The paper being reviewed here is titled "Stochastic Linear Programming and Conditional Value at Risk for Water Resources Management", by R. B. Webby, J.Boland, P. G. Howlett, A. V. Metcalfe published in the Australian and New Zealand Industrial and Applied Mathematics Journal (ANZIAM) in 2008.
This paper attempts to illustrates the use of Conditional Value-at-Risk (CVaR) as a decision support tool for water resources managers, focusing on irrigation requirements of a summer crop in a water deficient environment. Water may be available from a number of sources like precipitation, shallow ground aquifers, entitlements of river water and tailwaters (agricultural reuse water).
In financial analysis, Value-at-Risk(VaR) is defined as the maximum loss expected to be incurred over a given time horizon at a specified probability level. VaR gives the specified quantile of the distribution but does not give any info about the upper tail beyond the value. VaR describes the frequency of a sizeable loss butnot the likely severity of such loss. CVaR does contain information about the losses greater than the upper tail as it is the expected value of of the loss, given that a loss greater than or equal to a threshold VaR occurs. A cost model rather than loss is then built and VaR is computed for a given exceedence probability value of the ordered distribution, and CVaR is the mean of the values equal to and beyond the VaR. A stochastic linear programming model is used to optimize the objective function where its possible to have some stochasticity in the constraints of a classic LP problem. The author describes two ways to solve stochastic linear programming problems. One approach is to consider specific values of the variable and solve it deterministically the typical values being the expected value plus or minus multiples of the standard deviation, a full range of values. Another approach is to sample the variables from distributions and then solve deterministically. The author uses the second approach assuming a multivariate normal distribution involving correlated values of rainfall and groundwater. A cost per Ml of water is attributed to each source depending on pumping, storage and application costs and assuming that the same application method is used throughout as well as the environmental costs. No sensitivity tests were carried out.
Simulations were carried out for exceedence probability of 0.9 and time horizon to be the life of the crop throughout. The decision vector represents a course of action taken and the corresponding cost distribution assumed. Each distribution has a CVaR value. Managers for best performance should use the course of action with minimum CVaR. The CVaR value and expected returns on crop is discussed. Value of River water entitlement is also discussed and its shown that with greater valuation of the entitlement the CVaR increases. Finally, a model extension is proposed in order to accommodate multiple crops.
In conclusion, the author would like to quote that his model is able to reveal the exposure to risk pertaining to risky and devastating events. It also quantifies the rate at which supply fails to meet the demand. The stochasticity accounts for the variability in water availability and crop requirements.
My Comments:
I think this paper is a preliminary inquiry into the using the CVaR concept for assessing risk in water resources decision making. The paper introduces the CVaR concept and provides a hypothetical application which requires a lot more detailed analysis before applying to a real problem of water resources decision making. There is scope for including stochasticity in crop prices and climate change to give a realistic model prediction in hand.
Monday, January 26, 2009
Assignment #1(a)
The article in review is by Dr. John C. Liebman, Professor of Environmental Engineering, University of Illinois Urbana-Champaign published in the "INTERFACES" journal published by INFORMS (Institute For Operations Research and the Management Sciences) in August, 1976.
