Cumulative VRP with Time Windows: A Trade-Off Analysis

Abstract

In this work, the Cumulative Vehicle Routing Problem (CumVRP) is studied. It is a routing optimization problem, in which the objective is to construct a set of vehicle routes with the minimum cumulative cost in terms of distance and weight over a traveled arc. The CumVRP can be defined with hard and soft time windows constraints for incorporating customer service. To tackle this problem, a matheuristic approach based on combining mathematical programming and an iterative metaheuristic algorithm Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. In each step of our approach, a feasible solution (set of routes) is built using GRASP, and, afterward, the solution is optimized using a MILP optimizer. The main objective of this research is to analyze the trade-off between the environmental cost produced by the delivery of goods complying with the limits of time windows and the customer's dissatisfaction when these limits are violated at a certain time limit previously defined. The results show that the environmental cost is reduced if the violation of the upper limits of the customers' time windows is allowed. These violations generate a cost associated with penalties that are well balanced with respect to the reduction of emissions.

The cumulative vehicle routing problem with time windows: models and algorithm

“…The SA provides high-quality results for large size instances where the performance of the MILP was limited. In Fernández et al (2020), the CumVRP-TW is introduced for hard and soft time windows cases without a mathematical model. In that work, the problem is only presented descriptively and considered the objective function proposed by Kara et al (2008), which does not considers fuel consumption parameters and costs as part of the objective function.…”

A Review of Heuristics and Hybrid Methods for Green Vehicle Routing Problems considering Emissions

“…During the iterative phase, the selection mechanism can ensure that there is a diversity of solutions and that the process is not stuck in a local optimum. Fernández et al [105] addressed the cumulative VRP with hard (CumVRP-hTW) and soft time window (CumVRP-sTW) constraints. +e main objective of CumVRP is to minimize the cumulative cost, which considers the distance and weight over a traveled arc and can be proportional to the emissions of greenhouse gases.…”

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