Two Novel Heuristics Based on a New Density Measure for Vehicle Routing Problem

2015 ◽  
Vol 6 (1) ◽  
pp. 78-90 ◽  
Author(s):  
Abdesslem Layeb
Keyword(s):  
Density Matrix ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Nearest Neighbor ◽  
Routing Problem ◽  
Stochastic Version ◽  
Third Phase ◽  
Vehicle Capacity ◽  
Number Of Customers ◽  
Optimal Set

The vehicle routing problem (VRP) is a known optimization problem. The objective is to construct an optimal set of routes serving a number of customers where the demand of each customer is less than the vehicle' capacity, and each customer is visited exactly once like in TSP problem. The purpose of this paper is to present new deterministic heuristic and its stochastic version for solving the vehicle routing problem. The proposed algorithms are inspired from the density heuristic of knapsack problem. The proposed heuristic is based on four steps. In the first step a density matrix (demand/distance) is constructed by using given equations. In the second step, a giant tour is constructed by using the density matrix; the customer with highest density is firstly visited, the process is repeated until all customers will be visited. In the third phase, the split procedure is applied to this giant tour in order to get feasible routes subject to vehicles capacities. Finally, each route is improved by the application of the nearest neighbor heuristic. The results of the experiment indicate that the proposed heuristic is better than the nearest neighbor heuristic for VRP. Moreover, the proposed algorithm can easily be used to generate initial solutions for a wide variety of VRP algorithms.

scholarly journals On the Selective Vehicle Routing Problem

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 771 ◽  
Author(s):  
Cosmin Sabo ◽  
Petrică C. Pop ◽  
Andrei Horvat-Marc
Keyword(s):  
Mathematical Model ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Mixed Integer ◽  
The Novel ◽  
Routing Problem ◽  
Proposed Model ◽  
Benchmark Instances ◽  
Number Of Customers ◽  
Optimal Set

The Generalized Vehicle Routing Problem (GVRP) is an extension of the classical Vehicle Routing Problem (VRP), in which we are looking for an optimal set of delivery or collection routes from a given depot to a number of customers divided into predefined, mutually exclusive, and exhaustive clusters, visiting exactly one customer from each cluster and fulfilling the capacity restrictions. This paper deals with a more generic version of the GVRP, introduced recently and called Selective Vehicle Routing Problem (SVRP). This problem generalizes the GVRP in the sense that the customers are divided into clusters, but they may belong to one or more clusters. The aim of this work is to describe a novel mixed integer programming based mathematical model of the SVRP. To validate the consistency of the novel mathematical model, a comparison between the proposed model and the existing models from literature is performed, on the existing benchmark instances for SVRP and on a set of additional benchmark instances used in the case of GVRP and adapted for SVRP. The proposed model showed better results against the existing models.

scholarly journals Implementation of the Model Capacited Vehicle Routing Problem with Time Windows with a Goal Programming Approach in Determining the Best Route for Goods Distribution

2020 ◽  
Vol 17 (2) ◽  
pp. 231-239
Author(s):  
Wahri Irawan ◽  
Muhammad Manaqib ◽  
Nina Fitriyati
Keyword(s):  
Vehicle Routing ◽  
Goal Programming ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Goal Function ◽  
Programming Approach ◽  
Routing Problem ◽  
Total Capacity ◽  
Vehicle Capacity ◽  
Number Of Customers

This research discusses determination of the best route for the goods distribution from one depot to customers in various locations using the Capacitated Vehicle Routing Problem with Time of Windows (CVRPTW) model with a goal programming approach. The goal function of this model are minimize costs, minimize distribution time, maximize vehicle capacity and maximize the number of customers served. We use case study in CV. Oke Jaya companies which has 25 customers and one freight vehicle with 2000 kg capacities to serve the customers in the Serang, Pandeglang, Rangkasbitung and Cikande. For simulation we use software LINGO. Based on this CVRPTW model with a goal programming approach, there are four routes to distribute goods on the CV. Oke Jaya, which considers the customer’s operating hours, with total cost is Rp 233.000,00, the total distribution time is 17 hours 57 minutes and the total capacity of goods distributed is 6150 kg.

scholarly journals Hybrid Heuristic Algorithm for solving Capacitated Vehicle Routing problem

2014 ◽  
Vol 12 (9) ◽  
pp. 3844-3851 ◽  
Author(s):  
Moh. M. AbdElAziz ◽  
Haitham A. El-Ghareeb ◽  
M. S. M. Ksasy
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Nearest Neighbor ◽  
Hybrid Approach ◽  
Minimum Cost ◽  
Second Phase ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Vehicle Capacity ◽  
Capacitated Vehicle

