Search results for: Vehicle Routing Problem with Hard Time Windows

Authors: Imen Boudali, Marwa Ragmoun

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The Vehicle Routing Problem with Hard Time Windows (VRPHTW) is a basic distribution management problem that models many real-world problems. The objective of the problem is to deliver a set of customers with known demands on minimum-cost vehicle routes while satisfying vehicle capacity and hard time windows for customers. In this paper, we propose to deal with our optimization problem by using a new hybrid stochastic algorithm based on two metaheuristics: Chemical Reaction Optimization (CRO) and Greedy Randomized Adaptive Search Procedure (GRASP). The first method is inspired by the natural process of chemical reactions enabling the transformation of unstable substances with excessive energy to stable ones. During this process, the molecules interact with each other through a series of elementary reactions to reach minimum energy for their existence. This property is embedded in CRO to solve the VRPHTW. In order to enhance the population diversity throughout the search process, we integrated the GRASP in our method. Simulation results on the base of Solomon’s benchmark instances show the very satisfactory performances of the proposed approach.

Keywords: Benchmark Problems, Combinatorial Optimization, Vehicle Routing Problem with Hard Time Windows, Meta-heuristics, Hybridization, GRASP, CRO

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Authors: P. Parthiban, Sonu Rajak, R. Dhanalakshmi

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This paper presents an Ant Colony Optimization (ACO) approach, combined with a Speed Optimization Algorithm (SOA) to solve the Vehicle Routing Problem (VRP) with environmental considerations, which is well known as Pollution-Routing Problem (PRP). It consists of routing a number of vehicles to serve a set of customers, and determining fuel consumption, driver wages and their speed on each route segment, while respecting the capacity constraints and time windows. Since VRP is NP-hard problem, so PRP also a NP-hard problem, which requires metaheuristics to solve this type of problems. The proposed solution method consists of two stages. Stage one is to solve a Vehicle Routing Problem with Time Window (VRPTW) using ACO and in the second stage, a SOA is run on the resulting VRPTW solution. Given a vehicle route, the SOA consists of finding the optimal speed on each arc of the route to minimize an objective function comprising fuel consumption costs and driver wages. The proposed algorithm tested on benchmark problem, the preliminary results show that the proposed algorithm can provide good solutions within reasonable computational time.

Keywords: ant colony optimization, CO2 emissions, speed optimization, vehicle routing

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Authors: Lydia Wahid, Mona F. Ahmed, Nevin Darwish

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The vehicle routing problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two subproblems: The first subproblem is an assignment problem where the number of vehicles that will be used as well as the customers assigned to each vehicle are determined. The second subproblem is the routing problem in which for each vehicle having a number of customers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles, as well as optimal total distance, should be achieved. In this paper, an approach for solving the first subproblem (the assignment problem) is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. Finding the optimal number of clusters is NP-hard. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters and solving the assignment problem.

Keywords: vehicle routing problems, clustering algorithms, Clarke and Wright Saving Method, agglomerative hierarchical clustering

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Authors: P. Parthiban, Sonu Rajak, N. Kannan, R. Dhanalakshmi

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This paper deals with the Vehicle Routing Problem (VRP) with environmental considerations which is called Pollution Routing Problem (PRP). The objective is to minimize the operational and environmental costs. It consists of routing a number of vehicles to serve a set of customers, and determining fuel consumption, driver wages and their speed on each route segment, while respecting the capacity constraints and time windows. In this context, we presented an Ant Colony Optimization (ACO) approach, combined with a Speed Optimization Algorithm (SOA) to solve the PRP. The proposed solution method consists of two stages. Stage one is to solve a Vehicle Routing Problem with Time Window (VRPTW) using ACO and in the second stage a SOA is run on the resulting VRPTW solutions. Given a vehicle route, the SOA consists of finding the optimal speed on each arc of the route in order to minimize an objective function comprising fuel consumption costs and driver wages. The proposed algorithm tested on benchmark problem, the preliminary results show that the proposed algorithm is able to provide good solutions.

Keywords: ant colony optimization, CO2 emissions, combinatorial optimization, speed optimization, vehicle routing

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Authors: Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Alejandro Fuentes-Penna, Daniel Vélez-Díaz, Edith Olaco García

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In this paper, we present the use of the discriminant analysis to select evolutionary algorithms that better solve instances of the vehicle routing problem with time windows. We use indicators as independent variables to obtain the classification criteria, and the best algorithm from the generic genetic algorithm (GA), random search (RS), steady-state genetic algorithm (SSGA), and sexual genetic algorithm (SXGA) as the dependent variable for the classification. The discriminant classification was trained with classic instances of the vehicle routing problem with time windows obtained from the Solomon benchmark. We obtained a classification of the discriminant analysis of 66.7%.

