics of equity

Equity and public risk

Opns Res.

Utility functions for equity and public risk

Mgmt Sci.

Perspectives on queueing: social justice and the psychology of queueing

Opns Res.

A dual algorithm for the constrained shortest path problem

Networks

New polynomial shortest path algorithms and their computational attributes

Mgmt Sci.