System Optimization

A step-wise method to optimize production systems is presented. The proposed method requires a holistic view of the company activities and the ability to determine where the main bottlenecks for the optimization method are. The method includes goal setting, proactive leadership, modularizing of company activities, mathematical optimization, control in a broad sense and automation of the optimization procedure.

2 Optimization Method

If a production company is viewed as a system, the major cost function is profit (f(x)). The vector of input parameters (x) can be viewed as all factors, controllable and uncontrollable, that affect the company activities. The controllable part contains mainly people, capital and natural resources. The most important scalars in the vector of constraints (g_i(x)) are time aspects, return on investment issues, competitors, laws and regulations and market demand. The assumed ideal solution to that optimization problem would be to model the profit and the constraints as functions of the input parameters:

The problem with that approach is that it is extremely hard, if not impossible, to model the functions.

One possible solution to the problem is to modularize or divide the company activities in separate smaller units, which are possible to model. Optimization of those smaller modules should then be carried out in sync with the overarching goal, maximized profit.

To achieve good results with this approach it is advantageous to follow the six-step method below.

1. Consider how the profit is going to be made. What is the company strategy and how should the goals be clearly defined?

2. Clarify what measurement methods to use, the measurement frequency, the calibration methods and frequency.

3. Identify and handle possible obstacles to the optimization (insufficient staff information or communication, inadequate hardware or software, etc)

4. Modularize the company activities and consider how to optimize each module without sub-optimizing the whole system.

5. Consider modeling/simulation/optimization and control methods. What are the input parameters? What are the output parameters? How much do they vary and why do they vary. What is the optimal set of input parameters? How do we maintain these optimal input parameters? Are they always the same?

6. To achieve good results on a longer term, consider continuous based optimization[2][2]. How should the new sets of optimal input parameters be efficiently found, as products and raw material change?

2.1 Goals and Measurements

Consideration of company strategy is of major importance. How is profit to be made? The company strategy could be found within a number of choices:

The choice of strategy will have a fundamental impact on what cost function to use and how the optimization should be carried out. The choices of goal lead to the question of choices of measuring methods to identify to what extent the goals have been fulfilled. Ensuring consistency in, and good calibration routines for the measurements are vital for valid measurement figures.

It is also important to have an efficient way of optimizing several parameters jointly (se figure 1 for an example). Otherwise, we risk sub-optimizing the ultimate goal; the profit.

_{Figure 1. Membership surface plot,
showing optimization of NOx and NH3 as a joint response.}

2.2 Obstacles

Optimizing a system as a whole, considering all aspects from goal setting to mathematical analysis, requires a proactive approach. Possible hurdles have to be considered at an early stage.

Support from the staff is a crucial parameter of success. Is the staff fully informed about the “optimization project”? How will the staff benefit from the optimization (the change)? The optimization might lead to changes in work tasks and how will that change be smoothly handled?

To optimize can be defined as “changing from one initial situation to a new “better” situation”. Since the time of Machiavelli it has been known that the word “change” means problems for most organizations. Change will meet strong resistance from those who think they might lose from the change and only lukewarm support from those who think they might win. It is therefore of great importance to give detailed information about the optimization project (the change) to everybody involved and prepare the handling of those that think they might lose on the upcoming “change”. It is of great importance that it is thoroughly analyzed who "everybody" is.

The fact that optimizations should result in an improvement of company activities hints that the current situation is not good, which could mean that those in charge of the current situation feel an indirect criticism. For that reason some parts of management might therefore be reluctant of the optimization. Thus, it is vital for the success of the project that it is led or co-led by the management that is directly responsible for the production and/or operations.

An optimization has to begin somewhere. A clarification of how the current company situation looks like is therefore necessary to establish an “initial set” of input parameters that can be varied in order to arrive at an optimal set of input parameters. The clarification of the current company situation might reveal a number of facts that might cause controversy and, again, some parts of management (or other groups) might be resistant to the idea of optimization (change). Proper preparation for that eventuality is advised.