Keywords: Intelligent Transportation Systems, data-mining techniques, evolutionary algorithms, discriminant analysis, machine learning

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Authors: Wlodzimierz Ogryczak, Tomasz Sliwinski, Jaroslaw Hurkala, Mariusz Kaleta, Bartosz Kozlowski, Piotr Palka

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Implementation concepts of a decision support system for planning and management of mobile personnel tasks (sales representatives and others) are discussed. Large-scale periodic time-dependent vehicle routing and scheduling problems with complex constraints are solved for this purpose. Complex nonuniform constraints with respect to frequency, time windows, working time, etc. are taken into account with additional fast adaptive procedures for operational rescheduling of plans in the presence of various disturbances. Five individual solution quality indicators with respect to a single personnel person are considered. This paper deals with modeling issues corresponding to the problem and general solution concepts. The research was supported by the European Union through the European Regional Development Fund under the Operational Programme ‘Innovative Economy’ for the years 2007-2013; Priority 1 Research and development of modern technologies under the project POIG.01.03.01-14-076/12: 'Decision Support System for Large-Scale Periodic Vehicle Routing and Scheduling Problems with Complex Constraints.'

Keywords: mobile personnel management, multiple criteria, time dependent, time windows, vehicle routing and scheduling

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Authors: Elham Jelodari Mamaghani, Christian Prins, Haoxun Chen

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In this paper, there is concentration on collaborative transportation planning (CTP) among multiple carriers with pickup and delivery requests and time windows. This problem is a vehicle routing problem with constraints from standard vehicle routing problems and new constraints from a real-world application. In the problem, each carrier has a finite number of vehicles, and each request is a pickup and delivery request with time window. Moreover, each carrier has reserved requests, which must be served by itself, whereas its exchangeable requests can be outsourced to and served by other carriers. This collaboration among carriers can help them to reduce total transportation costs. A mixed integer programming model is proposed to the problem. To solve the model, a hybrid algorithm that combines Genetic Algorithm and Simulated Annealing (GASA) is proposed. This algorithm takes advantages of GASA at the same time. After tuning the parameters of the algorithm with the Taguchi method, the experiments are conducted and experimental results are provided for the hybrid algorithm. The results are compared with those obtained by a commercial solver. The comparison indicates that the GASA significantly outperforms the commercial solver.

Keywords: centralized collaborative transportation, collaborative transportation with pickup and delivery, collaborative transportation with time windows, hybrid algorithm of GA and SA

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Authors: Tarek Aboueldahab, Hanan Farag

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Cost minimization of Multiple Vehicle Routing Problem becomes a critical issue in the field of transportation because it is NP-hard optimization problem and the search space is complex. Many researches use the hybridization of artificial intelligence (AI) models to solve this problem; however, it can not guarantee to reach the best solution due to the difficulty of searching the whole search space. To overcome this problem, we introduce the hybrid model of Discrete Particle Swarm Optimization (DPSO) with a passive congregation which enable searching the whole search space to compromise between both local and global search. The practical experiment shows that our model obviously outperforms other hybrid models in cost minimization.

Keywords: cost minimization, multi-vehicle routing problem, passive congregation, discrete swarm, passive congregation

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Authors: Ons Sassi, Wahiba Ramdane Cherif-Khettaf, Ammar Oulamara

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In this paper, we consider a new real-life Heterogenous Electric Vehicle Routing Problem with Time Dependant Charging Costs and a Mixed Fleet (HEVRP-TDMF), in which a set of geographically scattered customers have to be served by a mixed fleet of vehicles composed of a heterogenous fleet of Electric Vehicles (EVs), having different battery capacities and operating costs, and Conventional Vehicles (CVs). We include the possibility of charging EVs in the available charging stations during the routes in order to serve all customers. Each charging station offers charging service with a known technology of chargers and time-dependent charging costs. Charging stations are also subject to operating time windows constraints. EVs are not necessarily compatible with all available charging technologies and a partial charging is allowed. Intermittent charging at the depot is also allowed provided that constraints related to the electricity grid are satisfied. The objective is to minimize the number of employed vehicles and then minimize the total travel and charging costs. In this study, we present a Mixed Integer Programming Model and develop a Charging Routing Heuristic and a Local Search Heuristic based on the Inject-Eject routine with three different insertion strategies. All heuristics are tested on real data instances.

