Research on Vehicle Routing Problem with Stochastic Demand Based on Multi-objective Method

As one of the most popular supply chain management problems, the Vehicle Routing Problem (VRP) has been thoroughly studied in the last decades, most of these studies focus on deterministic problem where the customer demands are known in advance. But the Vehicle Routing Problem with Stochastic Demands (VRPSD) has not received enough consideration. In the VRPSD, the vehicle does not know the customer demands until the vehicle arrive to them. This paper use a hybrid algorithm for solving VRPSD, the hybrid algorithm based on Particle Swarm Optimization (PSO) Algorithm, combines a Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, and Variable Neighborhood Search (VNS) algorithm. A real number encoding method is designed to build a suitable mapping between solutions of problem and particles in PSO. A number of computational studies, along with comparisons with other existing algorithms, showed that the proposed hybrid algorithm is a feasible and effective approach for Vehicle Routing Problem with Stochastic Demands.

The vehicle routing problem with stochastic demand (VRPSD) is one of the most important problems in distribution and transportation. The classical models for the vehicle routing problem with stochastic demand are the chance-constrained model and the penalty model. This paper proposes the hybrid model which combines the chance-constrained model and the penalty model. The travel cost of the hybrid model is less than that of the chance-constrained model and the worst case is guaranteed though the hybrid model may have more travel cost than the penalty model. We formulate the VRPSD as a set covering problem and this problem is solved using a column generation approach. We propose the solution methods for the hybrid model. The solution method is based on saving algorithm. In numerical results, we compare the results of the chance-constrained model, the penalty model and the hybrid model.

An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy

The primary objective of this study is to solve the Vehicle Routing Problem with Stochastic Demands (VRPSD) under restocking policy by using adaptive Genetic Algorithm (GA). The problem of VRPSD is one of the most important and studied combinatorial optimization problems, which finds its application on wide ranges of logistics and transportation area. It is a variant of a Vehicle Routing Problem (VRP). The algorithms for stochastic VRP are considerably more intricate than deterministic VRP and very time consuming. This has led us to explore the used of metaheuristics focusing on the permutation-based GA. The GA is enhanced by automatically adapting the mutation probability to capture dynamic changing in population. The GA becomes a more effective optimizer where the adaptive schemes are depend on population diversity measure. The proposed algorithm is compared with standard GA on a set of randomly generated problems following some discrete probability distributions inspired by real case of VRPSD in solid waste collection in Malaysia. The performances of several types of adaptive mutation probability were also investigated. Experimental results show performance enhancements when adaptive GA is used.

This paper presents the methodology for solving the municipal waste collection problem in urban areas.This problem is treated as a vehicle routing problem where the demand in nodes and travel times between all pairs of nodes in a transport network are taken as stochastic quantities, known in the literature as the vehicle routing problem with stochastic demands (VRPSD).This problem is formulated as a chance-constrained programming model with normal distribution.Heuristic and metaheuristic methods, as well as their combinations, are applied to efficiently solve this model.Finally, the paper presents a comparative analysis of the obtained results with real data.

An alternate formulation of the classical vehicle routing problem with stochastic demands (VRPSD) is considered. We propose a new heuristic method to solve the problem, based on the Cross-Entropy method. In order to better estimate the objective function at each point in the domain, we incorporate Monte Carlo sampling. This creates many practical issues, especially the decision as to when to draw new samples and how many samples to use. We also develop a framework for obtaining exact solutions and tight lower bounds for the problem under various conditions, which include specific families of demand distributions. This is used to assess the performance of the algorithm. Finally, numerical results are presented for various problem instances to illustrate the ideas.

In this paper, the Vehicle Routing Problem with Stochastic Demands (VRPSD) is considered where customer demands are normally distributed. We propose a new model for computing the expected length of a tour. Monte Carlo simulation is used to demonstrate the accuracy of the model on randomly generated test problems. It is assumed that the service policy is non-divisible, meaning that the entire demand at each customer must be served in a single visit by a unique vehicle.

