Proceedings of the American Society for Engineering Management 2014 International Annual Conference S. Long, E-H. Ng, and C. Downing eds. THE ENERGY CONVERSION EFFICIENCY PERSPECTIVE ON PRODUCTIVITY Katharina Renken Texas Tech University 201 Industrial Engineering Building, Lubbock, TX 79409 Katharina.Renken@ttu.edu Diana Barraza-Barraza Texas Tech University & Tecnológico de Monterrey Av. Eugenio Garza Sada 2501 Sur. Monterrey, NL 64849 Diana.Barraza@ttu.edu Leonidas Guadalupe Texas Tech University 201 Industrial Engineering Building, Lubbock, TX 79409 Leonidas.Guadalupe@ttu.edu ____________________________________________________________________________________________ Abstract Engineering managers use productivity measures for performance evaluation and decision-making. The common assessment of productivity normally considers a simple fractional relationship of revenues over costs, where desirable productivity occurs when the system delivers higher revenues than the volume point of costs, leading to a productivity index value larger than one; implying that the output is greater than the input. However, the second law of thermodynamics states it is impossible to convert energy completely into work in a closed system. Contemporary productivity tools do not follow this law because they assume open systems in which energy can enter and exit a system, and they do not concern themselves with externalities imposed on meta-systems. This leaves an opportunity to create a different perspective on the efficiency of work. This paper uses the laws of thermodynamics to develop a formula that shifts the perception of productivity measures. The dynamics of the formula are explored, and comparative examples show the advantages and disadvantages of this theoretical approach. Results of a pilot survey show that the new proposed method does not have an impact on managerial decisions. Keywords Productivity, measurement framing, closed system, decision-making, perception Introduction The theory of a zero energy universe supports the notion that the universe is a closed system, composed of negative and positive energy that balance out to zero (Berman, 2009). While no physical evidence is yet available to prove this hypothesis; if life cannot exist without energy, then it is prudent to behave as if the universe was a closed system with a finite amount of energy. A congruent argument has also been made for Earth’s natural resources (Hardin, 1968). Yet, when management evaluates productivity, it uses an open system perspective. The traditional productivity measure ( � for a system is the proportion of output to its respective input (Sumanth, 1997, p. 4), detailed in Equation (1). If this proportion is less than whole, then the system is considered unproductive because it consumes more than it produces. A system with productivity of one is at break-even, while a system with a productivity value above one is a productive system. � = � (1) This traditional way of calculating productivity considers producing more than what was put into the system as a productive venture. This dynamic violates the laws of physics and potentially distorts the perspective of management, because the belief in productivity above one ignores economic externalities created by the effort to increase productivity. Proceedings of the American Society for Engineering Management 2014 International Annual Conference S. Long, E-H. Ng, and C. Downing eds. Externalities are consequences incurred by parties outside of the system. Economist liken negative externalities, or “external costs”, to taxation without representation (Levitt & Dubner, 2009, p. 171). As an example, an engineering manager seeking to increase the productivity of a manufacturing facility could choose to increase sales at a cost that is lower than the output gained. This will increase the productivity of the manufacturing facility but does not take into account: increased emissions from manufacturing processes, increases in the local energy and water consumption, increase in the market supply, or the decrease in natural resources for raw materials . It ignores the laws of physics and removes a consciousness of the external meta-system. This perspective has the potential to create a negative decision frame. Research and lab experiments have shown that the frame of decision alternatives can actually influence human choice (Tversky & Kahneman, 1981). A decision frame is the way a person perceives the results of a decision. It is partially affected by the formulation of the problem, and the decision maker’s personal characteristics, norms or habits (Tversky & Kahneman, 1981, p. 453). This phenomena is still relevant in many fields, including: business (Clark, Quigley, & Stumpf), healthcare (Abhyankar, Summers, Velikova, & Bekker, 2014), and social work (Jacobson, 2013). In some contexts framing can have stronger