Minimizing Production Setups by Optimizing the Standard Tool Package

Minimizing Production Setups by Optimizing the Standard Tool Package

Submitted to The Ohio State University

Prepared By: Dan Rediger 237 E. 18th Columbus, Ohio 43201 Department of Industrial, Welding, and Systems Engineering

April 23, 2006

Table of Contents Introduction…………………………………………………………………………………………………1 Background…………………………………………………………………………………………………2 Data Collection………………..………………..………………..………………..………………………..3 Model……………………………………………………………………………………………………….4 Results and Discussion………………..………………..………………..………………..………………..7 Conclusion………………..………………..………………..………………..………………..…………...8 References………………………………..………………..………………..………………..……………..9

Introduction The global competition among manufactures has led many companies to reevaluate the way that they approach cost reduction. Methods employed in industry include Six Sigma, theory of constraints, scheduling to the advantage of sequence dependent setups, and material requirement planning have been praised as the solutions to many of the problems that American manufactures have been facing. While these practices have proven to be successful in industry, they may not be easily implemented and can mask the real underlying problems to solve. For instance, a sequence dependent scheduling problem can be very difficult to compute and may not result in an “optimal” solution. Furthermore, the best problem to solve here might be to reduce the setup time altogether. It was a prior attempt to solve one of these sequence dependent setup problems that resulted in the question: Is the right problem being attacked? Why are sequence dependent setups required or could the problem be attacked at a different level? Sequence dependent setups are typically used to minimize tooling and fixture changes, but if approximately the same number of tools needed to be changed no matter what job you switched to, then sequence wouldn’t matter. Basically, if all setups could be reduced to a minimum on a machine, then the order of production would not negatively affect machine utilization. In this context, a machine is being utilized any time that the machine is adding value to a part. Therefore any setup time, though a necessary step, would not be included in the machine utilization. As technology has developed, tooling setups have also become more extensive due to the fact that one machine may be responsible for a set of operations that once required several machines. A big part of this development was the capability of machines to hold many tools at once and to change them automatically. These tool changers can range from a simple carousel that holds less than 10 tools to a tool bin that can house up to 100 tools. It is the best utilization of these large tool bins that is the focus of this paper. This can be a computationally complex problem, for example if a machine can hold 60 tools but there are 126 tools that could be used on the numerous operations across part groups, what is the best way to fill your tool bin? There are 126 choose 60 different tool bin combinations or approximately 5 * 1036 combinations. If a super computer could evaluate 1 trillion combinations/second, it would take 1.6 * 1017 years to determine a best solution in terms of reduced setup. Based on the shear magnitude of this problem, one can see why an algorithm that could quickly evaluate a model of this problem would be very beneficial. The next section explains the background of the specific problem that is the basis for this paper. The section following that gives details of how the data for the problem were collected. It also provides insight as to why certain data were collected. Following that is a section that describes the model of the tool bin loading problem. This includes all of the assumptions made, the formulation of the integer programming model, and descriptions of the variables and constraints. The modeling section is followed by a discussion of the results. This discussion includes an analysis of how management judgments can be incorporated into the model to affect the outcome of the model. The paper ends with a conclusion summarizing the main points of this paper.

Background The setting of this study is a jet engine supplier, which provides engines to over five hundred different airlines around the world. While airlines used to purchase this supplier’s engines for its name, this is no longer the case. With rising costs, jet engines are being looked at as more of a commodity. Airlines now desire to buy the lowest cost engine they can purchase that will meet their technical requirements in the shortest time possible. These facts have lowered the brand value of this company’s engine and sent the company in search of new ways to reduce cost and to increase customer satisfaction. The reduction of setup time is one of the items that the company has identified as a potential cost savings opportunity. One of the ways that this can be done is by reducing the number of tools that need to be changed out on some of their bigger machines. For this study, it was decided that a standard tool package would be developed for the A55 Makino, a large 4-axis mill that has the capability to hold up to 60 tools at once. This particular machine is responsible for running 63 different operations which use a total of 126 different tools. The standard tool package is some subgroup of the 126 tools that will occupy a maximum number of tool slots in the machine such that they never have to be removed for any setup. The goal is then to determine the maximum number of slots out of sixty that can be occupied by tools that will never leave the machine. For example, if 45 tools are included in the machine, the maximum number of tools that any setup can have is 60 – 45 or 15 tools. In addition to the 126 tools, there is a standard probe used for all of the operations. This will require one of the 60 tool slots. Also, it was determined through discussion with the operator that two of the tools that are most often used (tool numbers 57 & 58) take two tool spots each because of their size. This means that whenever these two tools are in the machine that there are actually only 55 additional spots available. Since these two tools are used on a total of 26 different operations, the assumption was made that these two tools should be included in the standard tool package. Therefore, additional constraints are included that force the solution to include these two tools. 57 tool slots were then built into the model as being available. It is also important to consider the production schedule when since that affects the frequency of use of each tool. For example, some of the older spare parts that are produced may not have any scheduled production. Therefore, there should not be any setups for these parts and tool slots being taken by tools particular to these parts are not justified. The model will also have the capability to be altered to loosen constraints on low volume parts and tighten constraints on high volume parts. This will allow for additional analysis to be completed if requested.

