Rollout algorithms lead to effective heuristics for the single vehicle routing problem with stochastic demands (VRPSD), a prototypical model of logistics under uncertainty. However, they can be computationally intensive. To reduce their run time, we introduce a novel approach to approximate the expected cost of a route when executing any rollout algorithm for VRPSD with restocking. With a sufficiently large number of customers its theoretical speed-up factor is of big-o order 1/3. On a set of instances from the literature, our proposed technique applied to a known rollout algorithm and three variants thereof achieves speed-up factors that range from 0.26 to 0.34 when there are more than fifty customers, degrading only marginally the quality of the resulting routes. Our method also applies to the a priori case, in which case it is exact.
Given a set of geographically dispersed customers, a quantity to deliver to each customer, and a fleet of capacitated vehicles located at a depot, the vehicle routing problem consists of determining a set of minimal cost routes, each starting and ending at the depot, such that the demand of all the customers is satisfied without exceeding the capacity of the vehicles. Since its introduction by Dantzig and Ramser (1959), this problem and variants thereof have been well studied (see Fisher, 1995; Laporte, 1992; Toth & Vigo, 2014; and Laporte, 2009 for reviews). In the vehicle routing problem with stochastic demands (VRPSD), given probability distributions describe the customer demands and the realization of the demand of a customer becomes known upon the first visit to this customer. If the realized demand of a customer exceeds the remaining capacity of a vehicle when this customer is visited then a route failure occurs and a recourse action must be taken. VRPSD is relevant in both strategic distribution planning, when only estimates of customer demands are typically available, and tactical and operational decision making, when there remains residual uncertainty about the demands of the customers.
Publisher : ELSEVIER
By : Luca Bertazzi , Nicola Secomandi
File Information: English Language/ 11 Page / size: 682 KB
سال : ۱۳۹۶
ناشر : ELSEVIER
کاری از : لوکا برتازی، نیکولا سیکومندی
اطلاعات فایل : زبان انگلیسی / 11 صفحه / حجم : KB 682