Vehicle Routing Problem with Stochastic Demands and Simultaneous Delivery and Pickup

Vehicle routing problem belongs to classical Combination Optimization hard problem and has been extensively studied by many researchers. Vehicle Routing Problem with Weight Coefficients and Stochastic Demands (WVRPSD) is established and a new implementation for importance sampling method to solve this model is proposed in this paper, in which the classical exponential change of measure is adopted to construct the family of importance sampling distributions, and the optimal importance sampling distribution is obtained by minimizing the variance of importance sampling estimator. Numerical experiments have been conducted and the results indicate that the method can effectively solve this problem.

A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery

This work deals with the Vehicle Routing Problem with Simultaneous Pickup and Delivery. We propose undirected and directed two-commodity flow formulations, which are based on the one developed by Baldacci, Hadjiconstantinou and Mingozzi for the Capacitated Vehicle Routing Problem. These new formulations are theoretically compared with the one-commodity flow formulation proposed by Dell’Amico, Righini and Salani. The three formulations were tested within a branch-and-cut scheme and their practical performance was measured in well-known benchmark problems. The undirected two-commodity flow formulation obtained consistently better results. Several optimal solutions to open problems with up to 100 customers and new improved lower bounds for instances with up to 200 customers were found.KeywordsVehicle RoutingSimultaneous Pickup and DeliveryCommodity Flow Formulations

We consider a natural probabilistic variation of the classical vehicle routing problem (VRP), in which demands are stochastic. Given only a probabilistic description of the demand we need to design routes for the VRP. Motivated by applications in strategic planning and distribution systems, rather than resolving the problem when the demand becomes known, we propose to construct an a priori sequence among all customers of minimal expected total length. We analyze the problem using a variety of theoretical approaches. We find closed-form expressions and algorithms to compute the expected length of an a priori sequence under general probabilistic assumptions. Based on these expressions we find upper and lower bounds for the probabilistic VRP and the VRP re-optimization strategy, in which we find the optimal route at every instance. We propose heuristics and analyze their worst case performance as well as their average behavior using techniques from probabilistic analysis. Our results suggest that our approach is a strong and useful alternative to the strategy of re-optimization in capacitated routing problems.

Logistics is no longer seen as tactical and cost-driven – it is strategic. Considering the driver-on-time rules and with the perishable nature of the products, the travel length/time is one of the critical constraints in distribution logistics. We consider a typical logistics problem with maximum route length constraint. The variant is termed as simultaneous delivery and pick-up with maximum route length (SDPM). We developed a unified mixed-integer-linear programming (MILP) model and genetic algorithm to solve SDPM and the standard variant, vehicle routing problem with simultaneous delivery and pick-up (VRPSDP). Benchmark datasets for VRPSDP and randomly generated datasets for SDPM are solved using MILP model and genetic algorithm and the results are compared with best-known solution. The results of genetic algorithm are encouraging.

The aim of this work is to develop an intelligent optimization software based on enhanced VNS meta-heuristic to tackle Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). An optimization system developed based on enhanced Variable Neighborhood Search with Perturbation Mechanism and Adaptive Selection Mechanism as the simple but effective optimization approach presented in this work. The solution method composed by combining Perturbation based Variable Neighborhood Search (PVNS) with Adaptive Selection Mechanism (ASM) to control perturbation scheme. Instead of stochastic approach, selection of perturbation scheme used in the algorithm employed an empirical selection based on each perturbation scheme success along the search. The ASM help algorithm to get more diversification degree and jumping from local optimum condition using most successful perturbation scheme empirically in the search process. A comparative analysis with a well-known exact approach is presented to test the solution method in a generated VRPSPD benchmark instance in limited computation time. Then a test to VRPSPD scenario provided by a liquefied petroleum gas distribution company is performed. The test result confirms that solution method present superior performance against exact approach solution in giving best solution for larger sized instance and successfully obtain substantial improvements when compared to the basic VNS and original route planning technique used by a distributor company.

