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Register a new userVehicle Fleet Sizing, Positioning and Routing Problem with Stochastic Customers
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The Vehicle Fleet Sizing, Positioning and Routing Problem with Stochastic Customers (VFSPRP-SC) consists on pairing strategic decisions of depot positioning and fleet sizing with operational vehicle routing decisions while taking into account the inherent uncertainty of demand. We successfully solve the VFSPRP-SC with a methodology comprised of two main blocks: i) a scenario generation phase and ii) a two-stage stochastic program. For the first block, a set of scenarios is selected with a simulation-based approach that captures the behavior of the demand and allows us to come up with different solutions that could match different risk profiles. The second block is comprised of a facility location and allocation model and a Multi Depot Vehicle Routing Problem (MDVRP) assembled under a two-stage stochastic program. We propose several novel ideas within our methodology: problem specific cuts that serve as an approximation of the expected second stage costs as a function of first stage decisions; an activation paradigm that guides our main optimization procedure; and, a way of mapping feasible routes from one second-stage problem data into another; among others. We performed experiments for two cases: the first case considers the expected value of the demand, and the second case considers the right tail of the demand distribution, seeking a conservative solution. By using acceleration techniques we obtain solutions within 1 to 6 hours, reasonable times considering the strategic nature of the decision. For the ex-post evaluation, we solve 75% of the instances in less than 3 minutes, meaning that the methodology used to solve the MDVRP is well suited for daily operation.
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Given the rise of electric vehicle (EV) adoption, supported by government policies and dropping technology prices, new challenges arise in the modeling and operation of electric transportation. In this paper, we present a model for solving the EV routing problem while accounting for real-life stochastic demand behavior. We present a mathematical formulation that minimizes travel time and energy costs of an EV fleet. The EV is represented by a battery energy consumption model. To adapt our formulation to real-life scenarios, customer pick-ups and drop-offs were modeled as stochastic parameters. A chance-constrained optimization model is proposed for addressing pick-ups and drop-offs uncertainties. Computational validation of the model is provided based on representative transportation scenarios. Results obtained showed a quick convergence of our model with verifiable solutions. Finally, the impact of electric vehicles charging is validated in Downtown Manhattan, New York by assessing the effect on the distribution grid.
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