Question

Macon Controls produces three different types of control units used to protect industrial equipment from overheating. Each of these units must be processed by a machine that Macon considers to be their process bottleneck. The plant operates on two​ 8-hour shifts, 5 days per​ week, 52 weeks per year. The table below provides the time standards at the​ bottleneck, lot​ sizes, and demand forecasts for the three units. Because of demand​ uncertainties, the operations manager obtained three demand forecasts​ (pessimistic, expected, and​ optimistic). The manager believes that a 30 percent capacity cushion is best.

Component 40 Processing (hr/unit) 0.04 0.2 0.05 Setup (hr/lot) Lot Size (units/lot) Pessimistic 14,000 75 9,000 8.8 120 18,000 Expected 17,000 12,000 23,000 Optimistic 27,000 17,000 35,000 4.5

a. How many machines are required to meet minimum​ (Pessimistic) demand, expected​ demand, and maximum​ (Optimistic) demand? ​(Enter your responses rounded up to the next whole​ number.)

Demand Forecast Capacity Requirement​ (M)
Pessimistic _________ machines
Expected _________ machines
Optimisti _________ machines

Answer 1

Available capacity (hrs.) = 2 * 8 * 5 * 52 = 4,160 hrs.

Utilization = 1 - capacity cushion = 1 - 0.30 = 0.70

So, utilizable capacity = 4160*0.70 = 2,912 hrs.

Component	Processing time	Setup time	Lot size	Demand (P)	Demand (E)	Demand (O)
A	0.04	1.0	40	14,000	17,000	27,000
B	0.20	4.5	75	9,000	12,000	17,000
C	0.05	8.8	120	18,000	23,000	35,000
Pessimistic	Workload (hrs.)	Capacity (hrs.)	No. of m/c	No. of m/c rounded up
A	910
B	2,340
C	2,220
Total	5,470	2,912	1.88	2
Expected	Workload (hrs.)	Capacity (hrs.)	No. of m/c	No. of m/c rounded up
A	1,105
B	3,120
C	2,837
Total	7,062	2,912	2.43	3
Optimistic	Workload (hrs.)	Capacity (hrs.)	No. of m/c	No. of m/c rounded up
A	1,755
B	4,420
C	4,317
Total	10,492	2,912	3.60	4

B 1 Component Processing time Setup time Lot size Demand (P) Demand (E) Demand (0) A 0.04 0.2 0.05 1 4.5 8.8 40 75 120 14000 9000 18000 17000 12000 23000 27000 17000 35000 Pessimistic Workload (hrs.) Capacity (hrs.) No. of m/c No. of m/c rounded up =C3*F3+F3*D3/E3 =C4*F4+F4*D4/E4 =C5*F5+F5*D5/E5 =SUM(C8:010) 11 Total 2912 =C11/D11 =ROUNDUP(E11,0) Expected Capacity (hrs.) No. of m/C No. of m/c rounded up 13 14 15 B Workload (hrs.) =C3*G3+G3*D3/E3 =C4*G4+G4*D4/E4 =C5*G5+G5*D5/E5 ESUM(C14:016) Total 2912 =C17/D17 =ROUNDUP(E17,0) 18 Optimistic Workload (hrs.) Capacity (hrs.) No. of m/C No. of m/c rounded up A B =C3*H3+H3*D3/E3 =C4*H4+H4*D4/E4 =C5*H5+H5*D5/E5 =SUM(C20:c22) C Total 2912 =C23/D23 =ROUNDUP(E23,0)

Calculations: