AdvancesinMeasurementSystems556 contrary, in 2005 and 2006 (and in 2009 too; data are not presented here) the monthly average temperature at both points was below the norm and it was accompanied with the strongly pronounced spring maximum of the surface ozone concentration. Fig. 7. Comparison of day time ozone concentrations in Minsk and Preila in 2008 Positive deviations of temperature for the Preila station are a bit lower in the most cases than on the average for Belarus, and negative deviations are a bit higher on the amplitude. However, to directly link this distinction with the difference in monthly average values of the ozone concentration does not seem to be possible. It is also difficult to analyze relation of temperature fluctuations and the surface ozone concentration in winter months, when concentration of ozone is minimal, and an influence of measurement errors can be quite essential. An actual similarity of seasonal changes of the surface ozone concentration in Minsk and Preila, their identical dependence on the temperature (for the spring maximum) indicate that both stations most of the time are affected by the same field of the tropospheric ozone, originated from a global circulation of air masses in the Northern hemisphere. Only local factors specifically ‘modulate’ this field, resulting in differences of daytime results of measurements and a diurnal course. These distinctions disappear after averaging over the time interval, exceeding the period of the synoptic phenomena typical for territories of both countries (a few days and more). Multi-wavedifferentialopticalabsorption spectroscopysurfaceozonemeasurementwithopenpathmeters 557 Fig. 8. Diurnal course of the surface ozone concentration (average hour data) in Minsk and in Preila during 24-28 July 2008. One can view intensification of exchange with the upper troposphere under the exposition of the growing solar radiation as a main reason for the origination of the spring maximum of the surface ozone concentration. This suggestion is repeatedly expressed in Звягинцев, 2003, 2004; Звягинцев & Кузнецова, 2002 and other papers, though, the argumentation brought herein, has an indirect character. Quite evident, that the revealed anticorrelation of surface ozone concentration with the air temperature at a time of the spring maximum is not in any agreement with the mechanism of a photochemical generation of ozone in the polluted air. The similar situation has evolved with such a parameter of the atmosphere, as the total ozone amount (TOA). Concentration of the surface ozone is a TOA component and according to Белан et al., 2000 gain in the TOA leads to a reduction of the surface ozone concentration because of easing sun UV radiation initiating a surface photochemistry. We have compared a course of the total ozone amount over Belarus and the surface ozone concentration for the whole period of observation. As a result, any correlation appears not to be revealed (compare figures 5a, 5c). AdvancesinMeasurementSystems558 9. Conclusion The proposed multi-wave technique for determining surface ozone concentration by means of an optical open path meter is, in principle, of general type and may be modified to consider any specific realization. The given mathematical formalism allows analysing the influence of spectra discrepancy of the sounding radiation that emitted to the working and reference paths. It is shown that this discrepancy results in a constant systematic error of the ozone concentration. The given mathematical formalism is employed to assess the role of different errors in the formation of the resulting uncertainty in the calculated ozone concentration. An idea lies in finding the link between errors in signal measurements, errors in parameters of the instrument and parameters of the calculation method and generated by those errors distinction in sounding radiation spectra on the working and reference paths. Such a distinction is simply referred to an error in a calculated ozone concentration. Analytical expressions are given to estimate role of errors of different nature. For example, for the optical open path surface ozone meter TrIO-1 it is shown that the errors in signal measurements and errors in definition of absorption cross-sections have the dominant role in the formation of the resulting error in ozone concentration measurement. Some results received with the optical open path ozone meter TrIO-1 within the multi-wave method are presented. A revealed link of the spring ozone maximum and average temperature is of special interest. In particular, it is obviously conflicts with the hypothesis of the photochemical origin of the spring ozone maximum. 