Keywords: charging problem, electric vehicle, heuristics, local search, optimization, routing problem

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Authors: Ben Mansour Mouin, Elloumi Abdelkarim

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We will discuss the problem of routing a fleet of different vehicles from a central depot to different types of infrastructure-defaults with dynamic maintenance requests, modified time windows, and control of default maintained. For this reason, we propose a modified metaheuristicto to solve our mathematical model. SVRDP-CMTW is a variant VRP of an optimal vehicle plan that facilitates the maintenance task of different types of infrastructure-defaults. This task will be monitored after the maintenance, based on its priorities, the degree of danger associated with each default, and the neighborhood at the black-spots. We will present, in this paper, a multidimensional genetic algorithm “MGA” by detailing its characteristics, proposed mechanisms, and roles in our work. The coding of this algorithm represents the necessary parameters that characterize each infrastructure-default with the objective of minimizing a combination of cost, distance and maintenance times while satisfying the priority levels of the most urgent defaults. The developed algorithm will allow the dynamic integration of newly detected defaults at the execution time. This result will be displayed in our programmed interactive system at the routing time. This multidimensional genetic algorithm replaces N genetic algorithm to solve P different type problems of infrastructure defaults (instead of N algorithm for P problem we can solve in one multidimensional algorithm simultaneously who can solve all these problemsatonce).

Keywords: mathematical model, VRP, multidimensional genetic algorithm, metaheuristics

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Authors: Eki Ruskartina, Vincent F. Yu, Budi Santosa, A. A. N. Perwira Redi

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This paper introduces symbiotic organism search (SOS) for solving capacitated vehicle routing problem (CVRP). SOS is a new approach in metaheuristics fields and never been used to solve discrete problems. A sophisticated decoding method to deal with a discrete problem setting in CVRP is applied using the basic symbiotic organism search (SOS) framework. The performance of the algorithm was evaluated on a set of benchmark instances and compared results with best known solution. The computational results show that the proposed algorithm can produce good solution as a preliminary testing. These results indicated that the proposed SOS can be applied as an alternative to solve the capacitated vehicle routing problem.

Keywords: symbiotic organism search, capacitated vehicle routing problem, metaheuristic

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Authors: G. Sirbiladze, B. Ghvaberidze, B. Matsaberidze

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A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered.

Keywords: vehicle routing problem, fuzzy partitioning problem, multiple-criteria optimization, possibility theory

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Authors: Ahmed Tarek, Ahmed Alveed

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Vehicle routing problem is a well-known re-search avenue in computing. Modern vehicle routing is more focused with the GPS-based coordinate system, as the state-of-the-art vehicle, and trucking systems are equipped with digital navigation. In this paper, a new two dimensional coordinate-based algorithm for addressing the vehicle routing problem for a supply chain network is proposed and explored, and the algorithm is compared with other available, and recently devised heuristics. For the algorithms discussed, which includes the pro-posed coordinate-based search heuristic as well, the advantages and the disadvantages associated with the heuristics are explored. The proposed algorithm is studied from the stand point of a small supermarket chain delivery network that supplies to its stores in four different states around the East Coast area, and is trying to optimize its trucking delivery cost. Minimizing the delivery cost for the supply network of a supermarket chain is important to ensure its business success.

Keywords: coordinate-based optimal routing, Hamiltonian Circuit, heuristic algorithm, traveling salesman problem, vehicle routing problem

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Authors: Bezhan Ghvaberidze

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A multiple criteria optimization approach for the solution of the Fuzzy Vehicle Routing Problem (FVRP) is proposed. For the possibility environment the levels of movements between customers are calculated by the constructed simulation interactive algorithm. The first criterion of the bi-criteria optimization problem - minimization of the expectation of total fuzzy travel time on closed routes is constructed for the FVRP. A new, second criterion – maximization of feasibility of movement on the closed routes is constructed by the Choquet finite averaging operator. The FVRP is reduced to the bi-criteria partitioning problem for the so called “promising” routes which were selected from the all admissible closed routes. The convenient selection of the “promising” routes allows us to solve the reduced problem in the real-time computing. For the numerical solution of the bi-criteria partitioning problem the -constraint approach is used. An exact algorithm is implemented based on D. Knuth’s Dancing Links technique and the algorithm DLX. The Main objective was to present the new approach for FVRP, when there are some difficulties while moving on the roads. This approach is called FVRP for extreme conditions (FVRP-EC) on the roads. Also, the aim of this paper was to construct the solving model of the constructed FVRP. Results are illustrated on the numerical example where all Pareto-optimal solutions are found. Also, an approach for more complex model FVRP with time windows was developed. A numerical example is presented in which optimal routes are constructed for extreme conditions on the roads.