Title: SOME SIMPLE-MINDED OBSERVATIONS ON THE ROLE OF OPTIMIZATION IN PUBLIC SYSTEMS DECISION-MAKING
This paper tries to address the suitability and role of quantitative modeling methods like optimization as a tool in public-systems decision making. The author illustrates various problems encountered in modeling by using two examples where public sector decision making is involved. The application of optimization techniques for improvements of effectiveness of urban firefighting organizations and also the problem of river basin quality management are discussed. It was indicated that the use of optimization techniques has contributed in the betterment of one and hasn't been so effective in the other, and this inspired the author to investigate further and put this paper together. The author emphasizes on the character of the public applications as a major factor in the success of the application of these techniques. The relative simplicity and clarity in the formation of objective functions, clear-cut and non-controversial goals and easily identifiable constraints would produce a better model and reliable and accurate results whereas, the more complex the problem becomes the tougher to model it and hence that even effects the reliability of the results. Though the nature of the problems do not change much but the employment of a complex technique requires availability of computing power and technical skills. In olden days, the method of linear programming was used for solving all sorts of optimization problems and a lot about the systems was assumed to be able to use LP. Nowadays, problems are considered to be more multi-objective and with fuzzy constraints. Methods like dynamic programming and meta-heuristics are at our disposal and computational power has been improved exponentially and is relatively inexpensive. Even after being able to model complex physical systems, there are human factors which are very tough to model. Public systems are highly interconnected and a simplified causal model is not always possible. In fact, no single optimal scenario is possible leading to controversy. Such complex problems are termed as "wicked" problems.The author also suggests the following to be kept in mind while modeling systems: a) Modeling is thinking made public. Its a way in which specialized knowledge is published in order to be reviewed, understood, critiqued by public; b) A model is not unique. Any systems can be modeled in several different ways according to what factors have been accounted for, the modelers/analysts perspective on the processes and the utility of the model or the end user. It is very well possible that models may have contradictory results on comparison and hence a better picture of the system can be obtained through putting all these model and their results together and to have a holistic view; c) The model is the message. The more complex the model the more tough it is to be understood by the non-modelers. Hence, it is advisable to have a set of simpler models which break down the more complex models and are easier to understand by the decision makers; d) Reinventing the wheel is not always bad. Its not necessary to use complex models to be used for a relatively simple problem/use and hence its advisable to have a simpler model of one's own if required which is more suited to the needs of the user. In conclusion, the author states that optimization methods have been applied to the private sector fairly successfully but they fail to perform when applied public systems due to their inherent "wickedness". Its very tough to be able to come to consensus in terms of objective functions and form tangible constraints with a lot of non-cooperation and non-conformity in the public systems which lead to conflicts. Optimization may not be applied to these problems unless these conflicts are resolved. It may be noted that even without such a resolution it is possible to apply optimization techniques which may illuminate these conflicts and present scenarios of decision making hence providing insights into the problem. Though finding answers may not be feasible when dealing with these wicked problems.
My observations:
I find this paper to be very objective and as it deals with the general idea of modeling problems it does illuminate some common and important points which are to be kept in mind while modeling. Though I believe that the context of the paper which dates back to the mid 70's is not fairly relevant to the present day as we dont only boast having the brute computational power and effective optimization methods at our disposal but also the advances in public policy, politics, social sciences etc which provide us with not only a better understanding of the wickedness but also a host of performing models which can be quantified and integrated in our system model for better results.
A possible future work on this paper would be a review of these advancements which occurred after its publishing and the coming up with another paper on similar lines.
Title: SOME SIMPLE-MINDED OBSERVATIONS ON THE ROLE OF OPTIMIZATION IN PUBLIC SYSTEMS DECISION-MAKING
This paper tries to address the suitability and role of quantitative modeling methods like optimization as a tool in public-systems decision making. The author illustrates various problems encountered in modeling by using two examples where public sector decision making is involved. The application of optimization techniques for improvements of effectiveness of urban firefighting organizations and also the problem of river basin quality management are discussed. It was indicated that the use of optimization techniques has contributed in the betterment of one and hasn't been so effective in the other, and this inspired the author to investigate further and put this paper together. The author emphasizes on the character of the public applications as a major factor in the success of the application of these techniques. The relative simplicity and clarity in the formation of objective functions, clear-cut and non-controversial goals and easily