10. References Bolot’ko, L.M.; Pokatashkin, V.I.; Krasovskii, A.N. & Tavgin, V.L. (2004). Optical trace measurer of surface ozone concentration. Journal of Optical Technology, Vol. 71, No. 1, pp. 48-50, ISSN 1070-9762 Bolot’ko, L. M.; Krasovskii, A. N.; Lyudchik, A. M. & Pokatashkin V.I. (2005). Measurement of the terrestrial ozone concentration by absorption UV spectroscopy. Journal of Applied Spectroscopy, Vol. 72, No. 6, pp. 911-916, ISSN 0021-9037 (Print) 1573-8647 (Online) Bolot’ko, L.M.; Krasovskii, A.N., Lyudchik, A.M. & Pokatashkin, V.I. (2007). Optical track measurements of the near-earth ozone concentration using a multiwave technique under conditions of local thermal convection. Journal of Optical Technology, Vol. 74, No. 4, pp. 270-273, ISSN 1070-9762 Bolot’ko, L. M.; Krasovskii, A. N.; Lyudchik, A. M. & Pokatashkin, V. I. (2008a). Ozone optical track analyzer TrIO-1 and its metrological certification features. Measurement Techniques, Vol. 51, No 10, pp. 1139-1142, ISSN 0543-1972 (Print) 1573- 8906 (Online) Bolot’ko, L. M.; Demin, V.S.; Krasovskii, A. N.; Lyudchik, A. M. & Pokatashkin V.I. (2008b). Multiwavelength procedure for determining the concentration of near-ground ozone by an optical open-path measurement system. Journal of Applied Spectroscopy, Vol. 75, No 2, pp. 268-274, ISSN 0021-9037 (Print) 1573-8647 (Online) Edner, H.; Ragnarson, P.; Spännare, St. & Svanberg, S. (1993). Differential optical absorption spectroscopy (DOAS) system for urban atmospheric pollution monitoring. Appl.Opt., Vol. 32, No. 3, pp. 327-333, ISSN 0003-6935 (Print) 1593-4522 (Online) Multi-wavedifferentialopticalabsorption spectroscopysurfaceozonemeasurementwithopenpathmeters 559 Frohlich, C. & Shaw, G.E. (1980). New determination of Rayleigh scattering in the terrestrial atmosphere. Appl. 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ООО «Обнинская фотоника», Обнинск Intermediatemeasuresconsiderationforavaluechain ormultistagesystem:anefciencyanalysisusingDEAapproach 561 Intermediate measures consideration for a value chain or multistage system:anefciencyanalysisusingDEAapproach WaiPengWongandKuanYewWong X Intermediate measures consideration for a value chain or multistage system: an efficiency analysis using DEA approach Wai Peng Wong 1 and Kuan Yew Wong 2 1 School of Management, Universiti Sains Malaysia, Malaysia. 2 Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, Malaysia. 1. Introduction It has been recognized that performance evaluation is extremely important as the old adage says “you can’t improve what you don’t measure”. Companies using performance measurement were more likely to achieve leadership positions in their industry and were almost twice as likely to handle a major change successfully (Wisner et al., 2004). Today, business performance is evaluated not only in terms of a single business unit but rather the entire value chain. Performance measurement of the entire value chain is a lot more difficult and complex compared to the performance measurement of a single business unit. When managing a value chain, apart from the formidable multiple performance measures problem, assessing the performance of several tiers, e.g., suppliers, manufacturers, retailers and distributors further complicates the matter. Basically, there are two main problems in value chain performance measurement, which are a) existence of multiple measures that characterize the performance of each member, for which the data must be acquired, b) existence of intermediate measures between them, e.g., the output from the upstream can become the input to the downstream which further complicates the performance assessment. As noted in Wong and Wong (2007 and 2008), DEA is a powerful tool for measuring value chain efficiency. DEA, developed by Charnes et al. (1978), is a well-established methodology used to evaluate the relative efficiency of a set of comparable entities called Decision Making Units (DMUs) with multiple inputs and outputs by some specific mathematical programming models. DEA can handle multiple inputs and outputs and it does not require prior unrealistic assumptions on the variables which are inherent in typical supply chain optimization models (i.e. known demand rate, lead time etc) (Cooper et al. 2006). These advantages of DEA enable managers to evaluate any measure efficiently as managers do not need to find any relationship that relates the measures. We point out that DEA’s vitality, real-world relevance, diffusion and global acceptance are clearly evident, as supported from such literature studies as Seiford (1996) and Gattoufi et al. (2004a and 2004b). There are a number of DEA studies on value chain efficiency; yet, most of them tend to focus on a single chain member. This can be partly due to the lack of DEA models for the entire value chain or multi-stage systems. Note that DEA cannot be 23 AdvancesinMeasurementSystems562 directly applied to the problem of evaluating the entire value chain efficiency because the value chain cannot be simply viewed as a simple input-output system as conceptualized in DEA. Within the context of DEA, there are some recent models, e.g., by Fare and Grosskopf (2000) and Golany et al. (2006), which have the potential to address a value chain in a powerful way. Recently, Liang et al. (2006) developed two classes of DEA-based models for supply chain efficiency using a seller-buyer supply chain setting. They used the game theory approach to analyze the effect of one member having on another. One similarity of the recent models for addressing the chain effect or multilayer system is that they take into consideration the presence of intermediate measures; their differences lie in their mechanic system design. The issue of intermediate measures was initially addressed by Banker and Morey (1986) in a service industry which operates in a single layer. The model separates the inputs/outputs into two groups, i.e., discretionary and non-discretionary; non-discretionary inputs/outputs are exogenously fixed inputs/outputs that are not controllable and their values are