The time-dependent pollution-routing problem |
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| Affiliation: | 1. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Canada;2. Department of Industrial and Systems Engineering, University of Minnesota, United States;3. Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, United States;1. CIRRELT, Canada Research Chair in Distribution Management and HEC Montréal,nMontréal H3T 2A7, Canada;2. Southampton Business School and Centre for Operational Research, Management Science and Information Systems (CORMSIS),nUniversity of Southampton, Southampton SO17 1BJ, United Kingdom;3. CIRRELT and HEC Montréal, Montréal H3T 2A7, Canada |
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| Abstract: | The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure. |
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| Keywords: | Vehicle routing Fuel consumption Congestion Integer programming |
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