United States Department of Transportation
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NTL Classification:NTL-PLANNING AND POLICY-PLANNING AND POLICY;NTL-HIGHWAY/ROAD TRANSPORTATION-HIGHWAY/ROAD TRANSPORTATION;
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Abstract:Transit, touted as a solution to urban mobility problems, cannot match the addictive flexibility of
the automobile. 86.5% of all trips in the U.S. are in personal vehicles (USDOT 2001). A more recent approach to reduce
automobile ownership is through the use of vehicle sharing programs (VSPs). A VSP involves a fleet of vehicles located
strategically at stations across the transportation network. In its most flexible form, users are free to check out vehicles at
any station and return them to stations close to their destinations. Vehicle fleets can be comprised of bicycles, low
emission cars or electric vehicles. Such systems offer innovative, low-cost, and flexible solutions to the larger mobility
problem and can have positive impacts on the transportation system as a whole by reducing urban congestion.
To match automobile flexibility, users are free to determine all trip characteristics (where to checkout and return vehicles,
duration of travel and time of travel). This places exceptional logistical challenges on operators who must ensure demand
in the near future is met. Since flow from one station to another is seldom equal to flow in the opposing direction, the VSP
fleet can become spatially imbalanced. To meet near-future demand, operators must then redistribute vehicles to correct
this asymmetry. The focus of this report is to provide efficient, cost-effective operational strategies for fleet management.
A stochastic, mixed-integer program (MIP) involving joint chance constraints is developed that generates least-cost
vehicle redistribution plans for shared-vehicle systems such that a proportion of all near-term demand scenarios are met.
The model aims to correct short term demand asymmetry in shared-vehicle systems, where flow from one station to
another is seldom equal to the flow in the opposing direction. The model accounts for demand stochasticity and generates
partial redistribution plans in circumstances when demand outstrips supply. This stochastic MIP has a
non-convex feasible region that poses computational challenges. To solve the proposed program two solution procedures
are developed. The first procedure is based on enumerating p-efficient points, used to transform the problem into a set of
disjunctive, convex MIPs. A novel divide-and-conquer algorithm for generating p-efficient points that handles dualbounded
chance constraints is developed. Our technique has a smaller memory and computational footprint than
previously proposed methods. Since this method can be computationally prohibitive for large shared-vehicle systems, we
develop a faster cone-generation method that assumes that the random demand at each station is independent. Finally,
using an equal-failure apportionment assumption we develop a bound on the problem that can also be used to generate
redistribution strategies.
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