Linear programming approach for scheduling sports league problems in Malaysia

Sports league problems in Malaysia are usually made by manual method or so called ad-hoc method. This means that the construction of a particular schedule is based on the availability of the chosen venues (stadiums) and number of teams involved. Moreover, the popular style of scheduling team sport in Malaysia was Home-Away approach which has no mathematical formulation model and never consider important factors such as travelling cost. Thus, heuristic is used in the beginning to solve sports league problem in term of minimizing travelling distance. In this thesis we propose to formulate a linear programming (LP) model to schedule sports league problems in Malaysia whereby the tournament style will be definitely different from Home-Away restriction. We consider an important factor such as travelling cost while scheduling and efficient strategy to replace tournament with Home-Away style. Besides, the venues (stadiums) involve are predefined before the construction of the schedule begin. To validate the formulated model, we compare results obtain by heuristic approach using the same data. In order to solve the formulated LP model, we proposed several solution methods such as simplex and genetics algorithm. Besides, we also consider large problems in our formulated model as we introduced the cluster approach. In cluster approach, the large problems in scheduling sports league will be separated into few small clusters where all the small problems solve simultaneously and being linked back to the original problem in the end to achieve global optimal solution. A sensitivity analysis is performed towards our formulated model. In our case, we focus on solely the predefined venues while performing sensitivity analysis to see how our model reacted. We get a greater number of total travelling distances when we select different predefined venues which are at remote places. This means that our formulated model is suitable for solving our problems. Our numerical results show that the total travelling distance using our formulated model is lower than the conventional Home-Away style of tournament. The results shown is promising because the formulated model can lowered the cost associated with travelling distance

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