Keywords: combinatorial optimization, Fuzzy Vehicle routing problem, multiple objective programming, possibility theory

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Authors: Khaled Moh. Alhamad

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This paper describes a tabu search heuristic for a ship routing and scheduling problem (SRSP). The method was developed to address the problem of loading cargos for many customers using heterogeneous vessels. Constraints relate to delivery time windows imposed by customers, the time horizon by which all deliveries must be made and vessel capacities. The results of a computational investigation are presented. Solution quality and execution time are explored with respect to problem size and parameters controlling the tabu search such as tenure and neighbourhood size.

Keywords: heuristic, scheduling, tabu search, transportation

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Authors: Cagri Memis, Muzaffer Kapanoglu

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The school bus routing problem (SBRP) is a variant of the Vehicle Routing Problem (VRP) classified as a location-allocation-routing problem. In this study, the SBRP is decomposed into two sub-problems: (1) bus route generation and (2) bus stop selection to solve large instances of the SBRP in reasonable computational times. To solve the first sub-problem, we propose a genetic algorithm to generate bus routes. Once the routes have been fixed, a sub-problem remains of allocating students to stops considering the capacity of the buses and the walkability constraints of the students. While the exact method solves small-scale problems, treating large-scale problems with the exact method becomes complex due to computational problems, a deficiency that the genetic algorithm can overcome. Results obtained from the proposed approach on 150 instances up to 250 stops show that the matheuristic algorithm provides better solutions in reasonable computational times with respect to benchmark algorithms.

Keywords: genetic algorithm, matheuristic, school bus routing problem, vehicle routing problem

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Authors: Siliang Luan, Zhongtai Jiang

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The risk of highway incidents is commonly recognized as a major concern for transportation authorities due to the hazardous consequences and negative influence. It is crucial to respond to these unpredictable events as soon as possible faced by emergency management decision makers. In this paper, we focus on path planning for emergency vehicles, one of the most significant processes to avoid congestion and reduce rescue time. A Mixed-Integer Linear Programming with Semi-Soft Time Windows Model (MIPSSTWM) is conducted to plan an optimal routing respectively considering the time consumption of arcs and nodes of the urban road network and the highway network, especially in developing countries with an enormous population. Here, the arcs indicate the road segments and the nodes include the intersections of the urban road network and the on-ramp and off-ramp of the highway networks. An attempt in this research has been made to develop a comprehensive and executive strategy for emergency vehicle routing in heavy traffic conditions. The proposed Cuckoo Search (CS) algorithm is designed by imitating obligate brood parasitic behaviors of cuckoos and Lévy Flights (LF) to solve this hard and combinatorial problem. Using a Chinese city as our case study, the numerical results demonstrate the approach we applied in this paper outperforms the previous method without considering the nodes of the road network for a real-world situation. Meanwhile, the accuracy and validity of the CS algorithm also show better performances than the traditional algorithm.

Keywords: emergency vehicle, path planning, cs algorithm, urban traffic management and urban planning

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Authors: Mohanad Al-Behadili, Djamila Ouelhadj

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In this paper, a specific type of vehicle routing problem under stochastic demand (SVRP) is considered. This problem is of great importance because it models for many of the real world vehicle routing applications. This paper used a robust optimisation model to solve the problem along with the novel Simulation-Particle Swarm Optimisation (Sim-PSO) approach. The proposed Sim-PSO approach is based on the hybridization of the Monte Carlo simulation technique with the PSO algorithm. A comparative study between the proposed model and the Sim-PSO approach against other solution methods in the literature has been given in this paper. This comparison including the Analysis of Variance (ANOVA) to show the ability of the model and solution method in solving the complicated SVRP. The experimental results show that the proposed model and Sim-PSO approach has a significant impact on the obtained solution by providing better quality solutions comparing with well-known algorithms in the literature.

