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Extramural Research

Final Report: Environmentally Conscious Design and Manufacturing with Input Output Analysis and Markovian Decision Making

EPA Grant Number: R825345
Title: Environmentally Conscious Design and Manufacturing with Input Output Analysis and Markovian Decision Making
Investigators: Olson, Walter , Pandit, Sandar , Sutherland, John
Institution: Michigan Technological University , University of Toledo
EPA Project Officer: Karn, Barbara
Project Period: October 1, 1996 through September 30, 1999 (Extended to December 30, 2000)
Project Amount: $180,000
RFA: Technology for a Sustainable Environment (1996)
Research Category: Pollution Prevention/Sustainable Development

Description:

Objective:

The objective of this research was to develop analysis and decision making tools for the manufacturing plant manager that implement the Society of Environmental Toxicology and Chemistry (SETAC) life-cycle assessment (LCA) philosophy giving due consideration for manufacturing costs and environmental impacts. The proposed environmental decision-making methodology provides managers with a means to make better decisions about processes to minimize the costs and the environmental impacts associated with them. Envisioned in this project were the use of input-output analysis as developed by Wassily Leontief for inventory and impact analysis and the application of Markovian Decision Making (MDM) to optimize improvement analysis project selection. Because of the historical quantity of data found to exist, it was necessary to invoke time series analysis methods including autoregressive-moving average analyses to refine the data for control and decision making purposes.

Summary/Accomplishments (Outputs/Outcomes):

A summary of progress is presented below:

  • Developed the economic input-output models for manufacturing plants.
  • The theory of input-output hidden Markov modeling for estimating process data was researched.
  • Developed an ARMAV model for a manufacturing process and applied an optimal controller to reduce the environmental impact of the process.
  • Completed the Markov decision making methodology to decide which improvement projects to execute and what contingencies to that choice exist.
  • Procured the hardware necessary to establish a Web site for providing the results of this project.
  • Produced 12 publications and 5 Master of Science Theses.
  • Completed two Ph.D. thesis proposals with final theses due in 2001.

The initial efforts to meet the objectives were to develop an analysis methodology that catalogs the materials used by a manufacturing process as well as their interactions. It was clear from the start of the project that the machines and hardware of the process could be analyzed using the existing theory of LCA. However, the functions of the process had to be treated differently. Processes are subsystems of manufacturing plants. Processes are related by the input and output flows of materials between the processes and the conversions that occur.

Technically, there are four types of conversions that can occur as the result of a manufacturing process:

  1. The change of material chemistry, material formulation, or material structure.
  2. The deformation of material shape without addition or subtraction of material.
  3. The removal of material resulting in an increase of primary outputs over the primary inputs.
  4. The joining and assembly of materials resulting in a decrease of primary outputs over the primary inputs.

Each process is applied sequentially to the outputs of a process before it. The state of the product determines the next process operation. The structure of the plant flow is modeled by a linear Markov chain. It was these characteristics that led to the selection of input-output analysis and MDM for a solution to the problem of performing plant LCAs.

Data Collection and Generation. During the first phase of the project, an attempt was made to identify and apply input-output analysis to active industrial processes. A limited test and demonstration of feasibility was applied to a truck frame manufacturer. The test case resulted in the development of a data set which was amenable to input-output analysis and thus showed that the method was valid.

This method has not been fully applied to a large active plant due to the inaccessibility of the data. At first, the plant managers stated that the data requested were not being collected and kept. Where data did exist, the data were declared to be competitive and proprietary to the company. At the time of data collection, the U.S. Congress was considering making all data collected as a result of a federally funded project open to the public. Therefore, the corporate collaborators to this project withheld critical data. To gain data relevant to the project and to proceed with the research in light of this problem, several possible solutions were investigated. The researchers already had considerable data collected as the result of previous research projects. This was used extensively for various analysis purposes. Public information is available through the trade literature and through federal and state plant reporting requirements. Both data collected previously and the publicly available date proved to be incomplete. To solve the completeness problem, hidden Markov models (HMM) were explored to develop data representative of operating facilities.


