Abstract
This paper presents a saving-based heuristic for the vehicle routing problem with time windows and stochastic travel times (VRPTWSTT). One of the basic ideas of the heuristic is to advance the latest service start time of each customer by a certain period of time. In this way, the reserved time can be used to cope with unexpected travel time delay when necessary. Another important idea is to transform the VRPTWSTT to a set of vehicle routing problems with time windows (VRPTW), each of which is defined by a given percentage used to calculate the reserved time for customers. Based on the above two key ideas, a three-stage heuristic that includes the “problem transformation” stage, the “solution construction” stage, and the “solution improvement” stage is developed. After the problem transformation in the first stage, the work of the next two stages is to first construct an initial solution for each transformed VRPTW by improving the idea of the classical Clarke-Wright heuristic and then further improve the solution. Finally, a number of numerical experiments are conducted to evaluate the efficiency of the described methodology under different uncertainty levels.
Highlights
Many real-life logistics and distribution problems can be attributed to a kind of vehicle routing problems with time windows which has been widely studied
To solve the VRPTWSTT, we present a three-stage savingbased heuristic, in which the issue of solving VRPTWSTT is transformed into a new issue that consists of solving multiple vehicle routing problems with time windows (VRPTW)
This paper focuses on the VRPTWSTT which can be described in the following
Summary
Many real-life logistics and distribution problems can be attributed to a kind of vehicle routing problems with time windows which has been widely studied. Ignoring the travel time fluctuations when developing route plans for pickup and/or delivery vehicles can result in inefficient and suboptimal solutions [2]. Zhang et al studied the stochastic travel time vehicle routing problem. Discrete Dynamics in Nature and Society with simultaneous pickups and deliveries and developed a new scatter search approach for the problem by incorporating a new chance-constrained programming method [3]. Wang and Lin presented a flexible solution methodology for the capacitated vehicle routing problem with stochastic travel times [10]. These studies have advanced the research on VRPSTT, practical algorithms and solution approaches are still needed because the stochasticity of travel times poses a very challenging combinatorial optimization problem.
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