Other questions to be answered are: Do we have the necessary tools to identify the current sets of input and output parameters? Do we have the necessary tools to identify the current variation and reasons for variation of the input and output parameters? Could inadequate communication be a reason for the variations? Communication between managers and managers, managers and operators, operators and operators, operators and control system, control system and control system, sub-process to sub-process, instrument to machine, etc.

Satisfying answers to the questions above will increase the chances of success in the optimization procedure. Competent leadership is vital to handle the issues mentioned above. Ögård and Gallstad [ÖgG94] f.e. stress several times that leadership commonly accounts for 70-80% of project results.

2.3 Modularizing of Company Activities

Modularizing all the company activities will make it easier to determine the bottleneck activity to focus on in the optimization. Determining a company bottleneck activity can be a difficult task and various methods have been developed to describe certain company activities, to analyze and handle them in other ways. Below are a number of acronyms describing certain company activities that can be used as guidance of the thought.

· Virtual Product Development Management (VPDM) aims towards the efficient handing of product or process modeling, visualization and simulation.

· Product Data Management (PDM) aims at efficiently keeping various data in order: Finit Element Models, NC programs, project plans, control schemes, references, archives, reviews, classifications, rules for responsibilities and the efficient general information search among these data.

· Component supplier management (CSM) considers questions such as: What do we make ourselves? What do we license? Who are we selling to? And efficient balances between these.

· Enterprise Resource Planning (ERP) can shortly be described as efficient business development.

· Manufacturing Execution System (MES) is an attempt to systematically describe the production development.

· Total Productive Maintenance (TPM) considers product life cycle support issues.

· Supply Chain Management (SCM) aims at developments of material support methods.

· Logistics. Research has found that around 50% of a product cost is commonly due to external logistics.

Insufficient identification of company bottlenecks could itself be a company bottleneck since the increased resources necessary for that task might add costly information handling time, which already commonly consumes more than 50% of engineering time. CPC[3][3] is a web based computer tool, which attempts to reduce the time of parallel analysis of the areas mentioned.

It should be noted though, that the usefulness of the tools above will be directly correlated to a proper mapping of the company activities.

Strategic goals must also lead to a consideration of the design of the products. The focus on design for manufacturing, assembly, disassembly, etc will have a substantial impact on the production.

Modularization of the system make it easier to optimize the system for two additional reasons: It will give a good overview for everyone involved, of how the production flow actually looks like. To have a common view of how things work is important when a team is to work towards a common goal, it improves work focus and makes it easier to evaluate to what extent the work leads in the right direction.

It will be easier to concentrate the efforts on the most important module (bottleneck) and to leave less important modules for later. Figure 2 shows an example of a modularization of a fiberboard line.

_{Figure 2 Example of a how a
production line can be modularized into sub-processes}

2.4 Mathematical Optimization Methods

When the strategy and goals have been decided, the company activities have been modularized and the remaining bottleneck to be handled is the actual production process, focus should be on optimization of that part. The first step is to consider the measuring of input and output parameters. What to measure, how to measure it, how to store data, how to choose good subsets of data from large amounts of raw data and how to filter data must be decided.

When a satisfying measuring procedure has been established, three different types of optimization procedures can commence in parallel: Optimizing the machine availability and down time is one type. The optimization should lead to an optimal maintenance and machine use schedule. Optimizing production plans is a second type. Product changes, which will cause production disturbances, should be carefully analyzed. Response optimization applied on the non-down time process is a third type. By designing several good sets of input parameters it is possible to find out how output is depending on different sets of input data. By analyzing the output response it is possible to derive the optimal set of input parameters, Nelder-Meads Simplex [NeM65] method is useful (This method is refined and further developed in the software MultiSimplex® and OMM™). The response optimization method can sometimes be time consuming and other optimization methods may initially be preferable, if practically possible.