There are three basic requirements that must be met to use HMM: (1) the model generating the data has a Markovian structure, (2) the data are stochastic, and (3) the range of the data is bounded above and below. We already have shown that manufacturing data are both Markovian and stochastic. Manufacturing processes are capacitated?that is, they meet the requirements of upper and lower bounds. This technique was explored and has the potential of creating the missing data within the project. However, this part of the work was not completed because of the untimely departure of the Ph.D. student performing this investigation. Therefore, work remains to be completed in the future.

Input-Output Analysis. The first step was to build the transaction table. The transaction table usually is quite large with rows representing each plant input and columns representing each plant output. Mass of material is used as the unit of transfer. The transaction table is an inventory analysis under the LCA structure. Because most plants have stochastic inputs and outputs, the values used in the transaction table should be developed with a times series such as vector autoregressive moving averages (ARMAV), which was done for plant cutting fluid systems. Such method, if properly applied, will identify trends that may be useful in determining system impacts.

This table is converted to a transaction matrix, T, for IOA analysis. An entry of T, tij, represents
the conversion from an input on row i to an output on column j. In a plant transaction matrix, most elements are zero. The reason for this is that in most plants only a few materials are used ubiquitously in all processes. For example, in producing a steel truck frame, which was examined in this work, hydrochloric acid was used only in the scale removal step, one of 14 process steps. As a result, its contributions to other material outputs will be small or none.

An output vector, Y, is constructed such that element yi is the conversion to material i from another form either used internally in the model or from the final output. The element yi is formed by summing over columns of T on row i and then adding any final outputs, zi. These are the control variables that are varied to effect changes in related sectors. The matrix of technical coefficients represents the fraction of the input usage to the total output of column. The technical coefficient, aij, is created by dividing the t matrix entries by the output vector. For example, in the IOA analysis of the truck frame plant, the technical coefficient for the conversion of chemicals to the waste water was 0.0337. Thus, 3.37 percent of the waste water discharge is from chemicals used in body preparation. If the process remains stationary, a requirement to reduce waste water also requires that chemicals be reduced.

We assumed that we could halve the waste water output while maintaining the system. However, in reality, process changes are the result of multiple conditions including changes in external outputs and the results of engineering projects applied to the plant. The plant manager is faced with a large set of options, many of which are mutually exclusive. The plant manager rarely has the resources to perform all the possible options. Thus, the plant manager has to chose which projects to perform. To answer this question, we turned to Markovian decision making discussed later in this report.

ARMAV Modeling. Using the model of the manufacturing plant and of the processes within the plant, it is possible to make an improvement analysis and improvements using the data collected. In the model below, we used cutting fluid data collected during a previous research project to demonstrate the procedure. The ultimate goal is to reduce the impact of the cutting fluid systems. The models developed helped to understand the dynamics of the processes.

Cutting fluids are an essential part of the metal cutting process in large plants. Although one can question the need for cutting fluids in the cutting process, the cutting fluids play a critical role in moving swarf away from the cutting zone and the machine tool as well as in corrosion prevention. The cutting fluids in the examples are oil-water emulsions. At this time, the use of cutting fluids appears to be the least impact process available for machining operations. However, cutting fluids have drawbacks in waste disposal because the fluids must be treated before discharge to a municipal waste water plant. Focusing on this environmental impact, it was identified that the major reasons for disposal was the growth of bacteria in the oil and the failure of the cutting fluid to meet the oil concentration specifications. These were measured by observing the pH of fluid and the volume of oil.

The pH of the oil is important because it has been found that the bacteria growth is inhibited at pH values of 9 and above, whereas lower values encourage bacterial growth. Bacterial growth contributes to odor problems as well as potential human disease. The control factor for pH is the addition of the caustic, sodium hydroxide (NaOH). The oil concentration is controlled by adding oil to the fluid. These last two additions are the control variables in the model.