identifiable constraints would produce a better model and reliable and accurate results whereas, the more complex the problem becomes the tougher to model it and hence that even effects the reliability of the results. Though the nature of the problems do not change much but the employment of a complex technique requires availability of computing power and technical skills. In olden days, the method of linear programming was used for solving all sorts of optimization problems and a lot about the systems was assumed to be able to use LP. Nowadays, problems are considered to be more multi-objective and with fuzzy constraints. Methods like dynamic programming and meta-heuristics are at our disposal and computational power has been improved exponentially and is relatively inexpensive. Even after being able to model complex physical systems, there are human factors which are very tough to model. Public systems are highly interconnected and a simplified causal model is not always possible. In fact, no single optimal scenario is possible leading to controversy. Such complex problems are termed as "wicked" problems.The author also suggests the following to be kept in mind while modeling systems: a) Modeling is thinking made public. Its a way in which specialized knowledge is published in order to be reviewed, understood, critiqued by public; b) A model is not unique. Any systems can be modeled in several different ways according to what factors have been accounted for, the modelers/analysts perspective on the processes and the utility of the model or the end user. It is very well possible that models may have contradictory results on comparison and hence a better picture of the system can be obtained through putting all these model and their results together and to have a holistic view; c) The model is the message. The more complex the model the more tough it is to be understood by the non-modelers. Hence, it is advisable to have a set of simpler models which break down the more complex models and are easier to understand by the decision makers; d) Reinventing the wheel is not always bad. Its not necessary to use complex models to be used for a relatively simple problem/use and hence its advisable to have a simpler model of one's own if required which is more suited to the needs of the user. In conclusion, the author states that optimization methods have been applied to the private sector fairly successfully but they fail to perform when applied public systems due to their inherent "wickedness". Its very tough to be able to come to consensus in terms of objective functions and form tangible constraints with a lot of non-cooperation and non-conformity in the public systems which lead to conflicts. Optimization may not be applied to these problems unless these conflicts are resolved. It may be noted that even without such a resolution it is possible to apply optimization techniques which may illuminate these conflicts and present scenarios of decision making hence providing insights into the problem. Though finding answers may not be feasible when dealing with these wicked problems.
My observations:
I find this paper to be very objective and as it deals with the general idea of modeling problems it does illuminate some common and important points which are to be kept in mind while modeling. Though I believe that the context of the paper which dates back to the mid 70's is not fairly relevant to the present day as we dont only boast having the brute computational power and effective optimization methods at our disposal but also the advances in public policy, politics, social sciences etc which provide us with not only a better understanding of the wickedness but also a host of performing models which can be quantified and integrated in our system model for better results.
A possible future work on this paper would be a review of these advancements which occurred after its publishing and the coming up with another paper on similar lines.
Friday, January 23, 2009
On critical thinking and its need in engineering analysis!!
As quoted in Wikipedia.com (my favorite source for many things)
"Critical thinking consists of me processes of discernment, analysis and evaluation. It includes possible processes of reflecting upon a tangible or intangible item in order to form a solid judgment that reconciles scientific evidence with common sense. In contemporary usage "critical" has a certain negative connotation which does not apply to this specific case.[1] Though the term "analytical thinking" may seem to convey the idea more accurately, critical thinking clearly involves synthesis, evaluation, and reconstruction of thinking, in addition to analysis.
Critical thinkers gather information from all senses, verbal and/or written expressions, reflection, observation, experience and reasoning. Critical thinking has its basis in intellectual criteria that go beyond subject-matter divisions and which include: clarity, credibility, accuracy, precision, relevance, depth, breadth, logic, significance and fairness."
To me critical thinking constitutes analysis of a problem, process or event in an exhaustive way in means, knowledge and possibilities. It may or may not require a structured decomposition of an event and then studying each component (analysis) or studying the event with all the components together assuming interactions (systems approach). It may very well require us to think out of the box against general/well established approach towards such problems.
Introduction:
My first academic wish is to be able to be able to model/simulate anything i come across and like :D and I am sure I am not even close to be able to fulfill it yet. So, I have decided to keep it a little narrow and work on Environmental and Water Resources Systems and I find I may not still be able to fulfill my dream(Its not as narrow as I thought!!)
The CVEN-665 course is my first step towards acquiring skills in order to understand, model and simulate water resources systems and I am very excited about it.
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