An LP based approximate dynamic programming model to address airline overbooking under cancellation, refund and no-show

In this paper we simultaneously address four constraints relevant to airline revenue management problem: flight cancellation, customer no-shows, overbooking, and refunding. We develop a linear program closely related to the dynamic program formulation of the problem, which we later use to approximate the optimal decision rule for rejecting or accepting customers. First, we give a novel proof that the optimal objective function of this linear program is always an upper bound for the dynamic program. Secondly, we construct a decision rule based on this linear program and prove that it is asymptotically optimal under certain circumstances. Finally, using Monte Carlo simulation, we demonstrate that, numerically, the result of the linear programming policy presented in this paper has a short distance to the upper bound of the optimal answer, which makes it a fairly good approximate answer to the intractable dynamic program.

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Levando a Democracia a Sério: Uma Abordagem da Regra Decisória Ideal para o CONFAZ (Taking Democracy Seriously: An Approach to the Optimal Decision Rule for the Brazilian National Finance Policy Council)

SSRN Electronic Journal ◽

10.2139/ssrn.3522630 ◽

2017 ◽

Author(s):

Misabel Abreu Machado Derzi ◽

Tarcisio Diniz Magalhaes

Keyword(s):

Decision Rule ◽

Optimal Decision ◽

Optimal Decision Rule ◽

Finance Policy

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Optimal control of queueing networks: an approach via fluid models

Advances in Applied Probability ◽

10.1017/s0001867800011587 ◽

2002 ◽

Vol 34 (02) ◽

pp. 313-328

Author(s):

Nicole Bäuerle

Keyword(s):

Optimal Control ◽

Decision Rule ◽

Average Cost ◽

Queueing Networks ◽

Optimal Decision ◽

Stochastic Network ◽

Asymptotically Optimal ◽

Multiclass Queueing Networks ◽

Optimal Decision Rule ◽

Multiclass Queueing

We consider a general control problem for networks with linear dynamics which includes the special cases of scheduling in multiclass queueing networks and routeing problems. The fluid approximation of the network is used to derive new results about the optimal control for the stochastic network. The main emphasis lies on the average-cost criterion; however, the β-discounted as well as the finite-cost problems are also investigated. One of our main results states that the fluid problem provides a lower bound to the stochastic network problem. For scheduling problems in multiclass queueing networks we show the existence of an average-cost optimal decision rule, if the usual traffic conditions are satisfied. Moreover, we give under the same conditions a simple stabilizing scheduling policy. Another important issue that we address is the construction of simple asymptotically optimal decision rules. Asymptotic optimality is here seen with respect to fluid scaling. We show that every minimizer of the optimality equation is asymptotically optimal and, what is more important for practical purposes, we outline a general way to identify fluid optimal feedback rules as asymptotically optimal. Last, but not least, for routeing problems an asymptotically optimal decision rule is given explicitly, namely a so-called least-loaded-routeing rule.

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