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In this document the airline fleet decision process has been categorized in the following bullets: Forecast of expected traffic demand (RPK) Planning average load factor (%) ASK needed to be generated to meet the traffic demand The productivity of the aircraft (ASK per day) results in the number of aircraft to be acquired and its financial impact (Costs) ...


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The reason you're not finding anything about this in the literature is that airlines do everything they can to avoid having airplanes in reserve: an airplane on the ground is an airplane that's losing money. An airline will determine the fleet size needed to serve the anticipated demand (see Oguz's answer for literature on how they do this), and will cover ...


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You could try MDPtoolbox from here in which the package is ready to download for Matlab, R, and Python. The functions prepared in a manner that any user can easily modify it for specific problem instances.


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After having read Chapter 5.3 of Decision Making Under Uncertainty by Mykel J. Kochenderfer, I have come to some conclusions. We are dealing with model uncertainty, in which case we can formulate a Bayes Adaptive Model. In the book that I read, the term model uncertainty refers more to not knowing what the transition probabilities nor the structure of the ...


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I am trying to solve a workforce scheduling and optimization problem ... I want to schedule the minimum number of people in each shift to achieve maximum foretasted volumes with minimum AHT. Also if you can provide a comparison of different methods and their advantages and disadvantages that would be helpful. Make certain that your input data is correct. ...


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I hope to provide intuitively-appealing answers to both questions. $\textbf{Question 1:}$ Infinite horizon MDP's do not care about the initial state. They attempt to be optimal in the sense that the policy is optimal for all given allowable initial states. Finite MDP's are computed as optimal for a given state. The policy is intended to be optimal only if ...


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Markov decision problem theory and computation is based on using backward induction (dynamic programming) to recursively evaluate expected rewards. When we define a policy $\pi = (d_1, d_2,...,d_{N-1})$, we assume that $N$, the length of horizon or the number of epochs is given.While in the infinite horizon the policies can be defined as, $\nu = (d_1, d_2,......


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I will answer on the basis of one particular case of MDPs. There have been a few recent articles that extensively discuss the issues of the diversification of MDPs and introduce a new model known as the MDP-DIV (Markov Decision Process for Diversifying). For that I refer you to Xia et al. (2017). It is identified that the main causes for slow convergence ...


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Since you are assuming infinite capacity, this sounds like an $M/M/\infty$ queueing system.


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You can still use the MDP modeling approach for your system with unknown or non-stationary request distributions. I think the paper: MDP formulation and solution algorithms for inventory management with multiple suppliers and supply and demand uncertainty, is a good start point to deepen your search. Also, look at POMDPs(Partially Observable MDPs). In the ...


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It is just $$\sum_{n=1}^\infty a_n = \sum_{n=0}^\infty a_n - a_0 = \sum_{n=1}^\infty a_{n-1} - a_0,$$ where $$a_n=\lambda^n P^{d^\infty}(X_{n+1}=j\mid X_1=k).$$ In particular $$a_0=\lambda^0 P^{d^\infty}(X_1=j\mid X_1=k) = [j=k] = \begin{cases}1 &\text{if $j=k$}\\0 &\text{otherwise} \end{cases}$$


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I think this is an interesting question from an operations research / simulation exercise. As such you could attack the question very simply to start with and then go on more and more detailed if it makes sense. Not very different really from many other OR questions. A very first, very simple calculation can be done on the back of an envelope, say per week: ...


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