Four systems were analyzed using the modeling technique. System A was a 2,040-gallon system
used to steel machine turbine shafts. System B was a 5,060-gallon system provided cutting fluids for the manufacturing of aluminum automatic transmission valve bodies. System C was a 20,000-gallon system manufacturing planet gears. Finally, System D was a 24,000-gallon supply for machining automatic transmission stator supports. The critical variables modeled for these systems were the input of NaOH caustic, represented by variable X1t; the amount of soluble oil added, X2t; the pH measured, X3t; and the measured oil concentration, X4t. In each data set for each system, there were 241 data points with these four values. Each point corresponded to a working day of the plant.

Initially, an extended autoregressive-moving average (EARMA) model was constructed to represent the system dynamics between caustic and pH and between oil added and oil concentration. The EARMA (3,3,2) model satisfies the 95 percent confidence interval. The roots of the model are given in Table 1.

Table 1. Roots of the Caustic pH Model.

Roots Natural Frequency (days) Damping Ratio
Real Imaginary
0.1447 0.1394 3.532 0.9023
0.9737       

From the roots of the model, the period of the model is 3.532 days with a damping ratio of 0.9023. Because of the high damping ratio, the period does not exhibit a strong influence on the system. This also can be interpreted as any addition of caustic will have a pronounced delayed effect on the system. Additionally, because the roots are less than one, the system is stable.

The oil added-oil concentration model required an EARMA (4,4,3) with the results shown in Table 2.

Table 2. Roots of the Oil Added-Oil Concentration Model.

Roots Natural Frequency (days) Damping Ratio
Real Imaginary    
0.2301      
0.3661 0.8870 5.3248 0.03495
0.9923      

The low damping ratio of the model indicated that the system exhibits a high periodicity of 5.3 days. This corresponds to the normal work week of the plant, possibly suggesting that the lack of system maintenance on the weekends is very prominent when the work week begins with respect to oil concentration. Again, the steady state conditions show that oil additions have a positive effect on the oil concentration.

Next, a two input, two output, ARMAV model was built. The number of terms exceed the ability to display the model in this format. However, the summary information can be provided. Table 3 shows the steady state relationships between the various variables in the model. In addition to the expected results that the additions of caustic and oil have positive influences on their respective output measures, there is a strong positive relationship between caustic addition and oil concentration. This can be interpreted that eliminating bacteria growth results in less oil being consumed by the bacteria and, therefore, improving the oil concentration. Note, however, that adding oil decreases the pH because the oil pH is lower than 9.

Table 3. Steady State Relationships Between ARMAV System Variables.

  EARMA Models ARV Model      
  Added
C
Added
Oil
pH Oil
Conc.
Added
C
Added
Oil
pH Oil
Conc.
Added C - - -0.6262 - - 0.3861 -0.0771 -0.3391
Added
Oil
- - - -1.9579 0.1089 - -0.0604 -0.1507
pH 1.8267 - - - 22.06 4.1154 - 8.3385
Oil
Conc.
- 0.2167 - - -0.8648 5.6634 0.0324 -

The system inputs were used to control the output responses with the result that the overall impacts are reduced. An LQR optimal controller was formulated. Similar computations were performed for all systems. To determine the effectiveness of this control strategy, the system was simulated with a different set of actual data with 241 points. The existing results were compared with the simulations. These results are summarized in the Table 4.

Table 4. Summary of Analyses of Fluid Systems.

