SELECTING MANUFACTURING SYSTEM CONFIGURATIONS BASED ON PERFORMANCE USING AHP

Valerie Maier-Speredelozzi and S. Jack Hu Engineering Research Center for Reconfigurable Machining Systems University of Michigan Ann Arbor, Michigan

ABSTRACT During the early phases of manufacturing system development, manufacturers must choose not only machine specifications and vendors, but also the configuration of the system. The performance of different system alternatives must be quickly assessed with respect to performance areas such as productivity, quality, and cost, and also responsiveness issues such as convertibility and scalability. Trade-offs frequently exist between these various aspects of performance, so a comprehensive analysis methodology is needed. Selecting the best system and arranging it in the most preferred configuration can have dramatic effects on the performance of the line once it is in production. In this paper, the Analytic Hierarchy Process (AHP) is adapted for use in problems where manufacturing system configurations are selected with consideration of multiple performance criteria. An example is used to demonstrate the application of this technique, and sensitivity studies show the robustness of the solution. Given the assumptions and inputs in this example, the pure parallel configuration is shown to be preferred over five other configurations, including the pure serial and four hybrid configurations. Additional case studies are

proposed, as well as extensions to situations where uncertainty of the input values is present. INTRODUCTION The machines within a manufacturing system can be arranged in many different configurations, such as serial, parallel, or hybrid, with varying systemlevel performance results. Koren, Hu, and Weber (1998) reviewed a case in industry where a serial line with eighteen machines was compared to a configuration with three shorter lines of six machines each. In the serial line, if even one machine was down, the entire system was unproductive. Therefore, the latter configuration had better overall productivity, which was easy to observe with only two options. The number of possible system configurations, however, increases rapidly as the number of machines in the system increases. It is important to assess the performance of many configuration alternatives early in the design process, and following system reconfigurations. Critical performance metrics in this analysis include quality, productivity, convertibility, scalability, and cost, which are explained below. One way to assess quality is to simulate the flow of workpieces through different configurations and measure the mean deviation and standard

deviation of key product characteristics (Zhong, et al., 2000). Productivity is related to reliability and maintainability, which are measured with the mean time to failure (MTTF) and mean time to repair (MTTR). The availability of system components is based on these machine characteristics. Yang, et al. (2000) computed the expected system productivity for a certain configuration by applying these formulas to the states in which the system may exist with varying probabilities. System states are defined by whether components are operational or not. Convertibility is a metric that can be applied to different types of systems and focuses on how responsive a system is to changes in the product or the part mix. Similarly, scalability is the capability to accurately adjust the production capacity, or volume, of a system. Zhong, et al. (2000) analyze the increments of time for converting various configurations. Configurations with smaller increments of conversion are preferred over systems such as transfer lines where 100% of the system must be shut down during a conversion. Systems with high scalability require less lead-time when a change in capacity is required. Metrics of scalability include the average or minimum capacity increment, cost per increment of increased or decreased capacity, and the time or effort required to scale. A final performance metric that is almost always considered is cost. In manufacturing and other industries, many researchers turn to decision theory for scientific approaches to selection problems. Different decision theory methods that have been studied include vector criterion methods, Multi-Attribute Utility Theory (MAUT), game theory, and more recently, the Analytic Hierarchy Process (AHP), which was introduced by Saaty. AHP results for large-scale, complex decision-making problems are robust, even when inputs or hierarchical structures are varied slightly. Another advantage of the AHP methodology is the capability to assess the consistency of the decision-maker’s ratings. AHP allows for sensitivity analysis and systematic solution procedures with automated software and multiple decision makers. The AHP method a hierarchy that multiple levels comparisons are

begins with the construction of breaks a top-level goal into of sub-criteria. Pairwise used to evaluate how the

