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This paper presents a static overbooking model for a single-leg multi-fare class flight. A realistic distribution of no-show data in modeling the cost function was considered using data collected from the Ethiopian airlines. The overbooking model developed considers the interaction (i.e. the transfer of an extra passenger in a lower fare classes to higher fare class empty seat) between classes that may exist during boarding time. Furthermore, the overbooking problem is modelled in such a way that it could be  constrained by user defined constraints such as probability of loss of the revenue. The overbooking model developed was solved using derivatives that give a closed form  expression and Monte Carlo simulation with a derivative free optimization algorithm. A comparison of the revenue generated from no-overbooking policy, the closed form  solution, and the Monte Carlo simulation solution approach shows that the Monte Carlo simulation solution approach performs better. Generally, the numerical results show that the overbooking model is effective in determining the optimal number of overbooking for a number of classes and a variety of compensation cost plans. Keywords : Overbooking, Monte Carlo Simulation, Nelder Mead algorithm, Revenue management, Ethiopian Airline, Ethiopia.

Modeling and optimization of the single-leg multi-fare class overbooking problem