Modelling the West African Examination Council’s question paper depot inspection as a travelling salesman problem

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The travelling salesman problem is considered to be a classic example of what is known as a tour problem. Essentially, any type of tour problem involves making a series of stops along a designated route and making a return journey without ever making a second visit to any previous stop. Generally, a tour problem is present when there is concern on making the most of available resources such as time and mode of travel to accomplish the most in results. Finding a solution to a tour problem is sometimes referred to as discovering the least-cost path, implying that the strategic planning of the route will ensure maximum benefit with minimum expenditure incurred. The concept of the travelling salesman problem can be translated into a number of different disciplines. As a form of optimization that is useful in both mathematical and computer science disciplines, combinatorial optimization seeks to team relevant factors and apply them in a manner that will yield the best results with repeated usage. This study formulated a real-life problem of WAEC as a TSP, modelled as network problem and applies dynamic programming approach in solving the problem. It was observed that the route that gave minimum achievable inspection plan was 1 – 3 – 6 –9 – 10 at the minimum distance of 183 km, by visiting as many as five centres on the route.
A Thesis submitted to the School of Graduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the Degree of Master of Science in Industrial Mathematics