elements at each level relatively contribute to the element at the next highest level. The lowest level of the hierarchy includes all of the possible alternatives or options, which the decision-maker rates relative to each criterion. Matrices are calculated which mathematically represent the comparisons and ratings. Saaty proposed a subjective rating scale, but when objective measurements are available the entries are calculated by aij = wi / wj, where wi is the measurement of the element at the left and wj is the measurement of the element at the top. The inverse ratio, wj / wi, is used if the objective is to minimize the criterion. The principal eigenvector of each matrix then represents the relative importance of the hierarchy elements. Saaty (1980) suggested four methods for determining principal eigenvectors. The method used here is to multiply the (n) elements in each row together and then take the nth root and normalize. The eigenvectors of the matrices at the lowest level of the hierarchy are arranged into a matrix of column vectors and multiplied by the priority vector for the matrix at the next highest level. Ultimately, a single vector is found that represents the relative value of the alternatives at the lowest level of the hierarchy. Researchers who have used AHP on various manufacturing related problems include Partovi (1992) and Mohanty and Deshmukh (1997). Chick, et al. (2000) list possible performance attributes and suggest final selection of preferred suppliers and machining systems using either MAUT or AHP. Abdul-Hamid, et al. (1999) use AHP to select between three plant layouts, subject to flexibility, production volume, and cost attributes. Oeltjenbruns, et al. (1995) combine technical criteria such as spindle drive capacity with less tangible criteria such as flexibility in a hierarchy for equipment replacement decisions at a German company. The authors also acknowledge some of the criticisms that other researchers have had for AHP. Some research extends these methods to situations where decision-makers are uncertain of their input data. This includes White, et al. (1984) who introduced Imprecisely Specified Multi-Atrribute Utility Theory (ISMAUT) and Tsaur, Tzeng, and Wang (1997) who applied Fuzzy AHP to the selection of preferred tourist itineraries. In this paper, the Analytic Hierarchy Process is used in configuration selection problems. First, a

hierarchy is established using the key performance metrics described above and an example is formulated with six sample configurations. Then the performance of each of the candidate configurations are evaluated. The mathematics of the AHP process are described and the results and sensitivity analysis from this case study are discussed. Finally, comments on future work and concluding remarks are given. SYSTEM PERFORMANCE HIERARCHY Figure 1 shows one possible hierarchy for selecting preferred manufacturing system configurations. Maximizing system performance is the top-level goal, with productivity, quality, convertibility, and scalability in the second level (cost is not initially included). The third level criteria are sub-categories of the second level elements, which can be quantitatively assessed. At the bottommost level of the hierarchy are the configurations that will be compared. The quantitative criteria under productivity could include such measures as expected system throughput or average work in process. Under quality, the number of flowpaths that workpieces might follow through the system is intrinsic to the configuration design. However, to assess the mean or standard deviation of a key product quality dimension, X, machine accuracy data and CAD models must be entered into a simulation program. Similarly, under convertibility, the number of flowpaths and minimum conversion increment are intrinsic measures, but conversion cost or effort measurements require more detailed product information, and thus, are not included here. Scalability sub-criteria are based on approximations of cost, as well as the intrinsic average scaling increment. Figure 2 shows six configurations. Configuration (a) is pure serial where, hypothetically, each machine performs a single operation and there is only one workpiece flowpath. Configuration (f) is a pure parallel configuration of six duplicated machines that each perform all processing operations. Hybrid configurations (b) and (d) are parallel lines of several machines in series. Hybrid configurations (c) and (e) are serial lines of several groups of machines in parallel, which System Performance

Productivity

Exp. Prod.

Quality

Mean Dev (X)

Convertibility

Scalability

Standard # of Minimum Cost/ Dev (X) Flow - Increment Increment

1. SAMPLE HIERARCHY FOR CONFIGURATION SELECTION BASED ON SYSTEM PERFORMANCE.

(a) M S

DS

MS

DS

MS

BS YCNC

(b)

MC

DC

XC

MC

DC

XC

(f)

YCNC YCNC

(c)

MC

DC

XC

MC

DC

XC

YCNC YCNC YCNC

(d)

(e)

