Data envelopment analysis of reservoir system performance

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Abstract

In long-term performance analyses of water systems with surface reservoirs for different operating scenarios, the analyst (or decision maker) is faced with two connected problems: (1) how to handle the extensive output of the simulation model and derive information on the scenarios scores for a prescribed set of performance criteria, and (2) how to compare scenarios in a multi-criterial sense while identifying the most desired. The data sets may overburden the analyst, while an evaluating procedure may be subjective due to personal preferences, attitudes, knowledge and miscellaneous factors. The data envelopment analysis (DEA) approach proposed here seems to be reliable in treating these situations, and sufficiently objective in evaluating and ranking the scenarios. Certain performance indices are defined as evaluating criteria in a standard multi-criterial sense, and then virtually divided into scenarios' output and input measures. By considering scenarios as product units, the DEA optimizes the weights of inputs and outputs, computes productivity efficiency for each unit, and rank them appropriately. Omitting the analyst's personal judgment on the technical parameters that describe system's performance restricts, in this way, the influence of the decision maker. A case study application on the reservoir system in Brazil proved that a methodological connection for solving decision problems with discrete alternatives really exists between the DEA and standard multi-criteria methods.

Introduction

The reservoir system long-term operation is most often analyzed with a simulation model. Such a model must be capable to emulate the system behavior for various management scenarios and applied strategies of the reservoirs' control. The model must handle complex priority schemes in water allocation, treat both consumptive and non-consumptive water uses, and supply the user with reports on water balances at reservoirs and control points of interest. The simulation itself is a difficult task because it usually requires a comprehensive data preparation of the hydrologic part, such as the inflows, precipitation, evaporation, and demands, as well as the operational part, such as the system configuration, simulation parameters, rule curves for reservoirs, and priorities in allocation. Even when data has been prepared correctly and the model has been run with success, particular requirements exist in managing and interpreting its output. Namely, at the end of one typical simulation, the analyst can easily be disoriented by rich but distributed information contained in series of data describing supplies and shortages at demand points, reservoir storage levels and balances, flows in rivers and canals, and various summary reports.

Well-known models for reservoir system simulation are generally equipped with a graphical interface, which makes the results transparent and helps the analyst to derive certain conclusions on system performance. However, if several operating scenarios have to be compared, an output report might be significantly enlarged, and difficulties arise in cross-referencing important data. In reality, scenarios are usually characterized by different priority schemes related to demands and the reservoirs control strategies. With an increase in the number of reservoirs and/or demand points, reports on system operation even for very few scenarios may overburden the analyst, and make almost impossible deriving the right conclusions on advantages and disadvantages of simulated operating strategies. We argue that a new paradigm is required to compare scenarios and point to the best or most desirable one. A central issue is to define criteria set that would govern a comparison process. Because criteria are usually conflicting and of different importance, criteria weighting must be performed preferably by the analyst, or decision maker. A reasonable dilemma might be whether to compare scenarios in an unbiased manner, or to use the subjective judgments of the decision maker? Rather, the question is will the decision maker correctly and consistently compare scenarios, or whether it is more opportune to avoid the decision maker and let the scenarios decide for themselves which one is the best ? (Doyle [1]).

In this paper, we address the described problem and propose a methodology of evaluating the long-term performance of the reservoir system under different scenarios by multi-criteria analysis based on data envelopment analysis (DEA) (Charnes et al. [2]). We first define a number of indices of system performance: supply reliability, resiliency, vulnerability, and the dispersion of reservoirs' storage levels. As performance constructs, they enable the analyst to evaluate and rank scenarios in an unbiased manner once the scenarios are simulated, system performance indices computed, and necessary data is integrated into a multi-criteria analysis framework. The performance indices are adopted as a criteria set and treated within the DEA context.

Originally developed to evaluate efficiency of product units with multiple inputs and multiple outputs, the DEA method is recently used as a discrete multi-criteria decision making (MCDM) method as well. By implementing a methodological connection that allows the decision (performance) matrix typical for standard MCDM methods to be used as a productivity matrix typical for DEA (see, e.g., Sarkis [3]), we solve the comparison problem and measure the efficiency of scenarios searching for the most efficient and ranking the others. We argue that the most efficient scenario identified by the DEA may be considered the best in a MCDM sense. For the sake of completeness, several MCDM methods have been also used to check the result obtained by the DEA. A comparative analysis performed for a real system case example showed a good conformance of the scenarios ranking obtained by DEA and standard MCDM methods, and indicated that a methodological connection exists.

