# 6.8 Scenarios and Exercises

## 6.8.1 Operation Time versus Operation Cost, or the Effect of Varying Setup Time and Batch Size

This exercise will help to illustrate the need to find a balance between (1) short lead time, and (2) low cost, for any operation. These two factors are determined by setup time and batch size. You will find the effect of setup time and batch size on

1. The operation time, which is a measure of the lead time of the order.
2. The operation time per unit (that is, operation time divided by batch size), which is a measure of the cost of the operation and therefore of the cost of the production or procurement order.

(0) First, suppose a setup time of 200, a run time per unit of 100, and a batch size of 4. Calculate the operation time and the operation time per unit.

Solution:       Operation time: 600; operation time per unit: 150.

(1) If batch size is increased to 20, what are the effects on operation time and operation time per unit? In your opinion, what effects are positive or negative?

Solution:   Positive: operation time per unit clearly reduced to 110.
negative: operation time very much extended to 2200.

(2) Suppose that because of the hard work of the process engineers (e.g., by applying SMED measures), setup time could be reduced to 100. What is the effect of this, if the batch size is maintained at 20?

Answer:   Positive: operation time per unit slightly reduced to 105.
negative: operation time only very slightly reduced to 2100.

(3) To what extent can the batch size be reduced after the reduction of set¬up time to 100, so that the operation time does not exceed the original operation time of 600? What will the operation time per unit be?

Answer :   Batch size = 5; operation time per unit = 120.

(4) To what extent can the batch size be reduced after the reduction of setup time to 100, so that the operation time per unit does not exceed the original time per unit of 150? What will the operation time be?

Answer:   Batch size = 2; operation time = 300.

You can view the animated solution here:

Try out different values for setup time, run time per unit, and batch size.

## 6.8.2 The Effect of Cellular Manufacturing on Lead Time Reduction

Figure 6.8.2.1 shows a possible routing sheet for production of shafts. The batch size is 10.

Fig. 6.8.2.1        Routing sheet for production of shafts.

a. Calculate the lead time in traditional job shop production. Hint: For job shop production, lead time has to be calculated assuming a sequence of operations. Therefore, you can use the formula in Figure 6.2.2.3.

Solution: 14.22.

b. Calculate the maximum lead time for the case of cellular manufacturing, that is, using the formula in Figure 6.2.2.4. (Hint: First determine the cell drive

Solution: 10.98 (the cell driver is the operation “millcut nut” with an operation time of 7.60; setup time plus run time of all the other operations is 3.38).

c. For the given routing sheet shown in Figure 6.8.2.1, and for cellular production, find a temporal order of operations that yields minimum lead time.

Solution: Minimum total lead time is 7.88. The setup and the first unit of the batch of operations “millcut” and “lathe” can be fully executed during the setup of the cell driver, as well as the setup of the operations “pregrinding” and “final grinding”. Each unit of the batch can be run directly after its run on the cell driver operation. Thus, the run times for one unit for “pre-grinding” and “final grinding” have to be added to the cell driver operation time, or 0.12 + 0.16 + 7.6, making 7.88.

d. For the given routing sheet shown in Figure 6.8.2.1, and for cellular production, find a temporal order of operations that yields minimal load (or minimum allocated time for the operation, that is, operation time plus wait time between the units of the batch) at the workstations.

Solution: Lead time with minimum load is 8.24. Again, the setup and the first unit of the batch of operations “millcut” and “lathe” can be fully executed during the setup of the cell driver. For “pregrinding,” to be ready to execute the last unit of the batch just after the completion of the cell driver operation, the 9 units of “pregrinding” must have been just completed at point 7.6 in the time axis. Thus, the latest start date of “pregrinding” must be 7.6 – 9 * 0.12 – 1.2 = 5.32. For “final grinding,” the first unit of the batch can be executed directly after the first unit of “pregrinding” has been executed, that is, at 5.32

You can view the animated solution here:

By modifying setup and run times of the operations, change the cell driver. Try to find a combination where the variant “minimum total lead time” tends toward the “maximum lead time” value of the lead time formula for cell manufacturing.