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Data Collection A number of categories of information needed to be collected. The first category was what tools were needed for each operation. To accomplish this a database was created by pulling all of the routings for the parts that were run on this machine, and then extracting a list of the tools for each of the operations run on the A55. This information should hold a high degree of accuracy since the database must be updated any time a routing change is made to be in accordance with the ISO9000 regulations. The next important category of information was whether or not a particular part number had multiple operations that were run on the A55. If there were multiple operations, it was also important to note where they back-to-back. This is important because it determines whether or not the operator can setup the tools for multiple operations all at once. For example, if a particular part number runs operations 100 and 200 back to back on the A55, then the operator can change all of the tools for both operations at once. Essentially, the two setup operations will be considered to have one setup in the model. The information was then combined to create a n × m matrix of 0-1 indicator values where n is equal to the total number of different tools used on the setups, and m is equal to the total number of different setups performed. If a tool is used on a particular setup it is given the value of 1, otherwise it is deemed to be 0. From this matrix, it can be determined how many tools are used for each setup and how many different setups use a particular tool. It was also important to have a snapshot of the production schedule so that analysis could be performed to determine the affects of the model’s outcome. The schedule was also important to help determine whether or not some of the part numbers still had any demand as well as what parts had very high demand.

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Model This section will describe how to answer the following question: A manufacturing center produces parts on a large milling machine. There are m number of setups done on this machine that require n number of tools for each setup. Given that the machine has the capacity to hold y number of tools, maximize the standard tool package such that for any given setup, there are not any tools removed from the machine that are included in the standard tool pack (i.e. if there are 60 tool slots available and 49 tools are included in the standard tool package, then the largest setup allowed for any job is 11 tools). Parameters ci = number of times tool i is used for all of the jobs dj = number of tools used to run job j ai = 1 if tool i is used on job j and 0 otherwise bi = 1 if tool i is not used on job j and 0 otherwise y = Total number of tool slots available n = number of tools used on the machine m = number of setups done on the machine **the term job is used in place of operation because if a part has back to back operations on the same machine, they’re considered to be one job i.e. the tooling setup for both operations is done at once Variables wj = number of tools required to setup for job j

for

wi ∈ {0, 1, 2,Κ }

Decision Variables xi = 1 if tool i is included in the standard tool pack and 0 otherwise for xi ∈ {0, 1} Objective Function: An optimal solution is defined as the “a feasible solution that has the most desirable value(s) for the objective function(s) among all feasible solutions” (Murty 2). The optimal solution for this model will be defined as the solution that results in the maximum total number of times, summed over all of the tools for all of the jobs, the tools selected for the standard tool pack are used. This solution in turn, should result in minimal setups across the jobs by including all of tools that are used most often across all of the different jobs while staying within the constraints. The objective function is formulated below. n

Maximize

z = ∑ c i xi i =1

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Shown below in Table 1 is a small problem that will be used to illustrate the objective function as used in practice.

Job (Wj) / Tool (Xi) 1 2 3 TOTALS (Ci)

TABLE 1 – SAMPLE STANDARD TOOLING PROBLEM X1 X2 X3 1 1 0 1 1 1 0 1 0 2 3 1

X4 0 0 1 1

The objective function for this sample problem would read as follows: Maximize z = 2 x1 + 3 x2 + 1x3 + 1x4 Once the objective function has been defined, it is necessary to identify all constraints that may limit the objective function. The constraints for the standard tooling package problem, as it has been defined in this paper, are shown below. The equation below can be used as both a constraint and/or a source of information. For the base model, it is a source of information. When the results are outputted, each wi will inform the user how many tools will be changed out for the job corresponding to that wi. This is very useful when looking at a production schedule to make educated guesses for the setup times for each job. n

w j + ∑ ai xi = d j for j = 1 to m i =1

For the example shown in Table 1, the constraint for job 1 would look like the following:

w1 + 1x1 + 1x 2 = 2 wi will also be used in later alternative models as a way to incorporate the schedule. For instance, if there is a high demand for a certain group of parts during some period of time, additional constraints can be added that can force wj to be less than or equal to some number. Therefore, a certain number of tools must be included in the standard tool pack for that job. A constraint of this type would simply be: wi