A Heterogeneous Vehicle Routing Problem with Soft Time Windows for 3PL Company’s Deliveries: A Case Study

Route optimization is tactically important for companies that must fulfill the demands of different customers with fleet of vehicles, considering multiple factors like: the cost of the resources (vehicles) involved and the operating costs of the entire process. As a case study, a third-party logistics service provider, ABC Company, is introduced to implement optimization on. Furthermore, ABC Company’s problem is defined as route optimization and load consolidation problems that will be solved as heterogeneous vehicle routing problem with soft time windows (HVRPSTW). In this paper’s case, Vehicles travel from a central depot with a restricted capacity, serving clients just once within a defined time interval and providing a needed demand before returning to the central depot. ABC Company’s problem is mathematically formulated and solved using branch and bound method. The formulation is solved on LINGO. The final output is the route, time, cost, and load of each vehicle.

Data-Driven Robust Optimization for Solving the Heterogeneous Vehicle Routing Problem with Customer Demand Uncertainty

In practice, the parameters of the vehicle routing problem are uncertain, which is called the uncertain vehicle routing problem (UVRP). Therefore, a data-driven robust optimization approach to solve the heterogeneous UVRP is studied. The uncertain parameters of customer demand are introduced, and the uncertain model is established. The uncertain model is transformed into a robust model with adjustable parameters. At the same time, we use a least-squares data-driven method combined with historical data samples to design a function of robust adjustable parameters related to the maximum demand, demand range, and given vehicle capacity to optimize the robust model. We improve the deep Q-learning-based reinforcement learning algorithm for the fleet size and mix vehicle routing problem to solve the robust model. Through test experiments, it is proved that the robust optimization model can effectively reduce the number of customers affected by the uncertainty, greatly improve customer satisfaction, and effectively reduce total cost and demonstrate that the improved algorithm also exhibits good performance.

A Two-Stage Hybrid Metaheuristic for a Low-Carbon Vehicle Routing Problem in Hazardous Chemicals Road Transportation

Low-carbon economy advances the sustainable development of the transportation of hazardous chemicals. This paper focuses on the multi-trip heterogeneous vehicle routing problem that includes the prioritization of customers and transportation of incompatible cargoes (MTHVRP-PCIC) in which some customers are prioritized for delivery by heterogeneous vehicles and more than one type of cargo is transported. This is an issue because some cargoes are incompatible with each other and therefore cannot be loaded into the same vehicle. MFHVRP-PCIC aims to find a set of routes resulting in minimal costs including fixed cost, travel cost and carbon emission cost. This problem occurs in real-life applications in the hazardous chemicals road transportation industry. This paper contributes to addressing the MTHVRP-PCIC from a problem definition, model, and methodological point of view. We establish a mathematical formulation for this problem. A two-stage hybrid metaheuristic approach (TSHM) is also devised to solve this problem. First, an improved greedy randomized adaptive search procedure is designed to generate initial feasible solutions. Then, a hybrid genetic algorithm including local search strategies, split-feasibility procedure, and simulated annealing is designed to solve this problem. Finally, the proposed approach is applied to solve a real case of hazardous chemical delivery and a benchmark dataset, and the resulting solutions indicate the advantage of our algorithm compared with those solutions obtained from managerial experience and classical algorithms.

Time-Dependent Multi-Depot Heterogeneous Vehicle Routing Problem Considering Temporal–Spatial Distance

Aiming at the multi-depot heterogeneous vehicle routing problem under the time-dependent road network and soft time window, considering vehicle fixed cost, time window penalty cost and vehicle transportation cost, an optimization model of time-dependent multi-depot heterogeneous vehicle routing problem is established with the objective of minimizing distribution cost. According to the characteristics of the problem, a hybrid genetic algorithm with variable neighborhood search considering the temporal–spatial distance is designed. Customers are clustered according to the temporal–spatial distance to generate initial solutions, which improves the quality of the algorithm. The depth search capability of the variable neighborhood search algorithm is applied to the local search strategy of the genetic algorithm to enhance the local search capability of the algorithm. An adaptive neighborhood search number strategy and a new acceptance mechanism of simulated annealing are proposed to balance the breadth and depth required for population evolution. The validity of the model and algorithm is verified by several sets of examples of different scales. The research results not only deepen and expand the relevant research on vehicle routing problem, but also provide theoretical basis for logistics enterprises to optimize distribution scheme.

Mixed-Integer Linear Programming Model by Linear Approximation for a Strike Package-to-Target Assignment Problem

This study deals with an aircraft-to-target assignment (ATA) problem considering the modern air operation environment, such as the strike package concept, multiple targets for a sortie, and the strike packages’ survivability. For the ATA problem, this study introduces a novel mathematical model in which a heterogeneous vehicle routing problem (HVRP) and a weapon-to-target assignment (WTA) problem are conceptually integrated. The HVRP generates the flight routes for strike packages because this study confirms that the survivability of a strike package depends on the path, and the WTA problem evaluates the likelihood of successful target destruction of assigned weapons. Although the first version of the model is developed as a mixed-integer nonlinear programming (MINLP) model, this study attempts to convert it to a mixed-integer linear programming (MILP) model using the logarithmic transformation and piecewise linear approximation methods. For an ATA problem, this activity could provide an opportunity to use the excellent existing algorithms for searching the optimal solution of LP models. To maximize the operational effectiveness, the MILP model simultaneously determines the following for each strike package: (a) composition type, (b) targets, (c) flight route, (d) types, and (e) quantity of weapons for each target.

Half Open Multi-Depot Heterogeneous Vehicle Routing Problem for Hazardous Materials Transportation

How to reduce the accidents of hazardous materials has become an important and urgent research topic in the safety management of hazardous materials. In this study, we focus on the half open multi-depot heterogeneous vehicle routing problem for hazardous materials transportation. The goal is to determine the vehicle allocation and the optimal route with minimum risk and cost for hazardous materials transportation. A novel transportation risk model is presented considering the variation of vehicle loading, vehicle types, and hazardous materials category. In order to balance the transportation risk and the transportation cost, we propose a bi-objective mixed integer programming model. A hybrid intelligent algorithm is developed based on the ε-constraint method and genetic algorithm to obtain the Pareto optimal solutions. Numerical experiments are provided to demonstrate the effectiveness of the proposed model. Compared with the close multi-depot heterogeneous vehicle routing problem, the average risk and cost obtained by the proposed bi-objective mixed integer programming model can be reduced by 3.99% and 2.01%, respectively. In addition, compared with the half open multi-depot homogeneous vehicle routing problem, the cost is significantly reduced with the acceptable risk.