System A
Added Caustic
(gal)
Added Oil
(gal)
pH
Variance
Oil Conc. Variance
Original
System
24.1457
948.8921
0.5008
1.3131
Optimal
Maintenance
Strategy
15.5404
230.9577
0.2607
0.4451
System B
Added Caustic
(gal)
Added Oil
(gal)
pH
Variance
Oil Conc.
Variance
Original
System
236.8856
1,0767
0.030
0.4715
Optimal
Maintenance
Strategy
107.1653
8843.8
0.003
0.0298
System C
Added Caustic
Added Oil
pH
Variance
Oil Conc. Variance
Original
System
96.2305
5821.7
0.0321
1.7663
Optimal
Maintenance
Strategy
48.8669
588.6024
0.0233
1.4181
System D
Added Caustic
Added Oil
pH
Variance
Oil Conc.
Variance
Original
System
17.9992
2,390
0.04
0.3416
Optimal
Maintenance
Strategy
11.2997
1,442.4
0.0162
0.1305

The system performance gains are significant. In System A, over a period of 1 year, only 15.5 gallons of caustic were needed under the controlled system, while the current policy used 24.1 gallons. The reduction of oil consumption was especially marked: added oil was 231 gallons compared to 949 gallons. The system variance indicates that the controlled system performs considerably closer to the design system mean than it does under the current maintenance policy. Overall, the cutting fluid system uses far less inputs of chemicals and oil. This represents both an environmental impact gain and a considerable operational cost savings.

Markovian Decision Making (MDM) Processes. MDM is based upon a probabilistic description of how state space variables will change under the influence of decision choices. In the manufacturing plant, decisions about a process are rarely independent from decisions concerning other processes. Managers usually are faced with several competing projects from which to choose. In addition the sequence in which projects are chosen determines both the environmental impact and the costs associated with plant improvements. MDM is used here to find optimum project choices as well as optimum project sequencing. A recommended procedure for employing the MDM was investigated. This procedure is outlined below:

  • Analyze the data by DDS, and the Input-Output method to determine environmental impact.
  • Determine the candidate processes for improvement.
  • Develop a state space model of stochastic processes.
  • Determine the decision space.
  • Formulate a multi-objective decision with trade-offs between environmental impact and cost.
  • Create the optimality criterion to minimize the environmental impact, energy and material consumption, and cost of manufacturing process.
  • Determine the optimal policy.
  • Develop contingency plans from a modified MDM.
  • Verify the proposed environmental optimization methodology of manufacturing processes in industry.

The starting point for the improvement analysis is the list of possible projects with their costs, likelihood of success, and the results of successful completion. The results are the states for the Markovian analysis. It is assumed that there are N projects that could lead to improved environmental impact. The result is a Markov chain.

For purposes of demonstrating the techniques described, a simple example based on plant data has been created. In a stamping mill, acid is used to descale sheet metal before stamping. Management after inventory analysis and an impact analysis has determined that a desirable goal would be to reduce acid by 150 lbs/40,000 lb coil of steel. Engineering analysis has developed the potential of five separate projects, of which several can be linked together to reduce acid. The projects are listed, indicating the possible reductions and the project costs. If the sum total of achieved reductions is greater than the goal state, the achievement is truncated to the goal state. The problem faced by the management is to determine which projects should be selected for execution and what contingencies exist.

Each project or project combination has a certain outcome based on the starting conditions of the project. The starting conditions and the outcomes are defined to be environmental states of the system. By convention, the current state of the unimproved system is considered to be state 1 of the system. It is assumed that no benefit results from having an acid reduction greater than 150 units. This too could be incorporated into the state structure if that is the case. The units of reduction, lbs acid/coil of steel, for the projects above were based upon design nominal values. However, projects do not always achieve design goals. A critical factor in determining an optimal project combination is the evaluation of the probability of each project to reach each goal state. This is argumentatively subjective based upon the experience of the manager and the analyst. It is necessary to determine the likelihood that a project will be successful because none of the projects have been completed and there is uncertainty of future events. One can successfully argue that utility theory based on the utilities of the decision maker can be applied here. In practice, few managers know what their utilities values are or are able to determine them. Therefore, a stream-lined approach is presented here that is subject to certain mathematical inconsistencies that are beyond the scope of this work.