This paper deals with the Vehicle Routing Problem with Simultaneous Pick-up and Delivery and Time Limit (VRPSPDTL). Due to the combinatorial nature of the problem, heuristics methods are commonly used to generate good quality solutions within an acceptable computational time. Accordingly, an Iterated Local Search (ILS) procedure that uses a Variable Neighborhood Descent (VND) method to perform the local search is proposed. The algorithm was applied to test problems and, in most cases, was found to produce better results than those reported in the literature.KeywordsLocal SearchTravel Salesman ProblemVehicle Route ProblemReverse LogisticsCandidate ListThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We study a split vehicle routing problem (VRP) with simultaneous pickup and delivery. Our problem is motivated by the logistics operations practice of a third-party logistics provider (3PL) who serves the inbound logistics for an automobile manufacturing company. We develop several greedy algorithms and a competitive decision algorithm to solve the problem, and conduct computational experiments to investigate some managerial insights of the system. Our work provides useful guidance for the operations of the 3PL.

This paper considers a special vehicle routing problem, the two-echelon vehicle routing problem with simultaneous delivery and pickup demands (2E-VRPSDP). The 2EVRPSDP differs from classic transportation and vehicle routing problems in two ways. First, freight delivery from the depot to the customers is managed by shipping the freight through intermediate satellites. Second, each customer in the 2E-VRPSDP may have simultaneous delivery and pickup demands. The 2E-VRPSDP is an extension of the two-echelon vehicle routing problem (2E-VRP) and the vehicle routing problem with simultaneous delivery and pickup (VRPSDP). A variable neighborhood search algorithm is designed to solve the 2E-VRPSDP in which both feasible and infeasible solutions can be explored. Numerical results show that the proposed algorithm is effective and that the algorithm can provide reasonable solutions within an acceptable computational time.

Solving combinatorial optimization problems with single seekers society algorithm

Vehicle routing problems with simultaneous pickup and delivery with time windows are studied in this paper. In a closed-loop logistics network, vehicles visiting customers for pickup and delivery may be only allowed for certain time intervals. A mixed integer programming model of the problem is presented. It has been known that solving vehicle routing problems with time windows is NP-hard. A heuristic solution procedure is developed to solve the problem. The proposed heuristic is tested on a number of numerical examples based on modified benchmark problems in the literature.

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.

The problem of designing a set of routes with minimum cost to serve a collection of customers with a fleet of vehicles is a fundamental challenge when the number of customers to be dropped or picked up is not known during the planning horizon. The purpose of this paper is to develop a vehicle routing Problem (VRP) model that addresses stochastic simultaneous pickup and delivery in the urban public transport systems of Addis Ababa city Bus Enterprise, in Ethiopia. To this effect, a mathematical model is developed and fitted with real data collected from Anbessa City Bus Service Enterprise (ACBSE) and solved using Clark-Wright saving algorithm. The form-to-distance is computed from the data collected from Google Earth and the passenger data from the ACBSE. The findings of the study show that, the model is feasible and showed an improvement as compared to the current performances of the enterprise. It has shown that, an improvement on the current number of routes (number of buses used) and the total kilometer covered. The average performances of the model show that on average 6.48 routes are required to serve passenger demands of 271 and on average the simulation run was performed with 0.40 seconds of CPU time. During this instance, the average distance traveled by the vehicles in a single trip is 552.92kms.

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.

In the introductory section of this paper there is a view of several types of stochastic vehicle routing problems. In the second section of the paper the vehicle routing problem with stochastic demands is described. The following modifications to the vehicle routing problem are required: Customers demand is a random variable with a known probability distribution. Routes must be designed before the actual demands become known.The presence of nonlinear constraints, caused by random demands, can complicate the solution. Under the specific presumptions it is possible to transfer a nonlinear constraint to a linear form. This transformation enables to use the known algorithms of the deterministic vehicle routing problem for solution of the stochastic vehicle routing problem.