Hawkeye Electronics

8

’ manufacturing lineproduces circuit cards using four operations, which include solderpreparation, component placement and soldering, baking andInspection. Solder preparation is carried out using a semi-automatedmachine. The time taken to process a circuit card on this machine isnormally distributed with a mean of 10 seconds and a standarddeviation of 8 seconds.

After preparation, the card goes to thecomponent placement and soldering stage. In front of this stage is astorage bin which can hold a maximum of 2 cards. If this bin is full,the solder preparation stops because there is no more space to storethe cards. This limitation is Hawkeye management’s way ofcontrolling the amount of work-in-process inventory. A single workermanually performs the component placement and soldering operation. Astudy shows that the component placement time of each circuit card isnormally distributed with a mean processing time of 1.0 minute and astandard deviation of 0.108 minute. The worker is responsible for thequality of his work. He visually inspects each card and repairs it ifdefective. The repair time is also normally distributed with anaverage of 40 minutes and a standard deviation of 1.080 minute. About5% of the cards is expected to be defective.

After soldering the components, there is astorage bin which can hold a maximum of 10 cards. Circuit boards areprepared (setup) for baking. The oven’s capacity is 5 cards. Toload the oven, boards are coated with epoxy and vertically stacked ina metal tray that slides out of the oven. This takes 7 minutes.Baking takes exactly 15 minutes. After baking, the cards areinspected.

Hawkeye currently has 3 inspectors. An existingstudy reveals that the inspection time of each circuit card isnormally distributed with an average of 13 minutes and a standarddeviation of 1.08 minutes. Hawkeye’s management believes sufficientdemand exists for any additional circuit cards produced. Each cardcan be sold for a $ 2.00 profit.

Hawkeye in-house engineers have identified 4feasible projects to improve the existing process. First, the companycan either hire or layoff the inspectors, in which case eachadditional inspector will cost the company $1,000 in payroll costsannually while each laid off inspector will only save it $500, whichaccounts for severance paid out to the inspectors. Secondly, thestorage bin’s capacity can be remodelled between the solderpreparation and component placement and soldering stations. In thiscase there is a $400 fixed expense and a variable expense of $20 forevery additional circuit card that can be stored in the remodelledstorage bin. Thirdly, the company can reduce the proportion ofdefective cards that are reworked at the component placement andsoldering operation. This project will cost $100 for each 0.01reduction in the proportion of cards that are reworked. Finally, itcan reducethe cards preparation time prior to baking. Each minute reduction insetup time will cost $30. The management is willing to accept any ofthe four projects but it will only approve a project if the expensesincurred can be repaid within one year with additional profitsgenerated from new sales and/or cost savings.

Project Analysis

Project One

For project one, the optimal number of new inspectors to be hired isone. Hiring two more inspectors would result in a loss of $88, whilehiring three more would result in a loss of $1,088. On the otherhand, laying off one inspector would result in a loss of $14,594while laying off two inspectors would result in a loss of $31,325.This suggests that it is more optimal to hire new inspectors asopposed to laying them off. As such, the management’s ultimatedecision should entail hiring new inspectors. This is of coursesubject to a given upper limit, which is one in this case. Thisdecision would result in an incremental profit of $910 as illustratedin table one below.

Table1: Project one

Number of Inspectors

Storage Bin Capacity

Percentage Defective

Oven Setup Time

Completed Cards prior to Project

Completed

Cards after the Project

Project Cost

Incremental Profit

1

2

5%

7

24776

8613

-1000

-31326

2

2

5%

7

24776

17229

-500

-14594

4

2

5%

7

24776

25731

1000

910

5

2

5%

7

24776

25732

2000

-88

6

2

5%

7

24776

25732

3000

-1088

1

2

5%

7

24776

8613

-1000

-31326

It is also evident that the percentageutilization for solder preparation, component placement and bakingare directly proportional to the number of inspectors while thepercentage utilization for inspection is inversely proportional tothe number of inspectors. On the other hand, the average queue lengthremains constant while the average wait time is inverselyproportional to the number of inspectors.