The multiple Unmanned Aerial Vehicles (UAVs) reconnaissance problem with stochastic observation time (MURSOT) is modeled by modifying the typical vehicle routing problem with stochastic demand (VRPSD). The objective consists in optimizing mission duration, total time and the quantity of UAVs. This multi-objective optimization problem is solved using a steady-state multi-objective evolutionary algorithm MOEA with e - dominance conception. In this paper, we propose a heuristic evolutionary operation (HEO) using Insert-to-Nearest Method (INM). Route Simulation Method (RSM) is presented in details to estimate the expected cost of each route and this method is designed especially for our MURSOT. The developed algorithm is further validated on a series of test problems adapted from Solomon's vehicle routing problems. Experimental results show that the INM is capable of finding better solutions in contrast and its advantage is more remarkable as the size of the problem become larger.

A branch-cut-and-price algorithm for the vehicle routing problem with stochastic demands

Vehicle routing, with its many variants, is one of the most important and frequently solved problems in transportation engineering. The aim of this paper is to develop a decision-making support tool for addressing the issue of dispatching vehicles in scenarios characterized by uncertain demands within soft time windows. In real-world scenarios, it is not uncommon for customer demands to exhibit flexibility, where certain early arrivals or delays may be deemed acceptable. Therefore, this paper introduces vehicle routing in more realistic contexts, offering potential practical implementations. The methodology for solving the problem is based on a fuzzy logic system whose membership functions are additionally adjusted using a neural network. Such a tool, neuro-fuzzy logic, is suitable for solving a defined routing problem since it can consider all the mentioned uncertainties in the distribution systems. Each user is assigned a performance index that considers travel time, demand, and delivery time windows. Then, the performance index is used as input data in the proposed vehicle routing tool based on the Clarke-Wright algorithm. The described approach has been tested on a concrete example, mimicking a distribution network resembling real world conditions, incorporating estimated travel times between customers. The results demonstrate that the proposed approach can effectively handle customer demands, with an average delay of 5.05 minutes during the 80-minute distribution. In future research, some environmental factors could be included in the proposed model. In addition, one of the directions of future research could be vehicle re-routing using the ideas from this paper.

This paper investigates an integrated production scheduling and vehicle routing problem with soft time windows and fuzzy travel times, where orders are grouped into batches for production and delivered by a limited number of multi-trip heterogeneous vehicles. A bi-objective mixed integer nonlinear programming (MINLP) model is established, which takes total cost and total early and tardy weighted penalty time as optimization objectives. First, a fuzzy superposition operation is proposed to obtain the fuzzy weighted penalty time, and it is extended to a generalized fuzzy operation law in fuzzy sets and systems. Then, we propose a knowledge-driven co-evolutionary algorithm (KDCEA) to solve this problem. The algorithm fuses a dual-subpopulation co-evolution based on different update strategies and a knowledge-driven strategy based on dynamic knowledge sets and problem-specific knowledge. Finally, the correctness of the MINLP model is verified by the CPLEX solver using the ϵ-constraint method. A computational experiment is conducted based on different scale instances and a real-world case, and the results show the superiority of KDCEA in solving this problem.

