An optimal assignment/placement of customers to bus services from Kumasi to Accra

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This project involves the use of optimisation techniques, specifically the Assignment Model which is a variant of the Transportation model to optimally assign available bus services to different time schedules in any clay of the week. Average service times or Holding times with respect to the various parallel Servers (bus services) at a given time schedules are taken and analysed. These time averages provide a measure of the cost effectiveness or ne Assignment Tableau which has, as it resource the parallel servers and the time schedules as it operating pattern. The Hungarian Algorithm is used to optimally assign to each time schedule a server with a corresponding minimum holding time. For this service system a high server capacity is achieved by placing several medium capacity single channel servers iii parallel. A customer arrival stream is split into component streams with each stream being served by one server. The K11’ server serves its component process independent of the other as a single channel server with a first-come-first-served Service discipline. The inter arrival times of buses are also taken and analysed. With these parameters the respective probabilities that there would be idle servers at the various service points are calculated using the Poisson distribution. The results show that the STC Bus service has a minimum Service time between the hours of 4am — 8am throughout the week except on Sundays. The GPRTU Neoplan Bus was also observed to have the same trend between the hours of 8am - 11am. Additionally, there were idle servers at the GPRTU terminal almost invariably unlike the STC buses which arrive only within the hours to load and consequently depart for their respective destinations.
A thesis submitted to the Board of Postgraduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirement for the award of the Degree of Master of Science in Mathematics, 1998