The Capacitated Vehicle Routing Problem is the most common and basic variant of the vehicle routing problem, where it represents an important problem in the fields of transportation, distribution and logistics. It involves finding a set of optimal routes that achieve the minimum cost and serve scattered customer locations under several constraints such as the distance between customers’ locations, available vehicles, vehicle capacity and customer demands. The Cluster first – Route second is the proposed approach used to solve capacitated vehicle routing problem which applied in a real case study used in that research, it consists of two main phases. In the first phase, the objective is to group the closest geographical customer locations together into clusters based on their locations, vehicle capacity and demands by using Sweep algorithm. In the second phase, the objective is to generate the minimum cost route for each cluster by using the Nearest Neighbor algorithm. The hybrid approach is evaluated by Augerat’s Euclidean benchmark datasets.

scholarly journals OPTIMALISASI JUMLAH KENDARAAN DAN RUTE DISTRIBUSI LOGISTIK PEMILIHAN DI KABUPATEN KEDIRI PADA MASA PANDEMI

2021 ◽  
Vol 3 (1) ◽  
pp. 1-25
Author(s):  
Eka Wisnu Wardhana ◽  
Oki Anita Candra Dewi
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Nearest Neighbor ◽  
Visual Basic ◽  
Microsoft Excel ◽  
Google Maps ◽  
Routing Problem ◽  
Visual Basic Application

Artikel ini membahas tentang permasalahan distribusi logistik pemilihan kepala daerah (Pemilihan) yang berkaitan dengan penentuan jumlah kendaraan yang tepat dan pemilihan rute terdekat dengan mempertimbangkan jarak yang dapat dilalui oleh kendaraan roda 4 atau lebih. Penentuan jumlah kendaraan dan rute yang tepat ini sangat penting bagi Komisi Pemilihan Umum (KPU) karena aspek logistik dan distribusi sangat berpengaruh dalam memastikan suara masyarakat tersampaikan dengan baik. Selain itu aspek ini memiliki keterkaitan satu dengan lainnya baik bersifat strategis maupun teknis. Selama pandemi, distribusi logistik Pemilihan tidak hanya berkaitan dengan kebutuhan alat pemungutan suara namun juga alat pelindung diri (APD) selama pelaksanaan pemungutan. Oleh karena itu kegiatan logistik menjadi lebih banyak dengan tetap mempertimbangkan protokol kesehatan sehingga diperlukan sebuah aplikasi yang dapat menentukan jumlah kendaraan dan rute yang tepat sebagai dasar untuk mempercepat pengambilan keputusan. Penelitian ini fokus pada penentuan jumlah kendaraan dan rute distribusi logistik yang optimal pada Pemilihan tahun 2020 di masa pandemic COVID-19 di KPU Kabupaten Kediri menggunakan pendekatan vehicle routing problem dengan memperhatikan jarak dari google maps serta menggunakan algoritma nearest neighbor dalam menentukan jarak terdekat antar titik. Aplikasi yang dikembangkan adalah penentuan rute menggunakan Visual Basic Application (VBA) pada Microsoft Excel. Penelitian ini menghasilkan jumlah kendaraan sebanyak 12 kendaraan untuk pengiriman logistik Pemilihan maupun APD dengan batas maksimal total perjalanan setiap truk sepanjang 100 km. Selain itu terdapat 6 kecamatan yang dikunjungi dua kali karena total kebutuhan melebihi kapasitas kendaraan.

scholarly journals Single-Commodity Vehicle Routing Problem with Pickup and Delivery Service

2008 ◽  
Vol 2008 ◽  
pp. 1-17 ◽  
Author(s):  
Goran Martinovic ◽  
Ivan Aleksi ◽  
Alfonzo Baumgartner
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Search Space ◽  
Global Optimum ◽  
Pickup And Delivery ◽  
Routing Problem ◽  
Practical Applications ◽  
Delivery Service ◽  
Number Of Customers ◽  
Single Commodity

We present a novel variation of the vehicle routing problem (VRP). Single commodity cargo with pickup and delivery service is considered. Customers are labeled as either cargo sink or cargo source, depending on their pickup or delivery demand. This problem is called a single commodity vehicle routing problem with pickup and delivery service (1-VRPPD). 1-VRPPD deals with multiple vehicles and is the same as the single-commodity traveling salesman problem (1-PDTSP) when the number of vehicles is equal to 1. Since 1-VRPPD specializes VRP, it is hard in the strong sense. Iterative modified simulated annealing (IMSA) is presented along with greedy random-based initial solution algorithm. IMSA provides a good approximation to the global optimum in a large search space. Experiment is done for the instances with different number of customers and their demands. With respect to average values of IMSA execution times, proposed method is appropriate for practical applications.