Optimization through modeling can be useful if it is possible to model the process to a reasonable cost. The main obstacle to modeling is the cost in time and money due to the difficulty of the task. (Frequently it is almost impossible to create mathematical models of production facilities, useful for optimization, due to non-linear or discontinuous process behavior. However, recent developments indicate a somewhat increased usefulness of gray box modeling. The gray-box modeling method uses prior knowledge of the system in combination with measured data, while black box modeling only uses input-output data.). The cost and difficulties of the modeling efficiently blocks a wider use of this highly promising method, though. The continuous development of computer tools[4][4] makes it easier to carry out modeling though and modeling efforts are likely to gain momentum on processes that do not change too much over time. However, on continuously changing processes, it is believed that response optimization will remain superior.

When modeling, the first step is to define a set of candidate model system descriptions within which a model is to be found. It could be non-parametric models, state-space models, black-box or gray-box models. When the candidate system is chosen the best model is computed according to input and output data and a criterion of fit. The next step is to examine the properties of the different models. A number of analyses can be used: cross-correlation, frequency response, transient response, zeros and poles, noise spectrum, model residuals and model output. If the model is good enough then stop, otherwise go back and try other data frequencies or model structures. If the model is good enough an optimization routine can be carried out. Since a certain process module now is expressed as a mathematical function, it is possible to use common mathematical optimization techniques to arrive at the optimal set of input parameters.

Modeling is normally best used as an initial activity, to get a head start on the optimization prior to applying response optimization. Using response optimization is normally safer and more accurate to use in the day-to-day activities. Another benefit with computerized response optimization is that it does not require university education to carry out and it can even be configured to run automatically.

2.5 Control

Control should be given a rather broad definition for best results. The general advice is to consider proper choice of control strategies for each type of company activity. Commonly “control” refers to the implementation and control of well defined, optimized input parameters for the production process. Methods to handle control of company activities where such a control definition is useful are suggested by Åström and Wittenmark [ÅsW90]. They provide suggestions for various control strategies and control parameter optimization methods. Continuous tuning of control parameters and performance assessment methods are addressed as well.

If “control” refers to “soft” activities such as administration, the control strategies should consider efficient follow-up routines of the work methods agreed upon.

2.6 Continuous Based Optimization

A lot can be gained if the optimization procedure can be automated. If many products are made with varying raw material, different sets of optimal parameters have to be found for each raw material and for each product. If machines age, new process models, new optimal input parameters and optimal control parameters have to be found as the aging process affects the production. Automation considerations will have a positive impact on the production even if the analysis does not lead to an automation of the production. It has been shown that around 40% of profits resulting from automation projects are a consequence of the preparation part of the project.

The ability to optimize several response variables at the same time is extremely desirable when applying continuous based optimization, since optimization of individual responses may lead to sub-optimization of other responses. Another desirable feature is the ability to use fuzzy combination of optimization objectives.

In some cases, one of the larger benefits of the automated optimization is that it allows the operators to perform other tasks. This normally leads to indirect optimization of the activities/operations.

2.7 SPC

Statistical process control is a very useful tool if you want to get your process under control. However, if you have not optimized your process or operations prior to (or when) applying SPC, you will most probably end up with a stable and reliable, but not optimized, -process. Response optimization can be performed in combination with SPC by systematically varying the control variables within the upper and lower control limits. This approach would give you a safe way to find the optimal control variable settings, within the control limits. However, these settings may, in this case, represent a “local optimum”, since the optimization would be limited by the control limits.

[2][2] MultiSimplex® and OMM™ are examples of computerized tools for continuous based optimization.

[3][3] “CPC öppnar en ny värld för tekniskt samarbete”, Verkstadsforum vol. 2 pp. 6-7 2000

[4][4] Matlab System Identification Toolbox and the MultiSimplex computer program are two examples of increasingly useful computer tools

1. Introduction | 2. Optimization method | 3. Summary | 4. References