Progressive Focus Search for the Static and Stochastic VRPTW with both Random Customers and Reveal Times
This work addresses routing optimization under uncertainty for logistics and transportation industries, offering incremental improvements in computational methods.
The paper tackles the static stochastic vehicle routing problem with time windows and random customer reveal times by introducing a new recourse strategy that skips useless route parts and a meta-heuristic called Progressive Focus Search (PFS) to accelerate solution search. The result is evaluated on a new real-world benchmark, showing improved efficiency in handling uncertain customer requests.
Static stochastic VRPs aim at modeling real-life VRPs by considering uncertainty on data. In particular, the SS-VRPTW-CR considers stochastic customers with time windows and does not make any assumption on their reveal times, which are stochastic as well. Based on customer request probabilities, we look for an a priori solution composed preventive vehicle routes, minimizing the expected number of unsatisfied customer requests at the end of the day. A route describes a sequence of strategic vehicle relocations, from which nearby requests can be rapidly reached. Instead of reoptimizing online, a so-called recourse strategy defines the way the requests are handled, whenever they appear. In this paper, we describe a new recourse strategy for the SS-VRPTW-CR, improving vehicle routes by skipping useless parts. We show how to compute the expected cost of a priori solutions, in pseudo-polynomial time, for this recourse strategy. We introduce a new meta-heuristic, called Progressive Focus Search (PFS), which may be combined with any local-search based algorithm for solving static stochastic optimization problems. PFS accelerates the search by using approximation factors: from an initial rough simplified problem, the search progressively focuses to the actual problem description. We evaluate our contributions on a new, real-world based, public benchmark.