The Robust Vehicle Routing Problem with Time Window Assignments

Abstract

In practice, there are several applications in which logistics service providers determine the service time windows at the customers, for example, in parcel delivery, retail, and repair services. These companies face uncertain travel times and service times that have to be taken into account when determining the time windows and routes prior to departure. The objective of the proposed robust vehicle routing problem with time window assignments (RVRP-TWA) is to simultaneously determine routes and time window assignments such that the expected travel time and the risk of violating the time windows are minimized. We assume that the travel time probability distributions are not completely known but that some statistics, such as the mean, minimum, and maximum, can be estimated. We extend the robust framework based on the requirements’ violation index, which was originally developed for the case where the specific requirements (time windows) are given as inputs, to the case where they are also part of the decisions. The subproblem of finding the optimal time window assignment for the customers in a given route is shown to be convex, and the subgradients can be derived. The RVRP-TWA is solved by iteratively generating subgradient cuts from the subproblem that are added in a branch-and-cut fashion. Experiments address the performance of the proposed solution approach and examine the trade-off between expected travel time and risk of violating the time windows.

Emergency logistics network optimization with time window assignment

“… Jalilvand et al (2021) proposed an optimization model for TWAVRP to minimize the operating cost and designed an efficient progressive hedging algorithm to address this problem. A robust framework based on requirement violation was presented by Hoogeboom et al (2021) to minimize travel time and the risk of time window violations in TWAVRP.…”

Robust Optimization of Electric Vehicle Paths in Uncertain Environments

“…In summary, the constraint (15) of the deterministic probl em is replaced by equation (20) or (21). It is transformed int o a robust optimization model under the demand uncertainty set 12 ZZ 、 .…”

“…The results demonstrate that t his robust optimization method effectively prevents unmet de mand occurrences [19].Hooge et al addressed uncertainties i n both travel time and service time by developing a robust V RP model. The primary objective of their model was to mini mize the expected travel time while reducing the risk of time window violations [20]. Based on the robust optimization the ory, Sun et al have proposed a novel weakly robust optimiza tion model.…”

Optimization of Conventional and Green Vehicles Composition under Carbon Emission Cap

“…A two-stage simulation-based Adaptive Large Neighborhood Search (ALNS) heuristic was designed to solve the problem. Hoogeboom et al [15] determined the best routes in a VRP with time window assignment with a minimum possibility of time window violation. The VRP with time window was surveyed in studies of Bräysy and Gendreau [16,17] and Toth and Vigo [18].…”