predetermined. The current chapter provides an alternative way to measure value chain or multistage efficiency which is by taking into consideration the effect of the intermediate measures in the system. We draw on previous Banker’s model and extend the model construction for value chain. We analyze its dual formulation and explain how it suits the value chain setting. This chapter contributes to the existing value chain or multistage system literature by providing an alternative model to measure value chain or multistage efficiency. This model is simple and easy to understand. Though, this model may not have addressed all the concerns in value chain or multistage system, it can still serve as a tentative solution for measuring the efficiency of these systems. In the following section, we will review Banker’s model by analyzing its dual formulation and then provide the insight on how it can address the value chain or multistage efficiency. Then we present an application study to show the usefulness of the model. 2. Theoretical foundations In this section, we first discuss the foundations of DEA. Then, we show the dual formulation of the Banker’s model and explain how it can better characterize the value chain or multistage system. 2.1 Basic DEA methodology Build upon the earlier work of Farrell (1957), data envelopment analysis (DEA) is a mathematical programming technique that calculates the relative efficiencies of multiple decision-making units (DMUs) based on multiple inputs and outputs. Assume S to be the set of inputs and R the set of outputs. J is the set of DMUs. Further assume that DMU j consumes x sj 0 of input s to produce y rj 0 of output r and each DMU has at least one positive input and one positive output (Fare et al., 1994). Based on the efficiency concept in engineering, the efficiency of a DMU, says DMU j 0 (j 0 J), can be estimated by the ratio of its virtual output (weighted combination of outputs) to its virtual input (weighted combination of inputs). Intermediatemeasuresconsiderationforavaluechain ormultistagesystem:anefciencyanalysisusingDEAapproach 563 To avoid the arbitrariness in assigning the weights for inputs and outputs, Charnes et al. (1978) developed an optimization model known as the CCR model in ratio form to determine the optimal weight for DMUj 0 by maximizing its ratio of virtual output to virtual input while keeping the ratios for all the DMUs not more than one. The fractional form of a DEA mathematical programming model is given as follows: RrSsvu xv yu xv yu sr Ss sjs Rr rjr Ss sjs Rr rjr           ,0, 1.s.t max 0 0 (1) where u r and v s are the weights for the output r and input s respectively. The objective function of Model (1) seeks to maximize the efficiency score of a DMUj 0 by choosing a set of weights for all inputs and outputs. The first constraint ensures that, under the set of chosen weights, the efficiency score of the observed DMU is not greater than 1. The last constraint ensures that the weights are greater than 0 in order to consider all inputs and outputs in the model. A DMUj 0 is considered efficient if the objective function of the associated Model (1) results in an efficiency score of 1, otherwise it is considered inefficient. Using the Charnes-Cooper transformation, this problem can be further transformed into an equivalent “output maximization” linear programming problem as follows: RrSsvu xv Jjxvyu yu sr Ss sjs Ss sjs Rr rjr Rr rjr          ,0, 1 ,0.s.t max 0 0 (2) Model (2) is known as the CCR model in multiplier form. If the objective function value of (2) is equal to 1, it implies that the DMU concerned is relatively efficient since we can find a weight combination to make its efficiency score to be equal to one. Despite the linear form of (2), efficiency score is usually calculated based on its dual problem: AdvancesinMeasurementSystems564 Jj Rryy Ssxx j rj Jj jrj sj Jj jsj o o        ,0 , ,.s.t mi n     (3) Model (3) is known as the input-oriented CCR in envelopment form or the Farrell model, which attempts to proportionally contract DMUj 0 ’s inputs as much as possible while not decreasing its current level of outputs. The  j values are the weights (decision variables) of the inputs/outputs that optimize the efficiency score of DMU j 0 . These weights provide measures of the relative contributions of the inputs/outputs to the overall value of the efficiency score. The efficiency score will be equal to one if a DMU is efficient and less than one if a DMU is inefficient. The efficiency score also represents the proportion by which all inputs must be reduced in order to become efficient. In a similar way, we can also derive the output-oriented CCR in envelopment form if efficiency is initially specified as the ratio of virtual input to virtual output. A large number of extensions to the basic DEA model have appeared in the literature as described by Ramanathan (2003) and Cooper et al. (2006). We shall limit our discussion to this basic model as this is sufficient to lead us to the explanation of the following model to address a value chain or multistage system. 