Table 2: Project one process metrics

Number of Employees

Utilization

Average Wait time

Solder

Component placement

Oven

Inspection

Oven inflow

Oven outflow

Queue before component placement

1

1.198%

7.302%

30.409%

99.860%

141.90

43.38

26.78

2

2.403%

14.573%

60.794%

99.688%

66.90

21.59

11.97

4

3.579%

21.726%

90.758%

74.393%

34.19

2.05

6.23

5

3.579%

21.726%

90.758%

59.509%

34.19

2.00

6.23

6

3.579%

21.726%

90.758%

49.590%

34.19

2.00

6.23

Project Two

In this project, the storage bin’s capacity remodelled between thesolder preparation and component placement and soldering stations. Toachieve this, a $400 fixed expense and a variable expense of $20 willbe incurred for every additional circuit card that can be stored inthe remodelled storage bin. The most optimal storage bin capacity is8, at which point the incremental profit is $482 and the number ofcards completed after the project is 25,277. Because the incrementalprofit is directly proportional to the storage bin capacity, themanagement should strive to maximize the storage bin capacity toenhance the overall profitability of the company. It should howeverbe noted that Hawkeye’s management hadinitially limited the capacity of the storage bin to 2 to controlamount of work-in-process inventory. Inventory is more often than notassociated with holding costs, which might escalate the company’soperating costs and ultimately result in a decline in its overallprofitability. Apart from that, warehousing is also associated withseveral risks such as theft or damage. Additionally, the resourcesheld up in this inventory could be channelled to more productive useswithin the company. For these reasons, while the management shouldconsider increasing the storage bin capacity, it should also take thecompany’s working capital management policy into account.

Table 3: Project two

Number of Inspectors

Storage Bin Capacity

Percentage Defective

Oven Setup Time

Completed Cards prior to Project

Completed Cards after the Project

Project Cost

Incremental Profit

3

1

5%

7

24776

24415

0

-722

3

3

5%

7

24776

24995

420

18

3

4

5%

7

24776

25122

440

252

3

5

5%

7

24776

25177

460

342

3

6

5%

7

24776

25230

480

428

3

7

5%

7

24776

25256

500

460

3

8

5%

7

24776

25277

520

482

Like the incremental profit, the utilization, maximum que length andthe average wait time are also directly proportional to the storagebin capacity. This is illustrated in table 4 below.

Table4: Project two process metrics

Storage Bin Capacity

Utilization

Maximum Queue length

Average Wait time

Solder

Component placement

Oven

Inspection

Queue before component placement

Oven inflow

Oven outflow

Queue before component placement

1

3.396%

20.620%

86.115%

94.005%

1

35.78

10.29

3.22

3

3.477%

21.105%

88.166%

96.265%

3

39.05

11.30

10.64

4

3.495%

21.208%

88.622%

96.751%

4

39.89

11.52

14.76

5

3.504%

21.264%

88.817%

96.978%

5

40.30

11.68

18.89

6

3.510%

21.309%

89.005%

97.187%

6

40.76

11.84

23.38

7

3.513%

21.329%

89.096%

97.294%

7

40.90

11.90

27.72

8

3.517%

21.346%

89.164%

97.372%

8

41.11

11.92

32.54

Project Three

This project entails reducing the proportion of defective cards thatare reworked at the component placement and soldering operation,which will cost $100 for each 0.01 reduction in the proportion ofcards that are reworked. The most optimal reduction in the proportionof defective cards is by 3% down to 2%, which will yield anincremental profit of $1,724, with a total number of 25,778 completedcards after the project. The incremental profit increases with every1% decline in the percentage of defective cards from 5% to 2%, whereit begins to decline. A similar trend can be observed in theproportion of component placement in utilization. The average waittime and other aspect of utilization are however inverselyproportional to the percentage of defective cards. This isillustrated in table 6 below.