MC

DC

DC

MC

DC

DC

MC

DC

MC

DC

MC MC

2. SIX CONFIGURATIONS USED IN EXAMPLE.

also allow for crossover between processing stages. Each machine in (b) and (c) performs two operations, and each machine in (d) and (e) performs three operations. In Figure 2, MS and MC machines represent milling machines, DS and DC are drills, and BS represents a bore. XC and YCNC represent flexible machines that can perform both milling, drilling, and/or boring. SYSTEM PERFORMANCE ANALYSIS In this section, the methods for assessing productivity, quality, convertibility, and scalability are demonstrated for the sample configurations. Productivity and quality analysis is similar to that in Zhong, et al. (2000). It is assumed that more complex machines have more components and therefore, are more susceptible to failure. In this case, component failure and repair rates MTTF C and MTTR C are all assumed to be equal. A simple mill, drill, or bore (MS, DS, BS) is assumed

MTTFM

MTTRM

Availability

1000 1000 1000 1000 1000 1000 1000

20 20 20 20 20 20 20

100 100 100 66.67 66.67 50 33.33

20 20 20 20 20 20 20

0.833 0.833 0.833 0.769 0.769 0.714 0.625

the processing rate of the machines is set at 60 jobs per hour (JPH). The processing rates of the machines in other configurations are set such that the greatest possible system output if no failures occurred would also be 60 JPH (thus, in (b) and (c) the rate is 30 JPH for each machine, in (d) and (e) it is 20 JPH, and in (f) it is 10 JPH). The availabilities of the machines are combined into the serial, parallel, and hybrid configurations, and the expected system productivity values are calculated based on Yang, et al. (2000) and are given in the last column of Table 2. For quality, the sample part in Figure 3 is used. Raw material and product specifications, as well as machine accuracy and repeatability data is assumed. Kinematic errors are analyzed for milling operations on surfaces 1, 5, and 8 and boring hole 11. Using simulation, the mean and standard deviations of two key dimensions, H and D, are found. The number of flowpaths in each configuration is an additional attribute that is minimized since it is more difficult to identify the source of quality problems in industry when

Standard Deviation (D)

0.005 0.036 0.021 0.020 0.032 0.011

0.009 0.018 0.030 0.013 0.042 0.031

0.028 0.048 0.039 0.024 0.022 0.035

0.011 1 20.094 0.016 2 25.359 0.024 8 30.054 0.034 3 35.503 0.037 9 38.613 0.011 6 37.500 Output Part

2

1

8

PSk, System Productivity,

Mean Deviation (D)

# of Flowpaths

Standard Deviation (H)

10 10 10 15 15 20 30

MTTRC

# of components

MS DS BS MC DC XC YCNC

a b c d e f

Input Part MTTFC

Machine Type

TABLE 1. PRODUCTIVITY ASSUMPTIONS.

Mean Devieation (H)

The processing rates of the machines in a given configuration are assumed to be equal, and buffers are not considered. In configuration (a),

TABLE 2. QUALITY AND PRODUCTIVITY DATA.

Configuration

to have ten components. Adding a second, similar operation adds five components, for a total of fifteen (MC, DC). A machine that can perform very different operations such as milling and boring (XC) has twenty components, and a fully flexible CNC machine that performs all operation types (Y CNC) has thirty components. MTTF M, MTTRM, and machine availability are calculated and shown in Table 1.

20

40

H

7 6

4

5

3

150 100 4*

12~15

D 50

8

100 50

11 20

50 200

3. SAMPLE PART USED IN QUALITY ANALYSIS.

multiple flowpaths exist. Quality data is given in Table 2, based on Zhong, et al. (2000) and other ongoing work and simulations by these authors. Systems that currently manufacture Product A may be converted to a redesigned Product B over several time increments, depending on the configuration. Similar conversion tasks are needed in each configuration, so the overall loss of production is equal. Having at least a portion of a system converted quickly, however, provides value to an organization. In configuration (a), for example, all six machines must be converted before the system can be brought online again. For configuration (b), once one drill (DC), one mill (MC), and one flexible machine (XC) are converted,