We establish the likelihood of meeting the design outcome weight as 100 and then rate every other outcome in relation to that value. The weights can be altered at will. When satisfied with the appropriate weights, the weights are summed and each individual weight divided by that sum to arrive at estimated normalized probabilities.

In this example, the analyst weighted the design outcome at 100. Then, the likelihood of project failure, partial project success, and project outcomes become the design value were weighted. Partial project success was defined as a reduction of 25 acid units outcome for the remainder of the projects. Project over success was defined as achieving 25 units acid reduction more than the designed outcome. (Note: the first improvement state is 50 units reduction; therefore, if project A were applied at state 1 and achieved only a partial success, this would be deemed the same as a failure in this analysis. Of course, another state could be added at 25 units reduction, but that was not done here.)

Projects when executed cause transitions in the states depending upon their outcomes. In this chain, each node is a decision node where decisions about what project to commit is based upon the current state of the system in units of acid reduction. The structure may be classified as an "absorbing chain." That is, after some number of transitions, a sequence of projects will be successful. If this were not the case, the goals of improvement would not be met. In the case where a project fails, it is terminated and replaced by a new and different project. In the worst possible case, it may be decided that the goal cannot be met and all improvement project work is terminated, which also is an absorbing state. In the example, it was assumed that projects will be executed until the goal state is reached. The internal states contributing progress to projects are transient.

From this analysis, the relative risk of a set of improvement options can be determined. Plant managers are inherently risk adverse. Thus, plant managers need to know not only how likely an
improvement project will succeed, but also what could happen if the project fails or results in a state different than intended. Based on that knowledge, plant managers prepare contingency plans. Above and beyond the optimization of environmental project selection, the method also includes the mechanics to determine where failures are potentially possible. Furthermore, the economics of the improvement need to be incorporated into the decision process.

The goal in the example is to reach state 6 (150 units acid reduction). One could simply execute project E at a cost of $175K. Clearly, there are better ways of reaching the goals. Assuming that the outcomes of projects are additive (this is not a required assumption), a less expensive way of achieving the goal is to execute project A ($40K) to arrive at state 2 and project C ($80K) to arrive at state 6 to reach the goal for a cost of $120K. However, this does not take into account the likelihood that the projects will be successful. Project E has a probability of success to the design state of 0.771, whereas the less expensive method has only a 0.862 * 0.855 or 0.737 probability of success at the design state. Therefore, there are trade-offs between costs and risks. Taking every possible option, there are 3,125 possible combinations for this example.

This problem lends itself to the policy improvement algorithm. This algorithm was first explored by Howard in 1960. It does not appear from the literature, however, that this algorithm has heretofore been applied to environmental improvement projects. The algorithm consists of two steps: policy evaluation and policy improvement. To initialize the algorithm, a feasible set of projects to meet the goal is selected. This set of projects is a policy. Then two quantities, values (vi) and gains (gi), are computed for the policy using the formula:

equation

where pij is the Markov transition probabilities and qi is the policy state costs. The gains and values are found by solving the linear equations with the assumption that one or more of the values is zero. Because this case produces an absorbing state (state 6) without further benefits or costs, it is intuitive that state 6 will have a value of zero in the solution. Therefore, the value for state 6, v6, is set to zero for the solution of gains and values.

The second step of the algorithm requires that the gains and expected costs of other decision alternatives be computed using the solution for values obtained from the first step. The gains can be used as a test of optimality if they are different for the alternatives. In this case, however, they are not. If an alternative exists with a lesser cost, the policy is replaced with the policy containing the lesser expected cost alternative. Then, step one is executed again. Optimality exists only if no other alternative results in a lesser expected cost than the current policy. The algorithm stops when no further improvement is possible.

