Ertunga C. Özelkan

Multi-objective fuzzy regression: a general framework

Abstract Previous research has shown that in some cases fuzzy regression may perform better than statistical regression. On the other hand, fuzzy regression has also been criticized because it does not allow all data points to influence the estimated parameters, it is sensitive to data outliers, and the prediction intervals become wider as more data are collected. Here, several multi-objective fuzzy regression (MOFR) techniques are developed to overcome these problems by enabling the decision maker to select a non-dominated solution based on the tradeoff between data outliers and prediction vagueness. It is shown that MOFR models provide superior results to existing fuzzy regression techniques; furthermore the existing fuzzy regression approaches and classical least-squares regression are specific cases of the MOFR framework. The methodology is illustrated with rainfall-runoff modeling examples; more specifically, fuzzy linear conceptual rainfall-runoff relationships, which are essential components of hydrologic system models, are analyzed here. Scope and purpose The purpose of this paper is to develop a multi-objective fuzzy regression (MOFR) tool to overcome the shortcomings of existing fuzzy regression approaches while keeping their good characteristics, and to study systems with uncertain elements, using the example of rainfall-runoff processes to illustrate the approach. Previous research has shown that fuzzy regression might perform better than statistical regression in the following cases: when the data set is insufficient to support statistical regression analysis, when statistical distributional assumptions cannot be justified, if the aptness of the regression model is poor, when human judgements are involved (Bardossy. Fuzzy Sets and Systems 1990;37:65–75; Tanaka et al. IEEE Transactions on Systems, Man and Cyberneties, 1982;12 (6):903–7). On the other hand, fuzzy regression has also been criticized because it does not allow all data points to influence the estimated parameters, it is sensitive to data outliers, and the prediction intervals become wider as more data are collected (Redden and Woodall. Fuzzy Sets and Systems 1994;64:361–75, 1996;79:203–11). Here, several MOFR techniques are developed to overcome these problems by enabling the decision maker to select a non-dominated solution based on the tradeoff between data outliers and prediction vagueness. The methodology is illustrated with rainfall-runoff modeling examples; more specifically, fuzzy linear conceptual rainfall-runoff relationships, which are essential components of hydrologic system models, are analyzed here.

Fuzzy conceptual rainfall-runoff models

Abstract A fuzzy conceptual rainfall–runoff (CRR) framework is proposed herein to deal with those parameter uncertainties of conceptual rainfall–runoff models, that are related to data and/or model structure: with every element of the rainfall–runoff model assumed to be possibly uncertain, taken here as being fuzzy. First, the conceptual rainfall–runoff system is fuzzified and then different operational modes are formulated using fuzzy rules; second, the parameter identification aspect is examined using fuzzy regression techniques. In particular, bi-objective and tri-objective fuzzy regression models are applied in the case of linear conceptual rainfall–runoff models so that the decision maker may be able to trade off prediction vagueness (uncertainty) and the embedding outliers. For the non-linear models, a fuzzy least squares regression framework is applied to derive the model parameters. The methodology is illustrated using: (1) a linear conceptual rainfall–runoff model; (2) an experimental two-parameter model; and (3) a simplified version of the Sacramento soil moisture accounting model of the US National Weather Services river forecast system (SAC-SMA) known as the six-parameter model. It is shown that the fuzzy logic framework enables the decision maker to gain insight about the model sensitivity and the uncertainty stemming from the elements of the CRR model.

Reverse bullwhip effect in pricing

Price variability is one of the major causes of the bullwhip effect. This paper analyzes the impact of procurement price variability in the upstream of a supply chain on the downstream retail prices. Procurement prices may fluctuate over time, for example, when the supply chain players deploy auction type procurement mechanisms, or if the prices are dictated in market exchanges. A game theory framework is used here to model a serial supply chain. Sequential price game scenarios are investigated to show that there is an increase in retail price variability and an amplified reverse bullwhip effect on prices (RBP) under certain demand conditions.

Optimal fuzzy counterparts of scheduling rules

The optimality of a fuzzy logic alternative to the usual treatment of uncertainties in a scheduling system using probability theory is examined formally. Fuzzy scheduling techniques proposed in the literature either fuzzify directly the existing scheduling rules, or solve mathematical programming problems to determine the optimal schedules. In the former method, the fuzzy optimality for the optimal scheduling rules is usually not justified but still assumed. In this paper, the necessary conditions for fuzzy optimality are defined, and fuzzy counterparts of some of the well-known scheduling rules such as shortest processing time (SPT) and earliest due date (EDD) are developed.