## 6.8.3 Line Balancing — Harmonizing the Content of Work

Figure 6.8.3.1 shows a possible routing sheet for parts production out of sheet metal. Three different products are produced: items 1, 2, and 3. All have a similar routing sheet. For the different operations, the number in the table is the operation time, and the number in parentheses is the setup time.

Fig. 6.8.3.1        Harmonizing the content of work: routing sheets for three products.

In accordance with the discussion in Section 6.2.3, assume a duration of one unit of harmonized content of work of 12 time units. The task is to perform measures to change lead times of operations, chosen from the various possible measures to line ba­lance or harmonize the content of work listed according to Figure 6.2.3.3.

a. Suppose that the first two operations can be combined into one (why is this a feasible assumption?). Item 3 seems — at first glance — to fit quite well into three units of harmonized content of work. Thus, according to the first one of the measures listed in Figure 6.2.3.3, try to change lot sizes of items 1 and 2 (use the empty columns in Figure 6.8.3.1), to obtain for each of them a total operation time on the order of 36 units of time.

Solution: There are machines that perform both operations in one step (e.g., laser-cutting machines). Changing the lot size for product 1 to 200 results in a total operation time of 36, with 18 units of time for setup. Furthermore, the length of the combination of the two first operations is now 10 (or even less, due to complete processing), and this fits well into one unit of harmonized content of work. Changing the lot size for item 1 to 100 would result in a total operation time of 27, with 18 units of time for setup. Thus, a batch size of 200 is the better choice. In addition, changing the lot size for product 2 to 25 results in a total operation time of 31, with 10 units of time for setup. Again, the combination of the two first operations fits well into one unit of harmonized content of work, its total length being 11.

b. Is it possible, in practice, to combine the last two operations into one, fitting them into one unit of harmonized content of work?

Answer: Yes. Testing and preassembly can be done at the same physical work center. Furthermore, with a lot size of 200 for item 1, the combination of the two last operations would fit well into one unit of harmonized content of work.

c. For item 1, the third and fourth operations do not fit into a unit of harmonized content of work, despite significant changes to the batch size. What other possible measures listed in Figure 6.2.3.3 could be implemented?

Answer: Considering the very small run time per unit, the bending operation seems to be very simple (also, the second operation, pressing, appears to be rudimentary, as compared to the process for item 2). Thus, it might be possible to purchase sheet metal that is already profiled (bent). Another solution would be to combine this short process into the same unit of harmonized content of work together with cutting and pressing, using a dedicated (simple, but cheap) machine that could be installed not at work center C, but close to work center B.
Surface treatment is most likely a subcontracted process. This is probably the reason behind the long setup time, which may actually reflect transportation time rather than setup time at the supplier’s site. If so, why not look for a faster transportation vehicle or for a sub¬contractor in greater geographical proximity to the factory?

d. After implementing all these measures, are there still problems?

Answer: Yes. For product 1, setup time is now 50% of the operation time. If setup time is not reduced significantly with the measure in point c, then additional measures must be found to reduce the setup time (e.g., by implementing SMED techniques).

## 6.8.4 Calculating the Number of Kanban Cards

An automotive company has implemented a JIT program using Kanbans to signal the movement and production of product. The average inventory levels have been reduced to where they are roughly proportional to the number of Kanbans in use. Figure 6.8.4.1 shows the data for three of the products.

Fig. 6.8.4.1        Data on three products for calculation of the number of Kanban cards.

a. The process engineers have been hard at work improving the manufacturing process. They have initiated a new project to reduce lead time from 36 days to 21 days. What would the percentage change in average inventory be for each item?

Solution: Using the formula in Figure 6.3.2.3, calculate the required number of Kanban cards before and after the process improvement. As inventory is proportional to number of Kanbans, the inventory reduction corresponds to the reduction of the number of Kanban cards.

• Item 1:           before,   7; after, 5     à       Inventory reduction: 29%
• Item 2:           before,   9; after, 6     à      Inventory reduction: 33%
• Item 3:           before, 10; after, 7     à      Inventory reduction: 30%

b. Calculate the number of Kanban cards using other data values. Try to answer the following questions:

• What is the minimum number of Kanban cards required in any case?

• How do the safety factor and the number of containers per transport batch influence the number of Kanban cards required?

## Course sections and their intended learning outcomes

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