Travelling Salesman Problem (TSP) with Mixed Constraints and Multiple Job Facilities at each station
Journal Title: IOSR journal of Business and Management - Year 2018, Vol 20, Issue 3
Abstract
In this paper, mixed constraints (i.e., precedence and fixed position constraints) are considered in the usual travelling salesman problem with multiple job facilities at each station. The two constraints, i.e., precedence constraint(s) and fixed position constraint(s) should maintain feasibility among themselves. By precedence constraints, one means that the station(s) (cities or links or nodes) are visited (or completed) in such a way that a particular station is to be preceded (completed or visited) by another station and on the other hand, with fixed position(s) constraints, one means that the station(s) are visited in such a way that a particular station(s) is to be visited in a certain specific step(s). The aim of the paper is to find a tour of the salesman by using above two constraints in such a way that the total distance traveled is minimum while completing all the ‘M’ jobs, on the basis of first come first serve. The proposed algorithm is formulated and solved by the lexicographic search approach. It is seen that the time required for the search of the optimal solution is fairly less. Also the algorithm is applied to different order matrices with N = 5, 10, 25, 100, 150 and M = 6, 10, 20, 25, 40 to exhibit its effectiveness.
Authors and Affiliations
Dr. Nazimuddin Ahmed
Keywords
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- EP ID EP409882
- DOI 10.9790/487X-2003012330.
- Views 73
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