Question

JCL Inc. is a major chip manufacturing firm that sells its products to computer manufacturers like Dell, HP, and others. In simplified terms, chip making at JCL Inc. involves three basic operations: depositing, patterning, and etching.

• Depositing: Using chemical vapor deposition (CVD) technology, an insulating material is deposited on the wafer surface, forming a thin layer of solid material on the chip.
• Patterning: Photolithography projects a microscopic circuit pattern on the wafer surface, which has a light-sensitive chemical like the emulsion on photographic film. It is repeated many times as each layer of the chip is built.
• Etching: Etching removes selected material from the chip surface to create the device structures.

The following table lists the required processing times and setup times at each of the steps. Assume that the unit of production is a wafer, from which individual chips are cut at a later stage.

Note: A setup can only begin once the batch has arrived at the machine.

Process Step	1 Depositing	2 Patterning	3 Etching
Setup time	42 min.	32 min.	22 min.
Processing time	0.18 min./unit	0.28 min./unit	0.23 min./unit

(a) What is the process capacity in units per hour with a batch size of 100 wafers?

Looking for a table like:

Deposition ____ units/hour

Patterning _____ units/hour

Etching _______ units/hour

(c) Suppose JCL Inc. came up with a new technology that eliminated the setup time for step 1 (deposition), but increased the processing time to 0.42 minute/unit. What would be the batch size you would choose so as to maximize the overall capacity of the process? (Round your intermediate computations to 2 decimal places. Round your final answer to the nearest whole number.)

Batch size is ____ units.

Answer 1

JCL Inc.

(a)

Given:

Process Step	1 Depositing	2 Patterning	3 Etching
Setup time	42 min.	32 min.	22 min.
Processing time	0.18 min./unit	0.28 min./unit	0.23 min./unit

Batch size = 100

Capacity = Number of units produced/Total time taken to produce the units

Total time is taken = Total set up time + Total processing time

Processing time is per unit, so we have to convert the per-unit processing time for the batch time. Total processing time will be Batch size*processing time per unit

Capacity = Number of units produced i.e. batch size/Set up time + (Batch size*processing time per unit)

Process Step	1 Depositing	2 Patterning	3 Etching
Setup time	42 min.	32 min.	22 min.
Processing time	0.18 min./unit	0.28 min./unit	0.23 min./unit
Capacity	100/42+(100*0.18) =100/ (42+18) =100/60 =1.6667 Units/minute =1.6661*60 = 100 units/hour	100/32+(100*0.28+ =100/ (32+28) =100/60 =1.6667 =1.6667*60 =100 units/hour	100/22+(100*0.23) =100/ (22+23) =100/45 =2.2222 =2.222*60 =133.33 units/hour

Capacity:

Deposition = 100 units/hour

Patterning = 100 units/hour

Etching = 133.33 units/hour

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(b)

Just processing time is there, so the capacity will not be dependent on batch size.

The capacity = 1/processing time = 1/0.42=2.3809*60 = 142.8571 units/hr

This is the same capacity as step 3. So step 3 cannot be the bottleneck in any situation. If we want to maximize the capacity, we must have the capacity of step 2 that would be greater than the capacity of step 1. This will make step 1 bottleneck and the capacity will be maximized.

Suppose, x is the batch size

x/(32+0.28x) ≥1/0.42

0.42x≥32+0.28x

0.42x – 0.28x≥32

0.14x≥32

x≥32/0.14

x≥228.5714

x=229