the system can be brought online at 50% capacity for Product B if appropriate safety features exist. Similarly, configuration (d) can be converted in three increments, and configuration (f) in six. In systems that allow for crossover, the percentage of converted capacity that is achieved with each increment depends on the relative productivity of the different machine types. The number of potential increments of convertibility for each configuration is equal to the number of flowpaths. The minimum increment represents the percentage of the total conversion time that must be invested before a new product can be introduced. The first scalability metric is the average scaling increment, which in this case equals the minimum conversion increment. In addition, the cost per increase in capacity is considered. The six station transfer line in configuration (a) is assumed to cost $2 million. A flexible CNC, as in configuration (f), is assumed to cost $500,000. For configurations (b) and (c), four multi-operation milling machines ($400,000 each) and two boring/drilling machines ($450,000 each) are required. In configurations (d) and (e), three multioperation mills and three bore/drills are required. To add an increment of scaled capacity, it is assumed that all machines in a parallel flowpath need to be duplicated. For example, in configuration (b) the next increment of added capacity would require one mill, one drill, and one bore/mill machine, cost $1.25 million, and would increase gross capacity by 50%. The cost per capacity is thus $1.25 million/30, or $41,667. Convertibility and scalability data are given in Table 3.

Avg. or Min. Increment

Cost Per Capacity

# of Increments

Investment Cost-millions

a b c d e f

Cost Per Machine

Configuration

TABLE 3. CONVERTIBILITY, SCALABILITY DATA.

333,333 416,667 416,667 425,000 425,000 500,000

1.00 0.50 0.50 0.33 0.33 0.17

33,333 41,667 41,667 42,500 42,500 50,000

1 2 8 3 9 6

2.0 2.5 2.5 2.55 2.55 3.0

Given the above results, simple observations can be made. Configuration (a) has the lowest cost, which explains why many manufacturing lines are serial in nature. Configuration (a) has the lowest standard deviations, and thus good quality, but configuration (f) has the lowest mean deviations from target, also a sign of good quality. Configuration (f) also has the lowest minimum increments for scalability and convertibility. It is configuration (e), however, which achieves the best productivity. In order to aggregate this data into a meaningful, comprehensive evaluation, the Analytic Hierarchy Process (AHP) is employed. AHP EXAMPLE RESULTS Figure 4 shows the matrices and priority vectors for the third, or bottom level analyses of the six configurations with respect to the criteria for productivity, quality, convertibility, and scalability. For example, the first table is the analysis matrix for productivity. Along the diagonal, all entries are equal to 1.00, because every configuration is equally preferred when compared to itself. When different configurations are compared, however, the number in the matrix is calculated by dividing the expected system productivity of the configuration at the left by that of the configuration at the top. For example, the expected system productivity of configurations (a) and (b) were found earlier to be PSa = 20.09 JPH and PSb = 25.36 JPH. Consequently, the PSk a b c d e f

