scholarly journals On Vehicle routing Problem using Mixed Integer Non-Linear Programming

2020 ◽  
pp. 32-34
Keyword(s):  
Linear Programming ◽  
Vehicle Routing Problem ◽  
Programming Model ◽  
Minimum Cost ◽  
Mixed Integer ◽  
Routing Problem ◽  
Non Linear Programming ◽  
Electric Vehicle Charging ◽  
The Family ◽  
Non Linear

The family of (VRPs) has received remarkable attention in the field of combinatorial optimization after its introduction in the paper of Dantzig and Ramser. VRPs determine a set of vehicle routes in order to accomplish transportation requests at minimum cost. In this paper we develop a mixed-integer non-linear programming model for vrp and apply it in electric vehicle charging.

scholarly journals Near optimal minimal convex hulls of disks

2021 ◽  
Author(s):  
Josef Kallrath ◽  
Joonghyun Ryu ◽  
Chanyoung Song ◽  
Mokwon Lee ◽  
Deok-Soo Kim
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Programming Model ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Convex Hulls ◽  
Non Linear Programming ◽  
Minimal Convex ◽  
Non Linear ◽  
Problem Instances

AbstractThe minimal convex hulls of disks problem is to find such arrangements of circular disks in the plane that minimize the length of the convex hull boundary. The mixed-integer non-linear programming model, named [17], works only for small to moderate-sized problems. Here we propose a polylithic framework of the problem for big problem instances by combining the following algorithms and models: (i) A fast disk-packing algorithm based on Voronoi diagrams, non-linear programming (NLP) models for packing disks, and an NLP model for minimizing the discretized perimeter of convex hull; (ii) A fast convex-hull algorithm to compute the convex hulls of disk arrangements and their perimeter lengths; (iii) A mixed-integer NLP model taking the output of as its input. We present complete analytic solutions for small problems up to four disks and a semi-analytic mixed-integer linear programming model which yields exact solutions for strip packing problems with up to one thousand congruent disks. It turns out that the proposed polylithic approach works fine for large problem instances containing up to 1,000 disks. Monolithic and polylithic solutions using usually outperform other approaches. The polylithic approach yields better solutions than the results in [17] and provides a benchmark suite for further research.

scholarly journals A mixed-integer linear programming model for the selective full-truckload multi-depot vehicle routing problem with time windows

2021 ◽  
Vol 10 (4) ◽  
pp. 471-486 ◽  
Author(s):  
Karim EL Bouyahyiouy ◽  
Adil Bellabdaoui
Keyword(s):  
Linear Programming ◽  
Vehicle Routing ◽  
Integer Linear Programming ◽  
Vehicle Routing Problem ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Time Windows ◽  
Mixed Integer ◽  
Data Set ◽  
Routing Problem

This article has studied a full truckload transportation problem in the context of an empty return scenario, particularly an order selection and vehicle routing problem with full truckload, multiple depots and time windows (SFTMDVRPTW). The aim is to develop a solution where a set of truck routes serves a subset of selected transportation demands from a number of full truckload orders to maximize the total profit obtained from those orders. Each truck route is a chain of selected demands to serve, originating at a departure point and terminating at an arriving point of trucks in a way that respects the constraints of availability and time windows. It is not mandatory to serve all orders, and only the profitable ones are selected. In this study, we have formulated the SFTMDVRPTW as a mixed-integer linear programming (MILP) model. Finally, Computational results are conducted on a new data set that contains thirty randomly generated problem instances ranging from 16 to 30 orders using the CPLEX software. The findings prove that our model has provided good solutions in a reasonable time.

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