‘Route balance’ is the difference between the longest and the shortest among all the route lengths. The route balance is frequently considered in a vehicle routing problem (VRP) for balancing the distance travelled among delivery vehicles. This is a common practice since in VRPs there are no time elements. However, in recent years, some research works have considered route balance in a vehicle routing problem with time windows (VRPTW). As there are more time elements in VRPTW, this paper refutes that route balance is sufficient for VRPTW by simultaneously optimising makespan and workload imbalance using ‘total time balance’ instead of route balance. On the other hand, ‘total time balance’ is the difference between the longest total time taken and the shortest total time taken among delivery vehicles. As such, makespan is the longest total time taken among vehicles. Total time taken for a vehicle is the sum of vehicle run time, waiting time and service time. In order to demonstrate the importance of using total time balance instead of route balance on VRPTW, three different multi-objective VRPTW models, namely, (1) only with general VRPTW objectives (i.e. ‘total distance travelled’ by all vehicles and ‘total number of vehicles’ used), (2) general VRPTW objectives with route balance and (3) general VRPTW objectives with total time balance are developed and solved by fitness aggregated genetic algorithm (FAGA) for 36 Solomon’s benchmark instances. By comparison of the makespan produced by the FAGA between the three cases, the importance of using total time balance instead of route balance on multi-objective VRPTW is demonstrated. Also, the makespan produced by the FAGA for the third case, i.e. general VRPTW objectives with total time balance is compared with the makespan produced by fitness aggregated differential evolution (FADE). By comparing makespan with statistical testing between FAGA and FADE, the outperformance of FAGA over FADE is verified. To check the practicality of the total time balance on multi-objective VRPTW, an instance with real time windows is also solved for the three cases by the FAGA and its makespan are compared and reported.

The competition between companies requires finding the optimized vehicle routing, for this reason researches are more and more interested in transportation problems, this article attempts to address a practical variant of the vehicle routing problem (VRP), known as the VRP with soft time windows (VRPSTW), where deliveries are still possible outside the time windows, that often arise in practice.

Environmental concerns have called for several measures to be taken within the logistics and transportation fields. Among these measures is the adoption of electric vehicles instead of diesel-operated vehicles for personal and commercial-delivery use. The optimized routing of electric vehicles for the commercial delivery of products is the focus of this paper. We study the effect of several practical challenges that are faced when routing electric vehicles. Electric vehicle routing faces the additional challenge of the potential need for recharging while en route, leading to more travel time, and hence cost. Therefore, in this work, we address the issue of electric vehicle routing problem, allowing for partial recharging while en route. In addition, the practical mandate of the time windows set by customers is also considered, where electric vehicle routing problems with soft time windows are studied. Real-life experience shows that the delivery of customers’ demands might be uncertain. In addition, real-time traffic conditions are usually uncertain due to congestion. Therefore, in this work, uncertainties in customers’ demands and traffic conditions are modeled and solved using fuzzy methods. The problems of fuzzy real-time, fuzzy demand, and electric vehicle routing problems with soft time windows are addressed. A mixed-integer programming mathematical model to represent the problem is developed. A novel two-phase solution approach is proposed to solve the problem. In phase I, the classical genetic algorithm (GA) is utilized to obtain an optimum/near-optimum solution for the fuzzy demand electric vehicle routing problem with soft time windows (FD-EVRPSTW). In phase II, a novel fuzzy real-time-adaptive optimizer (FRTAO) is developed to overcome the challenges of recharging and real-time traffic conditions facing FD-EVRPSTW. The proposed solution approach is tested on several modified benchmark instances, and the results show the significance of recharging and congestion challenges for routing costs. In addition, the results show the efficiency of the proposed two-phase approach in overcoming the challenges and reducing the total costs.

Besides its economic purpose, the vehicle routing problem has also garnered attention due to its social and environmental objectives in recent years.In terms of ensuring sustainability, it is beneficial to consider these three objectives together.CO 2 emissions, which is one of the causes of global warming, which we have felt more prominently in the past few years, has also affected the policies of logistics companies.Organizing working hours and ensuring fairness among employees are also one of our motivations in this study.Financial objectives has always taken into account.Simulated annealing algorithm and adaptive large neighborhood search algorithm are developed for the solution of the multi-objective mix integer mathematical model, in which financial, environmental, and social objective functions, which include alternative ways with different properties between nodes and different speed options.Small problems can be solved with exact solution method in literature, but to solve medium and larger samples heuristic algorithms are needed.When comparing algorithms, Simulated Annealing also gives better results than Adaptive Large Neighborhood Search in a shorter time.