scholarly journals Development Of A New Genetic Algorithm For Solving Capacitated Vehicle Routing Problem In Short Time

2019 ◽  
Vol 8 (11) ◽  
pp. 903-907
Keyword(s):  
Genetic Algorithm ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Routing Problem ◽  
Capacitated Vehicle Routing Problem ◽  
Benchmark Instances ◽  
Full Capacity ◽  
Short Time ◽  
Number Of Customers ◽  
Capacitated Vehicle

In this paper a new genetic algorithm is developed for solving capacitated vehicle routing problem (CVRP) in situations where demand is unknown till the beginning of the trip. In these situations it is not possible normal metaheuristics due to time constraints. The new method proposed uses a new genetic algorithm based on modified sweep algorithm that produces a solution with the least number of vehicles, in a relatively short amount of time. The objective of having least number of vehicles is achieved by loading the vehicles nearly to their full capacity, by skipping some of the customers. The reduction in processing time is achieved by restricting the number of chromosomes to just one. This method is tested on 3 sets of standard benchmark instances (A, M, and G) found in the literature. The results are compared with the results from normal metaheuristic method which produces reasonably accurate results. The results indicate that whenever the number of customers and number of vehicles are large the new genetic algorithm provides a much better solution in terms of the CPU time without much increase in total distance traveled. If time permits the output from this method can be further improved by using normal established metaheuristics to get better solution

scholarly journals Solving Close-Open Mixed Vehicle Routing Problem Using Bat Algorithm

2020 ◽  
Vol 2 (1) ◽  
pp. 46
Author(s):  
Atika Dwi Hanun Amalia ◽  
Herry Suprajitno ◽  
Asri Bekti Pratiwi
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Large Data ◽  
Bat Algorithm ◽  
Small Data ◽  
Routing Problem ◽  
Java Programming ◽  
Implementation Program ◽  
Distribution Process ◽  
Vehicle Capacity

The purpose of this research is to solve the Close-Open Mixed Vehicle Routing Problem (COMVRP) using Bat Algorithm. COMVRP which is a combination of Close Vehicle Routing Problem or commonly known as Vehicle Routing Problem (VRP) with Open Vehicle Routing Problem (OVRP) is a problem to determine vehicles route in order to minimize total distance to serve customers without exceed vehicle capacity. COMVRP occurs when the company already has private vehicles but its capacity could not fulfill all customer demands so the company must rent several vehicles from other companies to complete the distribution process. In this case, the private vehicle returns to the depot after serving the last customer while the rental vehicle does not need to return. Bat algorithm is an algorithm inspired by the process of finding prey from small bats using echolocation. The implementation program to solve was created using Java programming with NetBeans IDE 8.2 software which was implemented using 3 cases, small data with 18 customers, medium data with 75 customers and large data with 100 customers. Based on the implementation results, it can be concluded that the more iterations, the smaller total costs are obtained, while for the pulse rate and the amount of bat tends not to affect the total cost obtained.

scholarly journals Vehicle Routing Problem with Deadline and Stochastic Service Times: Case of the Ice Cream Industry in Santiago City of Chile

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2750
Author(s):  
Sebastián Dávila ◽  
Miguel Alfaro ◽  
Guillermo Fuertes ◽  
Manuel Vargas ◽  
Mauricio Camargo
Keyword(s):  
Monte Carlo ◽  
Tabu Search ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Search Method ◽  
Superior Performance ◽  
Real Problem ◽  
Routing Problem ◽  
Chaotic Search ◽  
Number Of Customers

The research evaluates the vehicular routing problem for distributing refrigerated products. The mathematical model corresponds to the vehicle routing problem with hard time windows and a stochastic service time (VRPTW-ST) model applied in Santiago de Chile. For model optimization, we used tabu search, chaotic search and general algebraic modeling. The model’s objective function is to minimize the total distance traveled and the number of vehicles using stochastic waiting restrictions at the customers’ facilities. The experiments were implemented in ten scenarios by modifying the number of customers. Experiments were established with several customers that can be solved using the general algebraic modeling technique in order to validate the tabu search and the chaotic search methods. The study considered two algorithms modified with Monte Carlo (tabu search and chaotic search). Additionally, two modified algorithms, TSv2 and CSv2, were proposed to reduce execution time. These algorithms were modified by delaying the Monte Carlo procedure until the first set of sub-optimal routes were found. The results validate the metaheuristic chaotic search to solve the VRPTW-ST. The chaotic search method obtained a superior performance than the tabu search method when solving a real problem in a large city. Finally, the experiments demonstrated a direct relationship between the percentage of customers with stochastic waiting time and the model resolution time.