Table5: Project Three

Number of Inspectors

Storage Bin Capacity

Percentage Defective

Oven Setup Time

Completed Cards prior to Project

Completed Cards after the Project

Project Cost

Incremental Profit

3

2

4%

7

24776

25443

100

1234

3

2

3%

7

24776

25724

200

1696

3

2

2%

7

24776

25788

300

1724

3

2

1%

7

24776

25812

400

1672

Table6: Project Three process metrics

Percentage Defective

Utilization

Average Wait time

Solder

Component placement

Oven

Inspection

Oven inflow

Oven outflow

Queue before component placement

4%

3.535%

21.235%

89.753%

98.031%

40.90

12.08

6.80

3%

3.579%

21.237%

90.741%

99.121%

43.06

12.88

6.96

2%

3.587%

21.082%

90.968%

99.384%

44.93

13.34

7.24

1%

3.591%

20.915%

91.053%

99.472%

45.79

13.43

7.49

Project Four

This project entails reducing the cards preparation time prior tobaking. As aforementioned, each minute reduction in setup time willcost $30. Unlike project two and three, there is no clear pattern inthe relationship between the reductions of oven set up time and theincremental profit. Even though a similar trend can be observed inthe average wait time, the proportion of utilization for solder andcomponent placement are inversely proportional to the oven set uptime. Nonetheless, the optimal oven set up time is 2 minutes, whichgenerates a net profit of $240, having completed at total of 24,971cards after the project.

Table 7: Project Four

Number of Inspectors

Storage Bin Capacity

Percentage Defective

Oven Setup Time

Completed Cards prior to Project

Completed Cards after the Project

Project Cost

Incremental Profit

3

2

5%

6

24776

24841

30

100

3

2

5%

5

24776

24917

60

222

3

2

5%

4

24776

24917

90

192

3

2

5%

3

24776

24947

120

222

3

2

5%

2

24776

24971

150

240

3

2

5%

1

24776

24966

180

200

Table8: Project Four process metrics

Oven Setup Time

Utilization

Average Wait time

Solder

Component placement

Oven

Inspection

Oven inflow

Oven outflow

Queue before component placement

6

3.457%

20.979%

83.649%

95.690%

37.01

11.66

6.69

5

3.466%

21.037%

79.909%

95.986%

36.83

12.23

6.63

4

3.466%

21.037%

75.914%

95.986%

36.13

12.53

6.56

3

3.471%

21.065%

72.004%

96.097%

36.08

12.82

6.56

2

3.473%

21.076%

68.068%

96.174%

35.77

13.00

6.52

1

3.473%

21.079%

64.051%

96.159%

35.48

13.09

6.52

Graphical Representation

Figure1: Relationship between Number of Inspectors andIncremental Profit

Figure2: Relationship Between Storage Bin Capacity andincremental Profit

Figure3: Relationship between Percentage Defective and Incremental Profit

Figure4: Relationship between Oven Set Up Time and Incremental Profit

Figure5: Utilization for the Status Quo and Optimized Projects

Figure6: Average Wait Time for the Status Quo and Optimized Projects

Recommended Project Improvements

The most optimal incremental profits thatHawkeye can make from each project combination are summarised in thetable below.

Project

Number of Inspectors

Storage Bin Capacity

Percentage Defective

Oven Setup Time

Completed Cards prior to Project

Completed

Project Cost

Incremental Profit

Project 1&amp2

4

3

5%

7

24776

26092

1420

1212

Project 1&amp3

4

2

2%

7

24776

28187

1300

5522

Project 1&amp4

4

2

5%

1

24776

27642

-320

6052

Project 2&amp3

3

3

3%

7

24776

25748

620

1324

Project 2&amp4

3

8

5%

2

24776

25380

670

538

Project 3&amp4

3

2

3%

4

24776

25738

290

1634

From the foregoing, it is evident that the largest net profit will beobtained from a combination of project one and four, which wouldgenerate an incremental profit of $6052. This combination entailshiring a new inspector and reducing the cards preparation time priorto baking. This would result in a $1,000 increase in Hawkeye’sannual payroll cost and an incremental cost of $30 for each minutereduction in setup time. It should however be noted that with theexisting oven and quality of epoxy, setup time cannot be shorter thanone minute. In light of this, the project would involve 4 inspectorsand an oven set up time of one minute. The total cost of producingthe cards would decline by $320 and number of cards completed afterthis project would be 27,642.