effects if time between exposure is shorter (Lecheler & De Vreese, 2010). In engineering, framing contributes to an effect so strong that it influences measurements. The Pygmalion defect shows that illusory measurements can appear based on expected performance (Beruvides & James, 1997; James, 1998). Implanting an expectation of a high number of defects caused engineering students to spot more defects than were actually present (James, 1998). Other effects related to framing include: the money illusion (Shafir, Diamond, & Tversky, 1997), asymmetric dominance (Tversky & Simonson, 1993), and loss aversion (Kahneman & Tversky, 1979). All of these concepts work as evidence showing that the nature of information presented can have an effect on the decision maker. One of the main arguments against the power of decision framing is the thought that repeated decisions will tend to shift toward a rational equilibrium over time. However, compounding cognitive effects like arbitrary coherence and the optimism bias would lead to a contrary conclusion. The concept of arbitrary coherence explains that estimates and decisions deviate from an anchor point, which does not necessarily relate to the current situation. This effect was demonstrated by showing the differences in bids correlated to a random stimulus of social security numbers (Ariely, Loewenstein, & Prelec, 2003). It questions the assumptions of independence between management decisions based on measurements. Intensifying this course of action is the optimism bias, which provides managers with confidence about previous decisions without causal evidence (Sharot, 2011). The evidence of the psychological effects presented, pose an interesting quandary for engineering managers. If the way we measure affects our decision making process, then the measure of productivity itself must affect our decisions. Does changing the way productivity is measured, change the decisions of engineering managers? In particular, would adopting a productivity measure, based on energy conservation of efficiency, lead to more conservative decisions? This paper proposes a productivity measure based on the principle of energy conservation. It then contrasts the mathematical characteristics of both measures, and provides an illustrative example of implementation. Finally, the paper culminates with a discussion on the results of a pilot survey, which outlines the direction of future research in this area. Formulation The laws of thermodynamics serve as the basis for the formulation of this new measure‘s perspective. The first law of thermodynamics states that energy cannot be created nor destroyed (Young & Freedman, 2004). Therefore, when we consider a "black box" system, output cannot be greater than the input. In addition, the second law of thermodynamics says that it is impossible to convert heat completely into work (Young & Freedman, 2004). For that reason, we will consider it impossible for a system to be 100% productive. In addition, if no output is generated then the productivity measure is zero. With the support of these axioms, the range of the productivity measure can be set. The limits to the productivity measure will be a minimum of zero, and a maximum value infinitely close to one. The logical construction of this tool begins with the extremes. A situation in which no output is realized by the system should yield the productivity minimum limit of zero. This is similar to the traditional method in Equation (1), where an output of zero will yield zero productivity regardless of the amount of input. The mathematical maneuver that will generate this relationship is to ultimately multiply the rest of the unknown energy conservation efficiency ( ��� ) equation. Equation (2) illustrates this with an [�] representing the equations unknown part. ��� = ∗ [ �] (2) The logical development of the maximum now deals with an asymptote which resembles the inherit loss of energy through work within a closed system. If energy is lost through work, then the final stage of the system is The Energy Conversion Efficiency Perspective on Productivity smaller than that of the beginning stage. This is because the final stage has the output, but the beginning stage has the output component plus the components of the input that contributed to the work. Equation (3) mathematically expresses this proportional relationship. ��� = +� (3) Equation (3) satisfies the logical requirements for a closed system perspective on productivity because the output alone will never be as big as the output plus the input. There is an assumption that the input must always be bigger than zero, because the concept of energy conservation only applies if energy exists. If input is zero, then there is no energy to conserve. This new equation should provide a better decision frame for productivity, with respect to a closed meta-system. The formula