Reoptimization Approaches for the Vehicle-Routing Problem with Stochastic Demands

Abstract

We consider the vehicle routing problem with stochastic demands (VRPSD) under reoptimization. We develop and analyze a finite-horizon Markov decision process (MDP) formulation for the single vehicle case, and establish a partial characterization of the optimal policy. We also propose a heuristic solution methodology for our MDP, named partial reoptimization, based on the idea of restricting attention to a subset of all the possible states and computing an optimal policy on this restricted set of states. We discuss two families of computationally efficient partial reoptimization heuristics and illustrate their performance on a set of instances with up to and including 100 customers. Comparisons with an existing heuristic from the literature and a lower bound computed with complete knowledge of customer demands show that our best partial reoptimization heuristics outperform this heuristic and are on average no more than 10-13% away from this lower bound, depending on the type of instances.

A review of dynamic vehicle routing problems

“…From a static perspective, the problem is to design a set of robust routes a-priori, that will undergo minor changes during their execution [16,53]. From a dynamic perspective, the problem consists in designing the vehicle routes in an online fashion, communicating to the vehicle which customer to serve next as soon as it becomes idle [104,127,128]. Based on these dimensions, Table 1 identifies four categories of routing problems.…”

A look-ahead partial routing framework for the stochastic and dynamic vehicle routing problem

“…This limitation is certainly not desirable in situations where an immediate or at least a timely response to customer requests is crucial. Secomandi and Margot studied a vehicle routing problem with stochastic demands [28]. The actual demand is only known when the vehicle arrives at the customer.…”

Stochastic Vehicle Routing Problem: A Literature Survey

“…Using the Cross-Entropy Method (Yang et al, 2000;Chepuri and Tito, 2005) With restocking (Yangoural et al, 2000) Dynamic VRP With multiple vehicles priority (Smith et al, 2010) With Euclidian service region (Bertsimas, 1992;Van Ryzin, 1990, 1993) With di®erent route updating strategies (Bertsimas, 1991) With paired-vehicle recurs strategy (Ak and Erera, 2007) Using ant-based simulation (Rossetti et al, 2009) With dynamic or re-optimisation perspective (Secomandi and Margot, 2007;Novoa and Storer, 2009) (Dror, 1991;Erera and Daganzo, 2003;Ismail and Irhamah, 2008;Milić and Jovanović, 2011) With duration constraints (Erera et al, 2010) VRP with stochastic demands (Novoa et al, 2006) Using advanced Particle Swarm Optimisation (PSO) (Moghaddam et al, 2012;Yong and Hai-Ying, 2008) With uncertainty and omitted customers (Waters, 1989) With a known probability distribution and customer revisited (Bastian and Rinnooy, 1992) And Restricted Failures Customer and Customer Demand…”