Findings. This work established two new methodologies for reducing the environmental impact of manufacturing products or processes. State space modelling and optimization provide a method to select system operational parameters to minimize environmental impact. Historical data representing measurements of the investigated system inputs and outputs can be used for analyzing and modeling the system dynamics. Complex multiple input-multiple output ARV models are generated for system descriptions. After transferring the obtained vector model into a state space form, optimal feedback gain can be computed and the new control policy can be proposed. A new method identifying all possible contingency plans in order of preference was developed. The contingency planning can be done before any project execution with known statistical outcomes or during project execution after crises arise. This is extremely important in planning budgets and in choosing specific improvement projects. This method identifies the risks and what needs to be done to minimize risks.

Contributions Within Discipline. This work establishes a new methodology for reducing the environmental impact of manufacturing products or processes. An input-output analysis has been proposed as augmenting the current LCA inventory techniques to arrive at impact analysis on the manufacturing plant. Historical data representing measurements of the investigated system inputs and outputs can be used for analyzing and modeling the system dynamics. EARMA models can be computed for understanding the parameters of the system dynamics such as time constants, decay ratios, frequencies, etc. Additionally, complex multiple input-multiple output ARV models should be generated for complete system description. After transferring the obtained vector model into a state space form, optimal feedback gain can be computed and the new control policy can be proposed. New projects proposed for improvement analysis of LCA are prioritized for planning using Markovian Decision Making techniques.

Contributions to Education and Human Resources. This project has directly led to the education of nine graduate students. In addition, more than 200 other engineering college students have been exposed to the results of this project. Through outreach efforts via the automotive industries, and particularly the Society of Automotive Engineers, the findings of this project have been used in the education of engineers at Michigan Technological University, the University of Toledo, and the University of Wisconsin-Madison.

Contributions to Resources for Science and Technology. This research has explored directly the use of Operation Research tools and theory in the advancement of reducing environmental impacts. It has provided new information to various engineering courses and provides a sound foundation for further research. Through cost sharing arrangements at the University of Toledo, in which the university agreed to provide a cost match to the original research grant, this research project brought state-of-the-art computer workstations to the university. This, in part, led the university to reconsider how it networks computers and provides Web services as this project posed new demands on the existing systems.

Contributions Beyond Science and Engineering. This project has resulted in effective means to decrease environmental impacts of products used by the public. In addition, these results have been disseminated to the U.S. Environmental Protection Agency.


Journal Articles on this Report : 1 Displayed | Download in RIS Format

Other project views: All 18 publications 1 publications in selected types All 1 journal articles

Type Citation Project Document Sources
Journal Article Milacic D, Gowaikar H, Olson WW, Sutherland JW. A proposed LCA model of environmental effects with Markovian decision making. Transactions of the Society of Automotive Engineers-Journal of Passenger Cars 1997;6(6 Pt 1):2174-2181. R825345 (Final)
not available
Supplemental Keywords:

manufacturing environmental impact, input-output analysis, EARMA models, LCA improvement analysis, Markovian decision making techniques, integrated assessment, pollution prevention, clean technologies, waste reduction, waste minimization, decision making, non-market valuation, Bayesian, engineering, mathematics, economics, modeling, analytical, industry., Sustainable Industry/Business, cleaner production/pollution prevention, computational simulations, in-process changes, life cycle analysis, cleaner production, computer generated alternative synthesis, waste reduction, environmentally conscious manufacturing, modeling, industrial process, process modification, innovative technology, life cycle assessment, product life cycle, waste monitoring, waste streams, industrial innovations, pollution prevention, Markovian decision making

Relevant Websites:

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http://www.mfg.mtu.edu/Archives/MTU_4_ever.htm Exit EPA icon
http://www.mfg.mtu.edu/jws/part-ners.html Exit EPA icon
http://www.mfg.mtu.edu/docs/thesis1.html Exit EPA icon
http://www.mfg.mtu.edu/Archives/MTU_4_ever.htm Exit EPA icon
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The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.

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