Chapter 8: Stochastic Vehicle Routing Problems

Abstract

Vehicle routing problems (VRPs) have been the subject of numerous research studies since Dantzig and Ramser [16] first presented this general class of optimization problems in a practical setting. Since then, the operations research community has devoted collectively a large effort towards efficiently solving these problems, developing both exact and heuristic methods; see Laporte [40]. The majority of these studies have been conducted under the assumption that all the information necessary to formulate the problems is known and readily available (i.e., one is in a deterministic setting). In practical applications, this assumption is usually not verified given the presence of uncertainty affecting the parameters of the problem. Uncertainty may come from different sources, both from expected variations and unexpected events. Such variations can affect various aspects of the problem under study (e.g., stochastic parameters, which entail additional feasibility requirements and extra costs). This is particularly true in the case of VRP models, which are used both at the tactical level and at the operational level to plan and control logistical operations. In this case, uncertainty is present given the time lag separating the moments where routes are planned and executed, considering the informational flow that defines the problem. For example, if customer demands are uncertain and only revealed when customers are visited, a planned route performed by a vehicle on a given day may turn out to be infeasible if the total observed demand for the customers scheduled on the route exceeds the capacity of the vehicle. When such a situation occurs, additional costs often involving additional decisions must be taken to produce a feasible solution. The need to account for such extra costs when solving VRPs entails developing models that explicitly factor in all relevant uncertainty features of the problem.Therefore, in recent years, there has been a steadily growing interest in both formulating and solving Stochastic Vehicle Routing Problems (SVRPs); see the surveys of Gendreau, Laporte, and Séguin [25] and Cordeau et al. [15]. This interest has been further

Enabling a Freight Traffic Controller for Collaborative Multidrop Urban Logistics

“…If the data do not vary with time but change in a random fashion, then one would have to resort to using stochastic vehicle routing algorithms, in which data would be described in the form of a probability distribution. Stochastic vehicle routing problems can be formulated using chanceconstrained linear programs, or two-stage stochastic programming formulations with recourse, but they are more challenging to solve compared with their deterministic counterparts (41). iv) Access restrictions in urban areas might mean delivery routes that are longer than necessary, and traversed with variable speeds according to the traffic speed and road conditions.…”

Modelling and analysis of a strategic fleet sizing problem for a furniture distributor

“…We detail here only those making deterministic assumptions, as in our case. For the studies making stochastic assumptions on the VRP, the reader is referred to Gendreau et al (2014). Baldacci et al (2008) and Hoff et al (2010) are two surveys for fleet sizing and routing problems.…”

Robust Optimization of a Broad Class of Heterogeneous Vehicle Routing Problems Under Demand Uncertainty

“…The models take the form of stochastic programs [9] or Markov decision processes [6], and the goal is to optimize a risk measure (such as the expected value or the conditional-value-at-risk) of the transportation costs, subject to satisfying the constraints with high probability. We refer to [23] for an excellent survey of the stochastic vehicle routing literature.…”

“…According to the classification in [23], the three most common modeling paradigms are recourse models, chance-constrained models and reoptimization models. In recourse models, a planned or here-and-now solution must be designed before the true values of the uncertain parameters become known while recourse or wait-and-see actions can be taken in the future after observing their true values.…”