Designing, Managing, and Improving Operations

Question 1 (40 pts)

The following tasks have to be performed on a unit of raw material in order to convert it into a unit of finished product.

Task	Time (minutes)	Immediate Predecessors
a	3	-
b	4	-
c	3	a
d	6	c,b
e	5	d
f	1	d
g	7	e,f
h	4	e
i	3	g,h
j	5	i
Total	41

1. Draw a precedence network for these tasks. (5 pts)
2. Suppose that each task is performed at a separate station. The time taken is as shown in the above table. Once a task is performed it is picked up by the next station. Transfer times are included in the task times and so may be ignored. Thus you have an assembly line with 10 stations.

(i) What is the maximum production possible from this assembly line in an 8-hour day? (Hint: what is the bottleneck?) (5 pts)

(ii) what is the efficiency of this assembly line? (5 pts)

3. It is possible to achieve the same production as in (b) with fewer stations. Draw one possible arrangement that will do so. What is the efficiency of this arrangement? (10 pts)
4. Suppose that a production of 40 units per 8-hour day is desired.

(i) What is the minimum number of stations needed to meet this rate? (2 pts)

(ii) Design an assembly line that will meet this requirement. (8 pts)

(iii) What is the efficiency of this line? (3 pts)

(iv) What is the idle time per unit in this line? (2 pts)

Question 2 (30 pts)

A machine process units in batches. It has a setup time of 120 minutes and run time of 0.008 minutes per piece. After a batch is processed, the process has to be stopped and the machine has to be setup before the next batch can be processed. Assume that a day is 480 minutes long.

Find the capacity in pieces per day for this machine under the following assumptions:

(i) Batch size is 5,000 units (12 pts)

(ii) Batch size is 10,000 units. (12 pts)

(iii) What is the percent change in capacity as you go from (i) to (ii) (6 pts)

Question 3 (10 pts)

A particular operation may be performed by two kinds of process. Process A requires a setup time of 40 minutes, whereas Process B requires a setup time of 180 minutes. On the other hand, the per unit run times are: 0.012 minutes on A and 0.002 minutes on B. What is the minimum batch size you would route through B?

Question-4 (20 pts)

A process produces two types of products A and B. Product A is done in batches of 1000 units. It involves a setup time of 1 hour and a run time of 45 seconds. Product B is done in batches of 2000 units and involves a setup time of 0.5 hour and a run time of 30 seconds.

How many units can this process produce in a week of 40 hours, if:

1. only product A is produced? (5 pts)
2. only product B is produced? (5 pts)
3. A and B are produced in a mix of 20% A and 80% B? (10 pts)