Keywords: stochastic vehicle routing problem, robust optimisation model, Monte Carlo simulation, particle swarm optimisation

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Authors: Aydin Sipahioglu, Gokhan Celik

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Helicopter routing problem (HRP) is finding good tours for helicopter so as to pick up and deliver personnel or material among specified nodes, mutually. It can be encountered in case of being lots of supply and demand points for different commodities and requiring delivering commodities with helicopter. For instance, to deliver personnel or material from shore to oil rig is a good example. In fact, HRP is a branch of vehicle routing problem with pickup and delivery (VRPPD). However, it has additional constraints such that fuel capacity, performance of helicopter in different altitude and temperature, and the number of maximum takeoff and landing allowed. This kind of pickup and delivery problems can be classified into 3 groups, basically. 1-1 (one to one), M-M (many to many) and 1-M-1 (one to many to one). 1-1 means each commodity has only one supply and one demand point. M-M means there can be more than one supply and demand points for each kind of commodity. 1-M-1 means commodities at depot are delivered to demand points and commodities at customers are delivered to depot. In this case helicopter takes off from its own base, complete its tour and return to its own base. In this study, we define 1-M-M-1 type HRP. That means helicopter takes off from its home base, deliver commodities among the nodes as well as between depot and customers and return to its home base. These problems have NP-hard nature. Therefore, obtaining a good solution in a reasonable time is not easy. In this study, a model is offered for 1-M-M-1 type HRP. It is shown on small scale test instances that the model can find the optimal solution.

Keywords: helicopter routing problem, vehicle routing with pickup and delivery, integer programming

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Authors: Anna Sikharulidze, Gia Sirbiladze

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For the evaluation of unreliability levels of movement on the closed routes in the vehicle routing problem, the fuzzy operators family is constructed. The interactions between routing factors in extreme conditions on the roads are considered. A multi-criteria decision-making model (MCDM) is constructed. Constructed aggregations are based on the Choquet integral and the associated probability class of a fuzzy measure. Propositions on the correctness of the extension are proved. Connections between the operators and the compositions of dual triangular norms are described. The conjugate connections between the constructed operators are shown. Operators reflect interactions among all the combinations of the factors in the fuzzy MCDM process. Several variants of constructed operators are used in the decision-making problem regarding the assessment of unreliability and possibility levels of movement on closed routes.

Keywords: vehicle routing problem, associated probabilities of a fuzzy measure, choquet integral, fuzzy aggregation operator

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Authors: P. Vanichkobchinda

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The Logistics Transportation techniques, Open Vehicle Routing (OVR) is an approach toward transportation cost reduction, especially for long distance pickup and delivery nodes. The outstanding characteristic of OVR is that the route starting node and ending node are not necessary the same as in typical vehicle routing problems. This advantage enables the routing to flow continuously and the vehicle does not always return to its home base. This research aims to develop a heuristic for the open vehicle routing problem with pickup and delivery under time window and loading capacity constraints to minimize the total distance. The proposed heuristic is developed based on the Insertion method, which is a simple method and suitable for the rapid calculation that allows insertion of the new additional transportation requirements along the original paths. According to the heuristic analysis, cost comparisons between the proposed heuristic and companies are using method, nearest neighbor method show that the insertion heuristic. Moreover, the proposed heuristic gave superior solutions in all types of test problems. In conclusion, the proposed heuristic can effectively and efficiently solve the open vehicle routing. The research indicates that the improvement of new transport's calculation and the open vehicle routing with "Insertion Heuristic" represent a better outcome with 34.3 percent in average. in cost savings. Moreover, the proposed heuristic gave superior solutions in all types of test problems. In conclusion, the proposed heuristic can effectively and efficiently solve the open vehicle routing.

Keywords: business competitiveness, cost reduction, SMEs, logistics transportation, VRP

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Authors: Julio C. Ferreira, Maria T. A. Steiner

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The aim of this work is to present a solution procedure referred to here as the Multi-objective Optimization for Green Vehicle Routing Problem (MOOGVRP) to provide solutions for a case study. The proposed methodology consists of three stages to resolve Scenario A. Stage 1 consists of the “treatment” of data; Stage 2 consists of applying mathematical models of the p-Median Capacitated Problem (with the objectives of minimization of distances and homogenization of demands between groups) and the Asymmetric Traveling Salesman Problem (with the objectives of minimizing distances and minimizing time). The weighted method was used as the multi-objective procedure. In Stage 3, an analysis of the results is conducted, taking into consideration the environmental aspects related to the case study, more specifically with regard to fuel consumption and air pollutant emission. This methodology was applied to a (partial) database that addresses newspaper distribution in the municipality of Curitiba, Paraná State, Brazil. The preliminary findings for Scenario A showed that it was possible to improve the distribution of the load, reduce the mileage and the greenhouse gas by 17.32% and the journey time by 22.58% in comparison with the current scenario. The intention for future works is to use other multi-objective techniques and an expanded version of the database and explore the triple bottom line of sustainability.