a 1.00 1.26 1.50 1.77 1.92 1.87

b 0.79 1.00 1.19 1.40 1.52 1.48

c 0.67 0.84 1.00 1.18 1.28 1.25

d 0.57 0.71 0.85 1.00 1.09 1.06

e 0.52 0.66 0.78 0.92 1.00 0.97

f 0.54 0.68 0.80 0.95 1.03 1.00

PV 0.11 0.14 0.16 0.19 0.21 0.20

Mn Dev H a b c d e f

a

b

c

d

e

f

PV

1.00 0.14 0.24 0.25 0.16 0.45

7.20 1.00 1.71 1.80 1.13 3.27

4.20 0.58 1.00 1.05 0.66 1.91

4.00 0.56 0.95 1.00 0.63 1.82

6.40 0.89 1.52 1.60 1.00 2.91

2.20 0.31 0.52 0.55 0.34 1.00

.45 .06 .11 .11 .07 .20

Std Dev H

a

c

d

e

f

PV

b

a b c d e f

1.00 0.52 0.31 0.72 0.22 0.30

1.93 1.00 0.60 1.38 0.43 0.58

3.22 1.67 1.00 2.31 0.71 0.97

1.39 0.72 0.43 1.00 0.31 0.42

4.51 2.33 1.40 3.23 1.00 1.35

3.33 1.72 1.03 2.38 0.74 1.00

.33 .17 .10 .23 .07 .10

Min Incr a b c d e f

a

b

c

d

e

f

PV

1.00 2.00 2.00 3.00 3.00 6.00

0.50 1.00 1.00 1.50 1.50 3.00

0.50 1.00 1.00 1.50 1.50 3.00

0.33 0.67 0.67 1.00 1.00 2.00

0.33 0.67 0.67 1.00 1.00 2.00

0.17 0.33 0.33 0.50 0.50 1.00

.06 .12 .12 .18 .18 .35

Cost/ Incr a b c d e f

a

b

c

d

e

f

PV

1.00 0.80 0.80 0.78 0.78 0.67

1.25 1.00 1.00 0.98 0.98 0.83

1.25 1.00 1.00 0.98 0.98 0.83

1.28 1.02 1.02 1.00 1.00 0.85

1.28 1.02 1.02 1.00 1.00 0.85

1.50 1.20 1.20 1.18 1.18 1.00

.21 .17 .17 .16 .16 .14

4. BOTTOM LEVEL MATRICES AND PRIORITY VECTORS.

entry in the second column of the first row is 20.09/25.36, or 0.79. Once all of the matrix entries are calculated, the principal eigenvector (PV) is found. The objectives for all of the criteria other than productivity and convertibility flowpaths is minimization, so the formula must be reversed, such that each entry is equal to the performance metric for the top configuration divided by that of the configuration on the left. All matrices in this case study have perfect consistency because they use actual measurements, and not subjective evaluations. For quality, the matrices for the mean and standard deviation of H are shown, but those for dimension D are omitted. The matrix for minimum increment is applicable to both convertibility and scalability, and the cost per increment matrix is also shown. The matrix for the number of flowpaths in the configuration is omitted. This metric should be minimized for quality purposes, but maximized for convertibility, because with more flowpaths, manufacturers have more options for assigning resources to a conversion project. With opposite objectives, the matrix for flowpaths with respect to convertibility is the transpose of that for quality.

To determine the overall preferred configuration, the priority vectors for the criteria within each performance area are arranged into a matrix. Then this matrix is multiplied by the column vector for the relative weights of those criteria. For the quality sub-criteria, the matrix multiplication is:

?.45 ?.06 ? ?.11 ? ?.11 ?.07 ? ?.20

.33 .17 .10 .23 .07 .10

.18 .11 .13 .21 .23 .14

.26 .18 .12 .09 .08 .27

.45? ?.2? .22??? ? .2 .06?? ? ??.2? ? .15?? ? .2 .05?? ? ??.2? .07?? ?

?.33? ?.15? ? ? ?.10? ? ? ?.16? ?.10? ? ? ?.16?

In a similar manner, the equations for the convertibility and scalability metrics are:

?.03 .06? ?.05 ? ?.07 .12? ?.09 ? ? ? ? ? ?.28 .12??.5? ?.20 ? ? ?? ? ? ? ? ?.10 .18??.5? ?.14 ? ?.31 .18? ?.24 ? ? ? ? ? ?.21 .35? ?.28 ? ?.06 .21? ?.13? ?.12 .17 ? ?.14 ? ? ? ? ? ?.12 .17 ??.5? ?.14 ? and ? ?? ? ? ? ? ?.18 .16 ??.5? ?.17 ? ?.18 .16 ? ?.17 ? ? ? ? ? ?.35 .14 ? ?.25 ? Productivity has only one criterion, so the priority vector is simply the productivity column vector. The priority vectors for each of the performance areas are arranged into a matrix, which is multiplied by the column vector of weights for the second level objectives. Initially all criteria are assumed to contribute equally to the objectives in the next higher level. The equation is:

?.11 ?.14 ? ?.16 ? ?.19 ?.21 ? ?.20

.33 .15 .10 .16 .10 .16

.05 .09 .20 .14 .24 .28

.13? .14 ???.25? .14 ???.25?? ? ? .17 ??.25? ? ? .17 ??.25? ? .25?

?.15 ? ?.13 ? ? ? ?.15 ? ? ? ?.16 ? ?.18 ? ? ? ?.22 ?