scholarly journals Aplikasi Algoritma Tabu Search dan Safety Stock Pada Penentuan Rute Distribusi Air Mineral di Daerah Istimewa Yogyakarta

2018 ◽  
Vol 7 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Anita Nurul Firdaus ◽  
Pipit Pratiwi Rahayu
Keyword(s):  
Tabu Search ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Nearest Neighbor ◽  
Search Algorithm ◽  
Tabu Search Algorithm ◽  
Routing Problem ◽  
Safety Stock ◽  
Shortest Route ◽  
Calculation Process

Pendistribusian produk berperan penting dalam dunia industri.  Salah satu usaha yang dapat dilakukan perusahaan untuk mengoptimalkan pendistribusian produk adalah meminimalkan biaya tranportasi melalui penentuan rute optimal kendaraan yang disebut dengan VRP (Vehicle Routing Problem). Tujuan dari VRP adalah menentukan rute optimal yaitu rute dengan jarak minimum untuk mendistribusikan produk kepada konsumen. Salah satu variasi VRP adalah Capacitated Vehicle Routing Problem (CVRP), yaitu VRP dengan kendala kapasitas kendaraan. Kasus CVRP tersebut dapat diselesaikan dengan menggunakan Algoritma Tabu Search. Cara kerja Algoritma Tabu Search dimulai dengan penentuan initial solution menggunakan Nearest Neighbor, evaluasi move menggunakan  Exchange, 2-Opt, Relocated, dan Cross Exchange, update Tabu List, kemudian apabila kriteria pemberhentian terpenuhi  maka proses Algoritma Tabu Search berhenti jika tidak, maka kembali pada evaluasi move. Proses perhitungan Algoritma Tabu Search dilakukan secara manual pada PT IAP. Setiap perusahaan distributor atau pun jasa selalu mengadakan persediaan, salah satunya adalah Safety Stock. Perhitungan sederhana Safety Stock dapat membantu menyelesaikan persediaan pengaman yang harus dipersiapkan perusahaan untuk mengurangi tingkat kerugian. Berdasarkan proses perhitungan manual diperoleh solusi pendekatan optimal yaitu rute dengan total jarak terpendek sebesar 138,834 km dan nilai untuk Safety Stock adalah ± 9 karton. [Distribution of the product play an important role in the industry field. The effort done by the companies to optimize the distribution is minimize transportation fee by deciding the shortest route of the vehicle, known as Vehicle Routing Problem (VRP). The purpose of VRP is to determine the optimal route of the route with a minimum distance to distribute product to the consumer. One of the varieties of VRP is Capacitated Vehicle Routing Problem (CVRP), which is VRP with vehicle capacity problems. CVRP case can be solved by using Tabu Search Algorithm. How it works Tabu Search Algorithm starts with the determination of the initial solution using the Nearest Neighbor, evaluating the move using Exchange, 2-Opt, Relocated, and Cross Exchange, updates Tabu List, then when the criteria for termination are met then the Tabu Search algorithm stop if not, then go back to the evaluation of the move. Tabu Search Algorithm calculation process is done manually PT IAP.  Every distributor or service company always hold inventory, one of them is Safety Stock. The simple calculation of Safety Stock can help solve the safety availability that should be prepared by the companies and reduce the level of losses. Based on the manual calculation process obtained optimal solution approach that is route with the shortest route to the optimal total distance of 138,834 km and the value of safety stock is ± 9 cartons.]

scholarly journals VEHICLE ROUTING PROBLEM WITH TIME WINDOWS USING HYBRID ENCODING GENETIC ALGORITHM

2014 ◽  
Vol 12 (10) ◽  
pp. 3945-3951
Author(s):  
Dr P.K Chenniappan ◽  
Mrs.S.Aruna Devi
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Time Windows ◽  
Minimal Cost ◽  
Total Size ◽  
Routing Problem ◽  
Time Window Constraints ◽  
Vehicle Capacity ◽  
Vehicle Routes

The vehicle routing problem is to determine K vehicle routes, where a route is a tour that begins at the depot, traverses a subset of the customers in a specified sequence and returns to the depot. Each customer must be assigned to exactly one of the K vehicle routes and total size of deliveries for customers assigned to each vehicle must not exceed the vehicle capacity. The routes should be chosen to minimize total travel cost. Thispapergivesasolutiontofindanoptimumrouteforvehicle routingproblem using Hybrid Encoding GeneticAlgorithm (HEGA)technique tested on c++ programming.The objective is to find routes for the vehicles to service all the customers at a minimal cost and time without violating the capacity, travel time constraints and time window constraints

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