Keywords: Asymmetric Traveling Salesman Problem, Green Vehicle Routing Problem, Multi-objective Optimization, p-Median Capacitated Problem

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Authors: Onur Kaya, Ilknur Tukenmez

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In this study, we consider vehicle routing problems on networks with alternative direct links between nodes, and we analyze a multi-objective problem considering the financial, environmental and social objectives in this context. In real life, there might exist several alternative direct roads between two nodes, and these roads might have differences in terms of their lengths and durations. For example, a road might be shorter than another but might require longer time due to traffic and speed limits. Similarly, some toll roads might be shorter or faster but require additional payment, leading to higher costs. We consider such alternative links in our problem and develop a mixed integer linear programming model that determines which alternative link to use between two nodes, in addition to determining the optimal routes for different vehicles, depending on the model objectives and constraints. We consider the minimum cost routing as the financial objective for the company, minimizing the CO2 emissions and gas usage as the environmental objectives, and optimizing the driver working conditions/working hours, and minimizing the risks of accidents as the social objectives. With these objective functions, we aim to determine which routes, and which alternative links should be used in addition to the speed choices on each link. We discuss the results of the developed vehicle routing models and compare their results depending on the system parameters.

Keywords: vehicle routing, alternative links between nodes, mixed integer linear programming, triple bottom line accounting

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Authors: Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis

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The vehicle routing problem (VRP) is a well-known problem in Operations Research and has been widely studied during the last fifty-five years. The context of the VRP is that of delivering products located at a central depot to customers who are scattered in a geographical area and have placed orders for these products. A vehicle or a fleet of vehicles start their routes from the depot and visit the customers in order to satisfy their demands. Special attention has been given to the capacitated VRP in which the vehicles have limited carrying capacity of the goods that must be delivered. In the present work, we present a specific capacitated stochastic vehicle routing problem which has realistic applications to distributions of materials to shops or to healthcare facilities or to military units. A vehicle starts its route from a depot loaded with items of two similar but not identical products. We name these products, product 1 and product 2. The vehicle must deliver the products to N customers according to a predefined sequence. This means that first customer 1 must be serviced, then customer 2 must be serviced, then customer 3 must be serviced and so on. The vehicle has a finite capacity and after servicing all customers it returns to the depot. It is assumed that each customer prefers either product 1 or product 2 with known probabilities. The actual preference of each customer becomes known when the vehicle visits the customer. It is also assumed that the quantity that each customer demands is a random variable with known distribution. The actual demand is revealed upon the vehicle’s arrival at customer’s site. The demand of each customer cannot exceed the vehicle capacity and the vehicle is allowed during its route to return to the depot to restock with quantities of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. If there is shortage for the desired product, it is permitted to deliver the other product at a reduced price. The objective is to find the optimal routing strategy, i.e. the routing strategy that minimizes the expected total cost among all possible strategies. It is possible to find the optimal routing strategy using a suitable stochastic dynamic programming algorithm. It is also possible to prove that the optimal routing strategy has a specific threshold-type structure, i.e. it is characterized by critical numbers. This structural result enables us to construct an efficient special-purpose dynamic programming algorithm that operates only over those routing strategies having this structure. The findings of the present study lead us to the conclusion that the dynamic programming method may be a very useful tool for the solution of specific vehicle routing problems. A problem for future research could be the study of a similar stochastic vehicle routing problem in which the vehicle instead of delivering, it collects products from ordered customers.