does not internalize any externalities like the emissions or unintended consequences, but it just provides decision frame that is conscious of a system subject to externalities. Evaluation The two different methods for evaluating productivity ( ��� and � ) provide different perspectives for data evaluation. Graphical demonstrations of their dynamic behavior serve as testaments to this notion. First, consider a system that is able to produce more with the same level of input. Exhibit 1 (left graph) presents the trends where system output increases and input remains stable. The ��� increases, but it does so logarithmically. When input is significantly smaller than the growing output, ��� appears to rise sharply to one, but does not reach it. Conversely, ��� exhibits slower growth when input is closer in value of output. In situations where the output is fixed and the input increases, the ��� decays logarithmically (right graph). The intensity of this drop also depends on the magnitude of the relationship between output and input. Exhibit 1. Productivity behavior on output/input changes A direct comparison of dynamics of the two formulas serves as best evidence for the perceptual differences Exhibit 2 graphs the dynamics of both ��� (left graph) and � (right graph). The surface areas with lighter shading represent higher values of productivity. The values of encompassing the output range are 0 and 10, while input range was 1 to 3. It must be noted that � does not have a limit of one imposed on it. The graph only shows its behavior dynamics, which will be identical regardless of the vertical scale on this graph. The ��� surface shows a curved surface that reacts favorable toward decreasing input. While the � resembles a slanted plane that appears to equally favor increasing output, and decrease input. Proceedings of the American Society for Engineering Management 2014 International Annual Conference S. Long, E-H. Ng, and C. Downing eds. Exhibit 2. 3D Graph for ��� Exhibit 3. Example application for and ��� � and behavior � measurements Example To demonstrate the contrast between both measurements in an applied scenario, a productivity example was studied (Sumanth, 1997, pp. 229-230). The example details productivity measures for two product lines, which for this illustrative example are considered sequential projects. The measures for the first project are considered period one through three, while those for the second project are periods four through six. Exhibit 3 shows the calculated productivity for six periods using both approaches. The top graph shows both, � and ��� together. The graph shows that both measures exhibit the same pattern of behavior (increases and decreases), but the ��� tones down The Energy Conversion Efficiency Perspective on Productivity the magnitude of change. For example, from period two to three there appears to be sharp increase in � , but only a slight increase in ��� . In reality, they are both communicating the same information. When � falls below breakeven in period six, ��� also falls below break-even. The bottom graphs show the measures isolated, which reduces the visual illusion of difference. The bottom left graph shows � with its corresponding measure of break-even, while the bottom right graph shows ��� graph with its corresponding measure of break-even. An engineering manager looking at the bottom left graph might make a decision that does not necessarily correspond to a response by another manager that is provided the graphic on the bottom right. Pilot Study The proof of concept for the perceptual differences between these two measures requires empirical evidence gathered through different methods. This paper uses pilot survey to detect initial evidence of productivity measurement formulation affecting managers’ decision strategies. Survey methodology was selected as a costeffective way to gather information in a short period of time that allows observing a possible difference in decision making between the two productivity measures, from a convenient sample. This study surveyed 93 engineering students. Demographics were not collected in this survey, but the majority of students were undergraduates because the samples came from two undergraduate engineering classes, with a capacity of 50 students each, and one considerably smaller graduate class. The voluntary survey is in the Appendix. There were two versions of the survey. One version used � and the other used ��� to measure productivity. Both surveys were identical with respect to the decision strategies available. The participant could either reduce/increase costs or increase/reduce sales. Selecting either choice would lead to the same productivity measure. For example, an engineering manager at break-even could choose to focus on doubling sales or cutting cost in half. Both of these options would lead to the same productivity