Question

A company makes four products. the processing requirements for each product on each of the four machines are shown in the table.

work center	a	b	c	d
x	10	12	15	10
y	12	10	10	10
z	8	10	12	10

work centers X,Y, and Z are available for 40 hours per week and have no setup time when switching between products. Market demand is 40 As, 50 Bs, 60 Cs, and 70 Ds per week. Calculate the processing times on the four machines and find out on which work center the bottleneck occurs.

Answer 1

The dimensions of the processing requirements is not given. Let us assume it min/unit.

For the work center X, the total time it takes for processing the given requirement is (10*40)+(12*50)+(15*60)+(10*70) = 400+600+900+700 = 2600 min or 43.3 h

For the work center Y, the total time it takes for processing the given requirement is (12*40)+(10*50)+(10*60)+(10*70) = 480+500+600+700 = 2200 min or 36.6 h

For the work center Z, the total time it takes for processing the given requirement is (8*40)+(10*50)+(12*60)+(10*70) = 320+500+720+700 = 2240 min or 37.3 h.

The work centers Y and Z can complete the work within the available time. However, work center X needs 3.3 more hours for the product to be finished and hence, is at the bottleneck.

Therefore, the answer is work center X.