Keywords: collection of similar products, dynamic programming, stochastic demands, stochastic preferences, vehicle routing problem

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Authors: Mukhtiar Singh, Sumeet Nagar

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Vehicle routing problem (VRP) is a combinatorial optimization and nonlinear programming problem aiming to optimize decisions regarding given set of routes for a fleet of vehicles in order to provide cost-effective and efficient delivery of both services and goods to the intended customers. This paper proposes the application of integrated particle swarm optimization (PSO) and genetic optimization algorithm (GA) to address the Vehicle routing problem in sugarcane industry in India. Suger industry is very prominent agro-based industry in India due to its impacts on rural livelihood and estimated to be employing around 5 lakhs workers directly in sugar mills. Due to various inadequacies, inefficiencies and inappropriateness associated with the current vehicle routing model it costs huge money loss to the industry which needs to be addressed in proper context. The proposed algorithm utilizes the crossover operation that originally appears in genetic algorithm (GA) to improve its flexibility and manipulation more readily and avoid being trapped in local optimum, and simultaneously for improving the convergence speed of the algorithm, level set theory is also added to it. We employ the hybrid approach to an example of VRP and compare its result with those generated by PSO, GA, and parallel PSO algorithms. The experimental comparison results indicate that the performance of hybrid algorithm is superior to others, and it will become an effective approach for solving discrete combinatory problems.

Keywords: fuzzy logic, genetic algorithm, particle swarm optimization, vehicle routing problem

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Authors: Uyanga Sukhbaatar, Ahmed Lbath, Mendamar Majig

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The Orienteering Problem is the most known example to start modeling tourist trip design problem. In order to meet tourist’s interest and constraint the OP is becoming more and more complicate to solve. The Multi Constraint Team Orienteering Problem with Time Windows is the last extension of the OP which differentiates from other extensions by including more extra associated constraints. The goal of the MCTOPTW is maximizing tourist’s satisfaction score in same time not to violate any of these constraints. This paper presents a genetic algorithmic approach to tackle the MCTOPTW. The benchmark data from literature is tested by our algorithm and the performance results are compared.

Keywords: multi constraint team orienteering problem with time windows, genetic algorithm, tour planning system

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Authors: Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis

Abstract:

The vehicle routing problem (VRP) is a well-known problem in Operations Research and has been widely studied during the last fifty-five years. The context of the VRP is that of delivering or collecting products to or from customers who are scattered in a geographical area and have placed orders for these products. A vehicle or a fleet of vehicles start their routes from a depot and visit the customers in order to satisfy their demands. Special attention has been given to the capacitated VRP in which the vehicles have limited carrying capacity for the goods that are delivered or collected. In the present work, we present a specific capacitated stochastic vehicle routing problem which has many realistic applications. We develop and analyze a mathematical model for a specific vehicle routing problem in which a vehicle starts its route from a depot and visits N customers according to a particular sequence in order to collect from them two similar but not identical products. We name these products, product 1 and product 2. Each customer possesses items either of product 1 or product 2 with known probabilities. The number of the items of product 1 or product 2 that each customer possesses is a discrete random variable with known distribution. The actual quantity and the actual type of product that each customer possesses are revealed only when the vehicle arrives at the customer’s site. It is assumed that the vehicle has two compartments. We name these compartments, compartment 1 and compartment 2. It is assumed that compartment 1 is suitable for loading product 1 and compartment 2 is suitable for loading product 2. However, it is permitted to load items of product 1 into compartment 2 and items of product 2 into compartment 1. These actions cause costs that are due to extra labor. The vehicle is allowed during its route to return to the depot to unload the items of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. The objective is to find the optimal routing strategy, i.e. the routing strategy that minimizes the total expected cost among all possible strategies for servicing all customers. It is possible to develop a suitable dynamic programming algorithm for the determination of the optimal routing strategy. It is also possible to prove that the optimal routing strategy has a specific threshold-type strategy. Specifically, it is shown that for each customer the optimal actions are characterized by some critical integers. This structural result enables us to design a special-purpose dynamic programming algorithm that operates only over these strategies having this structural property. Extensive numerical results provide strong evidence that the special-purpose dynamic programming algorithm is considerably more efficient than the initial dynamic programming algorithm. Furthermore, if we consider the same problem without the assumption that the customers are ordered, numerical experiments indicate that the optimal routing strategy can be computed if N is smaller or equal to eight.

