Decision rule approximations for the risk averse reservoir management problem

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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Linear decision rule in reservoir management and design: 5. A general algorithm

Water Resources Research ◽

10.1029/wr011i002p00204 ◽

1975 ◽

Vol 11 (2) ◽

pp. 204-207 ◽

Cited By ~ 30

Author(s):

Jose Gundelach ◽

Charles ReVelle

Keyword(s):

Decision Rule ◽

Reservoir Management ◽

General Algorithm ◽

Linear Decision Rule

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Toward Understanding the Value of Climate Information for Multiobjective Reservoir Management under Present and Future Climate and Demand Scenarios

Journal of Applied Meteorology and Climatology ◽

10.1175/2009jamc2135.1 ◽

2010 ◽

Vol 49 (4) ◽

pp. 557-573 ◽

Cited By ~ 18

Author(s):

Nicholas E. Graham ◽

Konstantine P. Georgakakos

Keyword(s):

Adaptive Management ◽

Mathematical Problem ◽

Low Frequency ◽

Reservoir Management ◽

Management Problem ◽

Dimensionless Time ◽

Climate Information ◽

Reservoir Volume ◽

And Performance ◽

Volume Targets

Abstract Numerical simulation techniques and idealized reservoir management models are used to assess the utility of climate information for the effective management of a single multiobjective reservoir. Reservoir management considers meeting release and reservoir volume targets and minimizing wasteful spillage. The influence of reservoir size and inflow variability parameters on the management benefits is examined. The effects of climate and demand (release target) change on the management policies and performance are also quantified for various change scenarios. Inflow forecasts emulate ensembles of dynamical forecasts for a hypothetical climate system with somewhat predictable low-frequency variability. The analysis considers the impacts of forecast skill. The mathematical problem is cast in a dimensionless time and volume framework to allow generalization. The present work complements existing research results for specific applications and expands earlier analytical results for simpler management situations in an effort to draw general conclusions for the present-day reservoir management problem under uncertainty. The findings support the following conclusions: (i) reliable inflow forecasts are beneficial for reservoir management under most situations if adaptive management is employed; (ii) tolerance to forecasts of lower reliability tends to be higher for larger reservoirs; (iii) reliable inflow forecasts are most useful for a midrange of reservoir capacities; (iv) demand changes are more detrimental to reservoir management performance than inflow change effects of similar magnitude; (v) adaptive management is effective for mitigating climatic change effects and may even help to mitigate demand change effects.

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