39 A batch production plant works 40 hours per week and has

3.9 A batch production plant works 40 hours per week and has three machines. In a typical week, five batches of parts are processed through these machines. Production rates, batch times. and operation sequences for the parts are given in the table below for one week. (a) Determine the weekly production rate for the shop. (b) Is this weekly production rate equal to the plant capacity? If not. determine what the output would be if all three machines could be operated up to 40 hours per week, given the constraint that no reductions in weekly production rates are allowed for any part. Use of a spreadsheet calculator is recommended for this problem.

Solution

R p =1 / t b

R p = Average production Rate (parts/ min)

T b = Average production time (parts /min)

Machine 1

R p1 =1 / t b1

Part A

10= 1/15

=0.66

Part B

15=1/14

=1.07

Part D

20=1/5

=4

Machine 2

R p2 =1 / t b2

Part A

15=1/10

=1.5

Part c

8=1 / 21

=0.38

Part d

25= 1/4

=6.25

Part E

16= 1/ 5

=3.2

Machine 3

R p3 =1 / t b3

Part A

18.75 = 1/8

=2.34

Part B

10=1/21

=0.48

Part E

10= 1/8

=1.25

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b) No only Machine 2 working for 40 hours

b) Machine 2 working capacity of 40 hours, machine 1 having 34 hours ,Machine 3 having  37 hours

For Machine 1

Added Part c for 6 hours (Already 34 hours +6 hours = 40 hours

For Machine 3

Added Part d  for 3 hours( Already 37 hours +3 hours =40 hours)

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