Question

A whole grocery store uses a two step process to fill orders. Tomorrow’s work will consists of filing the seven orders shown. Determine the:

a. Schedule of  Step 1 that will minimize the time required to fill the orders.

b. Schedule of Step 2 that will minimize the time required to fill the orders.

	TIME ( Hours)
Order	step 1	Step 2
A	1.20	1.40
B	0.90	1.30
C	2.00	0.80
D	1.70	1.50
E	1.60	1.80
F	2.20	1.75
G	1.30	1.40

Answer 1

Since Step-2 always follows Step-1, separate schedules for Step-1 and Step-2 will not be possible.

Johnson's rule will give us the common schedule (for both step 1 and 2) that will minimize the makespan.

Step	Minimum processing time of an unscheduled job	Corresponding job	Corresponding Step	Sequence
1	0.8	C	Step-2	_, _, _, _, _, _, C
2	0.9	B	Step-1	B, _, _, _, _, _, C
3	1.2	A	Step-1	B, A, _, _, _, _, C
4	1.3	G	Step-1	B, A, G, _, _, _, C
5	1.5	D	Step-2	B, A, G, _, _, D, C
6	1.6	E	Step-1	B, A, G, E, _, D, C
7	1.75	F	Step-2	B, A, G, E, F, D, C

So,

The best sequence is B-A-G-E-F-D-C

Gantt Chart:

So,

as per the Gantt chart, the overall minimum makespan is 11.7 hours