International Journal of Production Research, 2015 http://dx.doi.org/10.1080/00207543.2015.1084061
A bi-level network interdiction model for solving the hazmat routing problem Amirsaman Kheirkhaha, HamidReza Navidib and Masume Messi Bidgolic* a
Industrial Engineering Department, Bu-Ali Sina University, Hamedan, Iran; bApplied Mathematical Department, Shahed University, Tehran, Iran; cIndustrial Engineering Department, Bu-Ali Sina University, Hamedan, Iran
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(Received 30 September 2014; accepted 10 August 2015) In the current work, we considered the problem of hazardous material distribution where the distributer chooses the routes on the network, and a regulatory agency controls the behaviour of the distributer to traverse the specified routes. In these circumstances, the distributer sets to select some routes to minimise the total distributing costs. Mostly, this occurs due to selecting risky arcs in which more individuals are exposed to risk. To prevent this and increase the capability to deal with the risk of hazardous material transportation through roads, the regulatory agency obliges carriers to traverse through the most secure arcs, though imposing more distribution costs. The problem is modelled as a bi-level routing problem. The bi-level model is difficult to solve and may be ill-posed. Two meta-heuristic algorithms are proposed to solve the bi-level model, and some randomly generated problems are applied to show the applicability and efficiency of the proposed algorithms. Keywords: network interdiction; vehicle routing problem; hazardous material distribution
1. Introduction Large quantities of hazardous materials (hazmat) are shipped through highways every day. Taking into account the nature of the hazardous material, their transportation is carried out with significant levels of risk. For example, an accident involving a gasoline truck or a chlorine truck can result in a huge fire on a highway, which may endanger many drivers and inhabitants’ lives. According to the Federal Hazardous Material Transportation Law, the following materials including explosive, radioactive, aetiologic agent, flammable or combustible liquid or solid, poisonous, oxidising or corrosive materials, and compressed gas and so on are known as hazardous materials. Since transporting these materials may impose irreversible effects on public health and safety, transporting them has recently received considerable attention by governors and researchers. To name a few, List et al. (1991), Karkazis and Boffey (1995), Verter and Erkut (1997), Erkut and Verter (1998), Erkut and Ingolfsson (2000), Frank, Thill, and Batta (2000), Leonelli, Bonvicini, and Spadoni (2000), Tarantilis and Kiranoudis (2001), Desai and Lim (2013), Bianco, Caramia, and Giordani (2009), Xie et al. (2012), Wang, Xiao, and Wei (2013), Jiang et al. (2014) and Erkut and Gzara (2008) made valuable contributions to this area. One way to mitigate the hazmat transport risks is to confine them to a subset of available roads. For this purpose, most cities designate ‘dangerous goods’ routes’ for hazmat trucks. Erkut and Gzara (2008) and Kara and Verter (2004) studied the hazmat transport network design problem where the government designates a proper network for transporting the hazmat, and the carriers choose the shortest routes on the network. Another way to reduce injuries resulting from unauthorised handling is setting regulations to control the urban and suburban roads via penalising the offending vehicles, preventing their transition, etc. To the best of our knowledge, there are no researches on the latter solution in the literature, so it is dealt with in the present inquiry. A considerable number of models have been developed to minimise the risk of a given origin-destination pair. However, in many real-life applications, these models try to determine some optimal routes for fleet of trucks to serve a set of customers rather than determining the optimal route between an origin-destination pair; this is known as ‘vehicle routing problem’. Vehicle routing problem, known as m-TSP, is one of the well-studied problems in operational research area, due to practical relevance and considerable difficulty. Hither, one distributor tries to find m least-cost vehicle routes among customers distributed in some nodes and connected to one another by some arcs. Each customer must be visited just once by exactly one vehicle, and also all vehicles start and end their routes at the depot. If each problem has some predetermined *Corresponding author. Email:
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