The proposed methodology has been applied in evaluating several long-term management scenarios for the selected two-reservoir system in Brazil. The chain of consecutive tasks is performed to come-up to the final task of the analysis—to compare scenarios. With data on system configuration and with parameter sets and rules that govern the system operation for a 30-year period, multiple simulations have been performed by the network LP-based model MODSIM (Labadie [4], Porto et al. [5]). A system operation is simulated for each scenario, and the selected model output has been evaluated by another programming system (SYSPER—acronym of `System Performance') to determine failures and non-failures in meeting specified system targets. Various demands are analyzed at the system level with adopted schemes of accounting for the total demands, total supplies, and other data that describe system performance. Tolerant shortages are specified to distinguish failures and non-failures, that is to enable computing behavioral characteristics of the system for each scenario such as: total supply reliability, resiliency, and vulnerability. An additional performance indice is defined to provide for measuring the reservoirs ability to follow their own rule curves and determine the stability of each reservoir performance, e.g. the recognition of extreme drawdowns related to hazard operating conditions such as extreme depletions during long drought periods.

The aforementioned system characteristics are adopted as performance criteria and used afterwards for ranking the scenarios. The synthesis part of the methodology requires creating the performance matrix with cross-reference data on system performance for analyzed scenarios. This matrix serves as the starting point for the application of DEA, computing scenarios efficiencies, and the final ranking. Two versions of the DEA method have been used to accomplish the task: the original CCR model developed by Charnes et al. [2], and its reduced version RCCR proposed by Andersen and Petersen [6]. To verify the results obtained by the DEA, the following MCDM methods have also been used: the Analytic Hierarchy Process (AHP) [7], the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) [8], the Compromise Programming (CP) [9], the Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE) [10], and the Simple Product Weighting Method (SPW) [11].

We first present the basic characteristics of two proposed DEA models (Section 2). Then we introduce four indices proposed as the principal criteria for measuring the reservoir system performance and evaluation of the water management scenarios (Section 3). A description of proposed methodology (Section 4) is followed by an example application (Section 5). The main conclusions (Section 6) close the paper.

Section snippets

DEA fundamentals

The DEA is a method based on linear programming, which is becoming an increasingly popular management tool. It is commonly used to evaluate the efficiency of a number of `units' such as a group of producers, banks, or hospitals characterized by multiple inputs and outputs. In fact, the DEA is suitable for evaluating almost any relatively homogeneous set of units, but nowadays it is also recognized as a decision aid in multi-criteria analyses of discrete alternatives.

In contrast to statistical

Measures of reservoir system performance

Long-term performance of the reservoir system is typically measured by an evaluation of the volumetric flows of water through a system, including those conserved in reservoirs. It was shown that the system's performance might efficiently be measured with respect to some prespecified targets and preferences [18], [19], [20], [21]. By defining the tolerant shortages in the water supply, or acceptable deviations from the prescribed reservoir rule curves, it was also shown that it is possible to

Ranking management scenarios by DEA

An analysis of the reservoir system performance for a given set of management scenarios means that multiple simulations of system operation should be performed by a certain computer model, followed by the creation of the multi-criteria decision-making environment, and concluded by a consistent comparison process which will produce the final ranking of the scenarios and point to the `best'. If possible, a simulation model would be instructed to record the desired information on system states

Phase 1: Problem statement, setting the evaluation criteria and creating scenarios

Given is the reservoir system in the Paraguacu river basin in Brazil, Fig. 2, which consists of reservoirs Franca and Sao Jose de Jacuipe with maximum capacities of 24 and 355 millions of m3, respectively. For given historical data in period 1930–1959 characterized by long droughts, and estimated demands for planning period 2001–2030 at 5 delivery points within the system, the total of 6 long-term management scenarios is created. The problem is to evaluate the scenarios' quality over a 30-year

Conclusions

We have shown how to apply the DEA in an unbiased evaluation of the reservoir system performance for various operating scenarios. A decision-making environment typical for water resources planning and management is assumed, and the evaluation of scenarios is considered as a multi-dimensional problem requiring various decision tools be applied. An underlying assumption is that the simulation models for the reservoir systems generate extensive output files for system configurations including more

Acknowledgements

The authors wish to thank CNPq and FAPESB in Brazil for financial support of this research.

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