2.2 The DEA analysis of value chain efficiency. Consider a value chain relationship as follows, e.g., supplier – manufacturer with inputs and outputs as described in Figure 1. This may also be viewed in terms of a multistage process, e.g., a product has to go through two stages of a manufacturing process: assembly (stage 1) and testing (stage 2). We may further categorize the inputs and outputs into two types, i.e., direct and indirect or intermediate. Direct inputs/outputs are associated with a single stage or member only and they do not affect the performance of other stages / members. For example, supplier cost and supplier revenue are direct inputs and outputs for the supplier only, they have no impact on the manufacturer. Intermediates are those inputs/outputs that are associated with two or more stages/members. For instances, ontime delivery is the performance of the supplier in delivering its products; it is also a cost measure to the manufacturer which relates to inventory holding cost. [...]... flexibility’ It refers to the agility of a value chain in responding to marketplace changes to gain or maintain competitive advantage It is also known as the ‘upside production flexibility‘ It refers to the number of days required to achieve an unplanned, 570 Advances in Measurement Systems sustainable, a certain percent increase in production One of the common constraints to cycle time is material availability... of the experiment is to provide an insight on the importance of characterizing a value chain or multistage system We will show from the results that, by considering the presence of intermediate measures in the value chain of multistage system, there are potential input savings in the system We present the DEA efficiency results in Table 3 572 Advances in Measurement Systems CCR model (Model 3) Stage... represents the timing diagram of the MDC during a single measurement cycle for accuracy better than  0 f t1 1 1 F 2 3 =1/f T=1/F n n-1 t2 N -1 N N high frequency pulses t3 N t t n low frequency pulses TC 1 TC2 TC t1 t2 t3 t Fig 10 Timing diagram of the MDC during a single measurement cycle (accuracy better than ) 586 Advances in Measurement Systems To obtain a relative measurement error... virtual sensor is a sensor that can provide indirect measurement of several variables by using data processing algorithms that are applied to direct measurement s results provided by a single sensor 5 Influence variables are variables that are cross-correlated with measuring variables affecting measurement s accuracy 2 578 Advances in Measurement Systems It is beyond the scope of this chapter to describe... the concerns in value chains or multistage systems, it can serve as a tentative solution for measuring the efficiency of these systems This model can be further enhanced by analyzing how different settings of weights affect the overall value chain or multistage performance In addition, future research can also look into how to adapt the model in uncertain environments, e.g., by utilizing the Monte... counted during conversion period (TC), respectively As represented in figure 10, TC is an integer number (n) of the low frequency signal period () The conversion period contains a number of high frequency pulses equal to N plus a remaining number of pulses N contained in time interval TC2 Minimum and maximum values of quantization error are associated with the minimum and maximum number remaining pulses... an International Journal, Vol .15, No.1, pp.25-51, ISSN: 14635771 Wong,W.P., Jaruphongsa, W., Lee, L.H (2008) Supply Chain Measurement System – A Monte Carlo DEA based approach International Journal of Industrial and Systems Engineering, Vol 3, No.2, pp.162-188, ISSN:1748-5037 Analog to Digital Conversion Methods for Smart Sensing Systems 575 24 X Analog to Digital Conversion Methods for Smart Sensing... we model a value chain setting based on the global value chain system of multinational semiconductor corporations There are three levels in the proposed setting, e.g., supplier, manufacturer and retailer This can also be viewed in terms of a multistage process, e.g., first stage (assembly), second stage (testing) and third stage (final inspection/packaging) We use the supply chain operations reference... intermediate (indirect) measures in Banker’s model From the basic DEA model in fractional (ratio) form, let’s denote IS as the set of intermediate inputs, DS as the set of direct inputs, x tj as the tth intermediate input of DMU j and observed DMU j0 Note that DS  IS  S xtj0 as the tth intermediate input for the 566 Advances in Measurement Systems max u y rj0  r rR v x t tIS v x u y  v x v x s sj0... (2009) Principles of Supply Chain Management: a Balanced Approach South-Western Cengage Learning, ISBN: ISBN13: 9780324657913, U.S Wong, W.P., Wong, K.Y (2007) Supply chain performance measurement system using DEA modeling Industrial Management & Data Systems, Vol 107, No.3, pp.361-381, ISSN: 0263-5577 Wong, W.P., Wong, K.Y (2008) A review on benchmarking of supply chain performance measures Benchmarking: . errors in the formation of the resulting uncertainty in the calculated ozone concentration. An idea lies in finding the link between errors in signal measurements, errors in parameters of the instrument. that the errors in signal measurements and errors in definition of absorption cross-sections have the dominant role in the formation of the resulting error in ozone concentration measurement. . days required to achieve an unplanned, Advances in Measurement Systems5 70 sustainable, a certain percent increase in production. One of the common constraints to cycle time is material availability.