Question

The manager of a car garage must schedule repairs on five (5) cars. he would like to minimize the total processing time of the five cars. Repairs on each car require two successive activities: sheet metal and painting. The relevant data for the five cars are given in the following table

Cars	Sheet metal (hours)	Painting (hours)
v1	8	7
v2	9	4
v3	7	9
v4	3	4
v5	12	5

a) Use Johnson's rule to determine the optimal sequence in which the cars should be repaired. Show the details of your process.

b) Construct the corresponding GANTT chart and deduce the total time from treatment of the five cars, as well as the total time out.

Answer 1

(a) The job v4 with shortest time (3) corresponds to machine 1, hence it would be placed at Position1.

The next job v2 is with shortest time (4) which corresponds to machine 2, hence placed at last position 5.

The next job with lowest duration is v5, with duration 5 corresponding to machine 2, hence placed at second last position 4.

The remaining jobs v1 and v3 have shortest duration time of 7 each can be arranged at positions 3 for v1( because the time corresponds to machine 2 ) and position 2 for v3.

The arrangement looks like

v4-->v3-->v1-->v5-->v2

(b)

M2

v4

v3

v1

v5

v2

M1

v4

v3

v1

v5

v2

Total completion time = 43

Total time out on machine 2 = 14