logo

Discrete Mathematics

11 Pages2311 Words311 Views
   

Added on  2020-11-23

About This Document

Discreet Mathematics TABLE OF CONTENTS INTRODUCTION 1 PROBLEM DEFINITION 1 APPLICATIONS OF TRAVELLING SALESMAN PROBLEM IN REAL WORLD 1 SOLUTIONS2 POSSIBLE ALGORITHMS 5 CONCLUSION 6 SHORT STATEMENT 7 REFERENCES 8 INTRODUCTION The mathematical concepts such as geometry, measurements, logics and statistics are widely used in real world applications. In its simplest form it is used in planning, logistic and supply chain of operational management process of business organisations as well as in manufacturing of microchips

Discrete Mathematics

   Added on 2020-11-23

ShareRelated Documents
Discreet Mathematics
Discrete Mathematics_1
TABLE OF CONTENTSINTRODUCTION ..........................................................................................................................1PROBLEM DEFINITION ..............................................................................................................1APPLICATIONS OF TRAVELLING SALESMAN PROBLEM IN REAL WORLD..................1SOLUTIONS ..................................................................................................................................2POSSIBLE ALGORITHMS ...........................................................................................................5CONCLUSION ...............................................................................................................................6SHORT STATEMENT ...................................................................................................................7REFERENCES ...............................................................................................................................8
Discrete Mathematics_2
INTRODUCTION The mathematical concepts such as geometry, measurements, logics and statistics arewidely used in real world applications. These concepts play significant role in academics andresearch but their application in dealing with practical life situations is also one of the populartrend (Kyritsis and et.al., 2017). The report will analyse one such problem named travellingsalesman problem (TSP) and its practical applications. It will also explain the available solutionmethods and algorithms for solving the problem. PROBLEM DEFINITION TSP is one of the most popular algorithm based problem which helps to determine theoptimum or most efficient route possible between given set of locations and distances. Usually inits problem statement different locations or points are given and an individual is required totravel between two points by taking the shortest possible path so that time, distance and cost canbe saved. Thus the problem is widely used by the business organisations in their supply chainmanagement (Ouaarab, Ahiod and Yang, 2015). TSP consist of large number of variables andthus it is very complex to solve these problems. The problem definition can be given as follows: An individual or salesman is required to travel to certain destinations. The salesman isrequired to cover each location exactly at once and must follow the shortest path. Everydestination is represented as vertex and path between two vertices is represented as its edge. Theproblem can be interpreted to all the applications which requires the analysis of shortest or thelongest paths between two destinations (Hazra and Hore, 2016). APPLICATIONS OF TRAVELLING SALESMAN PROBLEM IN REALWORLDThe TSP finds a wide range of applications in various fields. In its simplest form it isused in planning, logistic and supply chain of operational management process of businessorganisations as well as in manufacturing of microchips which requires the analysis of shortestpaths. In the applications associated with the travelling it is used as an essential tool to determinethe shortest path (Salazar-González and Santos-Hernández, 2015). Being an optimizationproblem it is also used in computer applications which requires the data transmission betweennodes through minimum distance. 1
Discrete Mathematics_3
Thus in logistic, packaging and scheduling of the objects TSP provides the effectivesolutions. The problem is also used for accomplishing tasks such as computer wiring, productionof printed circuit boards and routing problems which requires the analysis of the shortest path.The supply chain network of the organisations includes customers and suppliers which arelocated at diverse locations. Thus if supply chain path is not planned properly by theorganisations then it can lead to increment in distribution time, cost and distance. For determining the shortest geographical routes business organisations apply TSP intheir operational procedures. Similarly while defining networks or data transfer path incomputers and manufacturing of PCB the time delay can be increased if wiring paths are notoptimized (Bhatt and et.al., 2017). Thus during their manufacturing process special attention ispaid to the designing process to assure that between different connecting points or nodes shortestpath is maintained. This analysis is not possible without solving TSP. SOLUTIONS The TSP can be solved by using various methods such as Hungarian method, branch andbound method (B&B) and one's assignment method. However B&B can be considered as one ofthe effective way to find the optimum solution for the problem. B&B techniques can be appliedto the problems which cannot be solved by the dynamic programming and greedy method.Though number of iterations can lead make this solution much slower in worst cases but if it isapplied carefully then it can provide optimum solution fast (Cvetković and et.al., 2018). This method is based on the concept that the problem is divided into sub problems and then foreach of the sub problem solutions are determined. An example of TSP solution by using B&B isprovided as follows: A salesman has to start his journey from city A to cities B, C and D. The cost of travellingbetween these cities is given in figure below. The optimum path which must be covered to giveminimum cost is determined by applying B&B. 2
Discrete Mathematics_4

End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents
TSP 2 Traveling Salesperson Problem
|17
|3956
|29

Travelling Salesman Problem: Introduction, Applications, and Algorithms
|11
|3181
|392

Travelling Sales Person Model (TSP) (Analysis)
|10
|2392
|269

Evaluate the Dijkstra’s Algorithm
|4
|1819
|204

The heuristics and algorithms
|13
|3089
|24

Concept of Shortest Paths with Logistics Constraints
|49
|12847
|89