Linear quadratic dynamic programming for water reservoir management

Abstract Dynamic programming (DP) is applied in order to determine the optimal management policy for a water reservoir by modeling the physical problem via a linear quadratic (LQ) structure. A simplified solution to the LQ tracking problem is provided under mild assumptions. The model presents an aggregated multicriteria decision making problem where flood control, hydroelectric power, and water demand have to be satisfied: Simultaneously the energy production is to be maximized, the mismatch of water demand minimized, and the water release should not cause flooding. The system constraints are basically the conservation of mass within the reservoir system, and the minimum and the maximum allowable limits for the water release and the reservoir level. The stochastic variables consist of the water inflow from the reservoir drainage basin precipitation, and evaporation. The Tenkiller Ferry dam on the Illinois River basin in Oklahoma is analyzed as a case study.

When Does RFID Make Business Sense for Managing Supply Chain

Radio frequency identification (RFID) is believed to change how supply chains operate today. While RFID’s promise for improved inventory visibility and automation in inventory management is making many supply chain players hopeful for increased sales and reduced operating costs, these benefits do come at a cost and involve risks. This article presents a financial returns analysis that captures RFID’s costs and benefits, and quantifies the financial risks of implementing RFID for various business sizes and products with different unit profits to understand when RFID makes business sense. More precisely, the returns analysis is performed using an econometric model to understand how break-even sales volumes, unit profits, tag prices, return on investment, and risks vary between a manufacturer and a retailer in a supply chain. The results are extended to multiproduct cases as well. A sensitivity analysis is also performed to understand the returns in pessimistic and optimistic scenarios.

Relationship Between Monthly Atmospheric Circulation Patterns and Precipitation: Fuzzy Logic and Regression Approaches

In order to link the monthly areal precipitation to large-scale circulation patterns, a fuzzy indexing technique is used in conjunction with a fuzzy rule-based technique and also a standard linear regression. After clustering the lag-correlation centers, fuzziness is introduced, and several representative indices of the monthly areal precipitation in Arizona are calculated and interpreted. The relation between the indices and the precipitation is analyzed to develop the fuzzy model and then a multivariate linear regression model. To measure the forecasting capability of the models, the data are divided into a calibration period (1947–79) and a validation period (1980–1988). A comparison of the results shows that the fuzzy rule-based model performs better than the regression model and has potential for monthly precipitation forecasting. Moreover, an adaptive fuzzy rule-based framework is described so that the model can be used under climate change.

Conditions of reverse bullwhip effect in pricing for price-sensitive demand functions

Supply chain mechanisms that exacerbate price variation needs special attention, since price variation is one of the root causes of the bullwhip effect. In this study, we investigate conditions that create an amplification of price variation moving from the upstream suppliers to the downstream customers in a supply chain, which is referred as the “reverse bullwhip effect in pricing” (RBP). Considering initially a single-stage supply chain in which a retailer faces a random and price-sensitive demand, we derive conditions on a general demand function for which the retail price variation is higher than that of the wholesale price. The investigation is extended to a multi-stage supply chain in which the price at each stage is determined by a game theoretical framework. We illustrate the use of the conditions in identifying commonly used demand functions that induce RBP analytically and by means of several numerical examples.

FUZZIFIED EFFECT OF ENSO AND MACROCIRCULATION PATTERNS ON PRECIPITATION: AN ARIZONA CASE STUDY

A fuzzy rule-based model (FRBM) is developed to analyse local monthly precipitation events conditioned on macrocirculation patterns and El Nino-Southern Oscillation (ENSO). A case study in Arizona is presented to illustrate the methodology. The inputs of the FRBM are those Southern Oscillation Index (SOI) values which have high absolute lag correlation with monthly Arizona precipitation and the frequencies of all circulation patterns (CPs) in a given month; the output of the model is an estimate of local monthly precipitation. After analysing the basic properties of the precipitation events, fuzzy rules are constructed, and then the results are interpreted and compared with those of a multivariate linear regression model. Using two goodness-of-fit criteria, first, the root mean squared error (RMSE) and then the correlation between the model results and the observed values, the FRBM is found to perform better than the multiple linear regression model for the Arizona case investigated. The results show that the FRBM can provide a good basis for future work to downscale general circulation model results to study local precipitation under climate change. The results of using only SOI lags or CP frequencies as inputs, which are also presented here, clearly show how much the results are improved using both inputs jointly instead of only one. Copyright

A multi-objective fuzzy classification of large scale atmospheric circulation patterns for precipitation modeling

A multi-objective fuzzy rule-based classification (MOFRBC) technique is applied in order to cluster and classify daily large scale atmospheric circulation patterns (CPs) and analyze the relationship between the CPs and local precipitation. The methodology is illustrated by means of an Arizona case study. For this purpose, three indices are calculated to measure the information content of the clustering method in terms of predicted precipitation. A thorough sensitivity analysis is provided to gain more understanding on the robustness of MOFRBC model. Furthermore, it is shown that extending the daily premises to two-day and three-day sequences of CPs improves the information content of the classification. The results are also compared with the original subjective clustering. For the Arizona case study MOFRBC seems to be a competitive technique with the advantage that the physical aspects can be better represented by fuzzy rules (which tend to mimic the human way of decision making) than by objective methods.