measure. A difference in decision preference would indicate an influence by the productivity measure. Exhibit 4 presents the results of the surveys. Exhibit 4. Survey Results Costs- Response count 50 ��� Sales- ��� Costs- Sales- 40 30 20 10 0 Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Exhibit 4 shows no visually apparent difference between the strategy choices. It seems that the selection of a productivity improvement policy is independent from the approach followed to calculate productivity. The data was collected on a contingency table presented in Exhibit 5, where the table’s rows count the number of questions answered for each formula, and the columns present the number of responses that either cut costs or increased sales. A total of 651 responses were generated through 93 surveys. There was one case were a participant circled both options, this response was not considered in the analysis because no preference was shown. A Chi-Squared test for independence using contingency tables supported the insignificant results. The ChiSquared test for independence assumes that the sample of N observations is random, and each observation may be classified into exactly one row-category and one column-category (Conover, 1999). Both assumptions are met because the surveys were randomly assigned and answered with no interaction between students; and because a valid answer only considers one improvement strategy for each question of the survey. Proceedings of the American Society for Engineering Management 2014 International Annual Conference S. Long, E-H. Ng, and C. Downing eds. Exhibit 5 . Contingency table of responses and Chi-Squared test for Independence Output Contingency Table: Formula, Strategy Formula 1 2 All Strategy Sales Costs 170 159 166 156 336 315 Total 329 322 651 Pearson's Chi-squared = 0.001, df = 1, P-Value = 0.976 Conclusion This paper proposes the notion that the decisions of an engineering manager could be affected by how productivity is calculated. It formulates a productivity measure based on energy conservation efficiency. The ��� shows that reduction of costs is more favorable than increasing revenue once the measure is above break-even. A side by side demonstration of the tool also shows that the effects of the changes in productivity are more pronounced with � . A pilot survey did not find that the use of either formula influenced the decision strategy of 93 engineering students. This venture did not find any significant results showing a difference between the two measures. However, this pilot study also served as a quick method of collecting feedback. Future studies examining the phenomena of measurement framing should involve more detailed design of experiments; including case studies where the different measures are actually implemented. A study on the demographics of the respondents might also contribute valuable insights, as suggested by one of the reviewers of this paper. Engineering managers are not capable of internalizing all of the externalities incurred by the meta-system caused by a managerial decision. Instead embedding a consciousness into the measurement tools of engineering managers could have a positive impact on the way we manage. References Abhyankar, P., Summers, B. A., Velikova, G., & Bekker, H. L. (2014). Framing Options as Choice or Opportunity Does the Frame Influence Decisions? Medical Decision Making, 0272989X14529624. Ariely, D., Loewenstein, G., & Prelec, D. (2003). 'COHERENT ARBITRARINESS': STABLE DEMAND CURVES WITHOUT STABLE PREFERENCES. Quarterly Journal of Economics, 118(1), 73. Berman, M. S. (2009). On the Zero-Energy Universe. International Journal of Theoretical Physics, 48(11), 32783286. Beruvides, M. G., & James, M. R. (1997). The Pygmalion Deffect: Measurement Systems Corruptibility under Conditions of Innocent Bias. Proceedings from ASEM Annual Conference, Virginia Beach, VA. 1-4p. Clark, K. D., Quigley, N. R., & Stumpf, S. A. The Influence of Decision Frames and Vision Priming on Decision Outcomes in Work Groups: Motivating Stakeholder Considerations. Journal of Business Ethics, 1-12. Hardin, G. (1968). The Tragedy of the Commons. Science, 162(3859), 1243-1248. Jacobson, H. (2013). Framing Adoption: The Media and Parental Decision Making. Journal of Family Issues, 0192513X13479333. James, M. R. (1998). The corruption of a simple measurement system due to unintentional bias. (Masters Thesis), Texas Tech University. