Question

Problem 6 A plant produces six families of products. Production consists of parts fabrication followed by assembly. Only one family can be fabricated or assembled at a time. Given the data in Table below Family Setup and Processing Days FamilyParts Fabrication Assembly 2 10 1 a) Find the minimum completion time schedule for the plant. b) llustrate solution with a Gantt chart and determine completion time

Answer 1

First of all we have to find the sequence for the processing of the families of the product on the basis of completion time.

It will be done using Johnson's rule which involves the following steps:

1. Find out the minimum time taken from the parts fabrication time and assembly time.
2. If the minimum is from parts fabrication time column then it will be preferred at the start, otherwise, if it is from assembly time column then it will be preferred at the last.
3. The family which has been assigned a place in the sequence once will not be considered again.
4. Continue in the similar manner until all the jobs are assigned.

Following the aforementioned rule, we will find out the sequence for shortest completion time as follows:

3    6    2    1    5    4

Now, tabulating according to the sequence:

	Parts Fabrication		Assembly
Family	In	Out	In	Out
3	0	0+4=4	4	4+9=13
6	4	4+5=9	13	13+6=19
2	9	9+10=19	19	19+8=27
1	19	19+6=25	27	27+4=31
5	25	25+6=31	31	31+3=34
4	31	31+3=34	34	34+2=36

(a)

From the above table, we can see that the minimum completion time comes out to be 36 days (the time by which the last family is assembled).

(b)

Gantt Chart:

Duration (In Days) - Day O Day 4 Day 9 Day 13 Day 19 Day 25 27 31 34 36 Parts Fabrication Assembly