The resultant column vector represents the relative value of the six configurations. In this case, configuration (f) has the highest rating of 0.22. Assuming accurate performance data and appropriate relative weights for the hierarchy elements, configuration (f) should be selected. SENSITIVITY ANALYSIS The relative weights of criteria in the AHP process are determined by the decision-maker, so some degree of uncertainty or subjectivity exists. The advantage is that the methodology can be easily adapted for different industries, companies, and applications. Criteria weights were systematically varied in six different sensitivity studies. In the original solution, criteria were assumed to contribute equally to the next highest level in the hierarchy. In the first sensitivity case, quality was assumed to be twice as important as the other objectives. Configuration (f) was still most preferred, with a relative value of 0.21, but configuration (a) is now second most preferred, with a value of 0.19. In the next case, convertibility and scalability are weighted 0.45 each and are assumed to be much more important than productivity or quality which are weighted 0.05 each. Configuration (f) is still most preferred with a value of 0.25, followed by (e) which now has a value of 0.20. Next, the relative weights of the second level objectives were manipulated until a solution other than configuration (f) resulted. One way that this can be achieved is by heavily weighting productivity (0.95). Convertibility was still included with a weight of 0.05, but quality and scalability considerations were excluded altogether. Even with such manipulated weights, configuration (f) has a resulting relative value of 0.20 and is still a close second choice to configuration (e) which has a value of 0.21. Another level of sensitivity is varying the weights of the criteria within a performance area such as quality. The importance placed upon the number of flowpaths was changed to be six times greater than each of the simulated workpiece dimensions. This changed the priority vector for the quality related criteria. The new priority vector is substituted into the top level matrix equation and the performance areas are again equally weighted. The results show configuration (f) being most preferred with a value of 0.21, followed by a tie of configurations (a) and (e), which each had

values of 0.17. With the new priority vector for quality, the top level weights were again varied such that quality was 0.6, productivity was 0.2, and convertibility and scalability were each 0.1. The resulting solution showed configuration (a) being most preferred by a large margin. Configuration (a) had a relative value of 0.27, while a three way tie existed between configurations (b), (e), and (f) which each had values of 0.16. Finally, an AHP example with a slightly different hierarchy was examined. The new top-level matrix multiplication is as follows, where the last column represents how the six configurations rate in terms of approximate total investment cost:

?.11 ?.14 ? ?.16 ? ?.19 ?.21 ? ?.20

.33 .15 .10 .16 .10 .16

.05 .09 .20 .14 .24 .28

.13 .14 .14 .17 .17 .25

.21? ?.2 ? .17 ??? ? .2 .17 ?? ? ??.2 ? ? .16 ?? ? .2 .16 ?? ? ??.2 ? .14 ?? ?

?.17 ? ?.14 ? ? ? ?.15 ? ? ? ?.16 ? ?.18 ? ? ? ?.20 ?

Configuration (f) is again most preferred, despite the fact that stand alone CNC machines are typically considered to cost much more than traditional machine tools and dedicated systems. SUMMARY AND FUTURE WORK The manufacturing system configuration can have significant effects on the resulting performance. Especially when reconfigurable manufacturing systems are used, a line can exist in multiple configurations over time. The AHP methodology has been shown to be highly effective for identifying preferred manufacturing system configurations during the early phases of design. AHP can help decision-makers consider all aspects of performance as they select and purchase systems. The sensitivity analysis indicates that configuration (f) is best, but it must be noted that this conclusion is dependent upon the accuracy of the input data and assumptions. Additional case studies are needed to compare more of the many potential hybrid configurations and determine if generalizations can be made regarding preferred configurations. At the system level of analysis, metrics such as convertibility, scalability, productivity, and quality are relevant to many different types of manufacturing systems. Therefore, this research

can be applied to dedicated manufacturing lines (DML), flexible manufacturing systems (FMS), and reconfigurable manufacturing systems (RMS) in disciplines including machining, forming, casting, assembly, micro-processing, and other less common manufacturing environments. The methodology presented in this paper can also be extended to incorporate uncertainty in the AHP input values. ACKNOWLEDGMENTS The authors are pleased to acknowledge the financial support of the Engineering Research Center (ERC) for Reconfigurable Machining Systems (National Science Foundation Grant #EEC-9529125), and assistance from members of the ERC, especially Dr. Ying Huang.

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