Finite Stage Simulation Solutions Model of Markov Chains to Maintenance Management Problems for Nigerian River Basin Engineering Schemes

Abstract

The aim of this study is to investigate a case where N100 billion is to be spent on the maintenance of the twelve Nigeria River Basin Engineering Development schemes. The purposes of interest are: Irrigation, Water supply, Hydro-Electric Power Generation, Flood control, Drainage, Navigation, Recreation and Erosion control. The returns (objectives) to be optimized in stages as a multi-stage decision problems are: Economic Efficiency, Federal, Regional, State and Local Economic Redistribution, Social Well-Being, Youth Employment and Environmental Quality Improvement. The problem then becomes how to apportion (allocation) the N100 billion development funds among the various purposes so as to optimize the returns (objectives) even under the worst conflict situation to avoid flooding of the lower regions or plains. A benefit (return) study of the eight purposes under each of the eight objectives was carried out. The conception of the study is as shown in table 1 with maintenance and table 2 without maintenance. Methods of experiments involve the gardener’s problem case 1 and steady state probabilities and mean return times of ergodic chains of markov chain. In conclusion result of the performance of experiment 1 shows that for years 1,2,and 3, the planning and management engineer should maintain the river basin engineering development  regardless of the state of the system. For experiment 2, it interprets that it takes approximately 8(seasons) years for the system to return to a very excellent state and 10 to 16 years for poor and very poor state. The total expected revenue for the eight years ranges from N828.56billion to N822billion.