Lshaped Method for the Stochastic Vehicle Routing Problem The number of cargos transported by the logistics industry is increasing every year due to the growth of sales on the internet. It is thus crucial to address issues such as long working hours for employees, fewer personnel, and increasing CO2 emissions for an effective transportation system. However, it is possible to create a productive delivery plan by considering uncertainties in time fluctuations, such as delays in work and delays in transportation due to the traffic congestion. Previous studies have defined mathematical programming models to build delivery plans that satisfy customer demand. However, few studies consider time fluctuations with multiple vehicles. Therefore, this study proposes an effective solution for the stochastic vehicle routing problem (VRP) using the Lshaped method, demonstrating the effectiveness of the proposed model by evaluating the value of stochastic solution (VSS). Specifically, we develop a model for VRP using multiple vehicles, taking into consideration the fluctuations in service and travel time between customers.

A Reactive GRASP Heuristic Algorithm for Vehicle Routing Problem with Release Date and Due Date Incurring Inventory Holding Cost and Tardiness Cost In this paper, vehicle routing problems with release dates and due dates (VRPRDD) are considered. Each customer order will incur an inventory holding cost if the order is held back at the depot after its release date and a tardiness cost if the delivery happens after its due date. The mathematical model is proposed and solved using Reactive GRASP heuristics. The results from the heuristics are compared with that of the mathematical model solved by CPLEX. Results of various data sets are used to analyze the effect of cost and due date flexibility on the routes generated. The proposed heuristic method outperforms the MILP solver of CPLEX in terms of quality of solution and the computation time taken. We study the managerial implications and insights subject to flexibility in due dates, and cost structure.