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. Lecheler, S., & De Vreese, C. (2010). What a Difference a Day Made? The Effects of Repetitive and Competitive News Framing Over Time. Conference Papers -- International Communication Association, 1. Levitt, S. D., & Dubner, S. J. (2009). SuperFreakonomics: Global cooling, patriotic prostitutes, and why suicide bombers should buy life insurance. New York: William Morrow. Shafir, E., Diamond, P., & Tversky, A. (1997). Money illusion. The Quarterly Journal of Economics, 112(2), 341374. Sharot, T. (2011). The optimism bias. Current Biology, 21(23), R941-R945. Sumanth, D. J. (1997). Total Productivity Management (TPmgt): A Systemic and Quantitative Approach to Compete in Quality, Price and Time: Taylor & Francis. The Energy Conversion Efficiency Perspective on Productivity Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science, 211(4481), 453-458. Tversky, A., & Simonson, I. (1993). Context-dependent preferences. Management Science, 39(10), 1179-1189. Young, H. D., & Freedman, R. A. (2004). University Physics (11th Edition ed.). San Francisco, CA: Pearson Education Inc. About the Authors Katharina Renken, is a teaching assistant and Ph.D. student in Industrial Engineering at Texas Tech University. She obtained two master’s degrees in Engineering, one from Texas Tech University and one from Jade Hochschule, Germany. Furthermore, she gained knowledge and experience in the container port industry while working as a project engineer at JadeWeserPort in Germany. Her research focuses on green energy, business processes and emergency management. Diana Barraza-Barraza, is a Ph.D. student in a dual program between Texas Tech University and Tecnológico de Monterrey with majors in Systems and Engineering Management and Industrial Engineering, respectively. She obtained a master’s degree in Applied Statistics from Tecnológico de Monterrey, Mexico. Her major areas of interest are maintenance management, reliability, engineering management, design of experiments and response surface methodology. Leonidas J. Guadalupe, is a research assistant and Ph.D. student in Systems and Engineering Management in the Industrial Engineering Department at Texas Tech University. He holds an MBA and a BS in Industrial and Systems Engineering from Florida International University. His research focuses on improving systems through quantitative analysis of decision-making and behavioral observations. Proceedings of the American Society for Engineering Management 2014 International Annual Conference S. Long, E-H. Ng, and C. Downing eds. Appendix Exhibit 6 and Exhibit 7 display the two versions of the survey used in the pilot study. Exhibit 6 . Survey Version A Imagine you are a manager of a manufacturing plant. You measure your productivity with the formula: Sales / Costs = Productivity When Productivity is 1, you breakeven and you neither gain nor lose money. A series of choice sets will now be presented to you. Please circle which of the choices indicate the course of action you would take as the manager for the manufacturing plant. 1. Your current productivity is now 1.0. Which of the two alternatives would you prefer? Double Sales OR Cut Cost in Half 2. Your current productivity is now 2.0. Which of the two alternatives would you prefer? Increase Sales by 25% OR Decrease Costs by 20% 3. Your current productivity is now 2.5. Which of the two alternatives would you prefer? Multiply your Sales by four OR Reduce Costs by 75% 4. Your current productivity is now 10. Which of the two alternatives would you prefer? Quintuple Sales OR Reduce Cost by 80% 5. Your current productivity is now 50. Which of the two alternatives would you prefer? Triple your Sales OR Reduce Costs by 2/3 6. Your current productivity is now 150. Which of the two alternatives would you prefer? Increase Sales by one third OR Reduce Cost by 25% 7. In general, which strategy would you prefer as a Manager? Increase Sales OR Reduce Cost The Energy Conversion Efficiency Perspective on Productivity Exhibit 7 . Survey Version B Imagine you are a manager of a manufacturing plant. You measure your productivity with the formula: � � �= �� �� +� When Productivity is 0.5, you breakeven and you neither gain nor lose money. A series of choice sets will now be presented to you. Please circle which of the choices indicate the course of action you would take as the Manager for the manufacturing plant. 1. Your current productivity is now 0.5. Which of the two alternatives would you prefer? Double Sales OR Cut Cost in Half 2. Your current productivity is now 0.667. Which of the two alternatives would you prefer? Increase Sales by 25% OR Decrease Costs by 20% 3. Your current productivity is now 0.714. Which of the two alternatives would you prefer? Multiply your Sales by four OR Reduce Costs by 75% 4. Your current productivity is now 0.909. Which of the two alternatives would you prefer? Quintuple Sales OR Reduce Cost by 80% 5. Your current productivity is now 0.980. Which of the two alternatives would you prefer? Triple your Sales OR Reduce Costs by 2/3 6. Your current productivity is now 0.993. Which of the two alternatives would you prefer? Increase Sales by one third OR Reduce Cost by 25% 7. In general, which strategy would you prefer as a Manager? Increase Sales OR Reduce Cost