Keywords: dynamic programming, similar products, stochastic demands, stochastic preferences, vehicle routing problem

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Authors: Ming-Jong Yao, Chin-Sum Shui, Chih-Han Wang

Abstract:

This paper is developed based on a real-world decision scenario that an industrial gas company that applies the Vendor Managed Inventory model and supplies liquid oxygen with a self-operated heterogeneous vehicle fleet to hospitals in nearby cities. We name it as a Joint Replenishment and Heterogeneous Vehicle Routing Problem with Cyclical Schedule and formulate it as a non-linear mixed-integer linear programming problem which simultaneously determines the length of the planning cycle (PC), the length of the replenishment cycle and the dates of replenishment for each customer and the vehicle routes of each day within PC, such that the average daily operation cost within PC, including inventory holding cost, setup cost, transportation cost, and overtime labor cost, is minimized. A solution method based on genetic algorithm, embedded with an encoding and decoding mechanism and local search operators, is then proposed, and the hash function is adopted to avoid repetitive fitness evaluation for identical solutions. Numerical experiments demonstrate that the proposed solution method can effectively solve the problem under different lengths of PC and number of customers. The method is also shown to be effective in determining whether the company should expand the storage capacity of a customer whose demand increases. Sensitivity analysis of the vehicle fleet composition shows that deploying a mixed fleet can reduce the daily operating cost.

Keywords: cyclic inventory routing problem, joint replenishment, heterogeneous vehicle, genetic algorithm

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Authors: Fatemeh Torfi

Abstract:

Estimation of stochastic demand in physical distribution in general and efficient transport routs management in particular is emerging as a crucial factor in urban planning domain. It is particularly important in some municipalities such as Tehran where a sound demand management calls for a realistic analysis of the routing system. The methodology involved critically investigating a fuzzy least-squares linear regression approach (FLLRs) to estimate the stochastic demands in the vehicle routing problem (VRP) bearing in mind the customer's preferences order. A FLLR method is proposed in solving the VRP with stochastic demands. Approximate-distance fuzzy least-squares (ADFL) estimator ADFL estimator is applied to original data taken from a case study. The SSR values of the ADFL estimator and real demand are obtained and then compared to SSR values of the nominal demand and real demand. Empirical results showed that the proposed methods can be viable in solving problems under circumstances of having vague and imprecise performance ratings. The results further proved that application of the ADFL was realistic and efficient estimator to face the stochastic demand challenges in vehicle routing system management and solve relevant problems.

Keywords: fuzzy least-squares, stochastic, location, routing problems

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Authors: Christofas Stergianos, Jason Atkin, Herve Morvan

Abstract:

As air traffic increases, more airports are interested in utilizing optimization methods. Many processes happen in parallel at an airport, and complex models are needed in order to have a reliable solution that can be implemented for ground movement operations. The ground movement for aircraft in an airport, allocating a path to each aircraft to follow in order to reach their destination (e.g. runway or gate), is one process that could be optimized. The Quickest Path Problem with Time Windows (QPPTW) algorithm has been developed to provide a conflict-free routing of vehicles and has been applied to routing aircraft around an airport. It was subsequently modified to increase the accuracy for airport applications. These modifications take into consideration specific characteristics of the problem, such as: the pushback process, which considers the extra time that is needed for pushing back an aircraft and turning its engines on; stand holding where any waiting should be allocated to the stand; and runway sequencing, where the sequence of the aircraft that take off is optimized and has to be respected. QPPTW involves searching for the quickest path by expanding the search in all directions, similarly to Dijkstra’s algorithm. Finding a way to direct the expansion can potentially assist the search and achieve a better performance. We have further modified the QPPTW algorithm to use a heuristic approach in order to guide the search. This new algorithm is based on the A-star search method but estimates the remaining time (instead of distance) in order to assess how far the target is. It is important to consider the remaining time that it is needed to reach the target, so that delays that are caused by other aircraft can be part of the optimization method. All of the other characteristics are still considered and time windows are still used in order to route multiple aircraft rather than a single aircraft. In this way the quickest path is found for each aircraft while taking into account the movements of the previously routed aircraft. After running experiments using a week of real aircraft data from Zurich Airport, the new algorithm (A-star QPPTW) was found to route aircraft much more quickly, being especially fast in routing the departing aircraft where pushback delays are significant. On average A-star QPPTW could route a full day (755 to 837 aircraft movements) 56% faster than the original algorithm. In total the routing of a full week of aircraft took only 12 seconds with the new algorithm, 15 seconds faster than the original algorithm. For real time application, the algorithm needs to be very fast, and this speed increase will allow us to add additional features and complexity, allowing further integration with other processes in airports and leading to more optimized and environmentally friendly airports.

Keywords: a-star search, airport operations, ground movement optimization, routing and scheduling

Procedia PDF Downloads 200