Up, Up, and Away is a producer of kites and wind socks in Washington. Relevant d

ID: 468042 • Letter: U

Question

Up, Up, and Away is a producer of kites and wind socks in Washington. Relevant data on the bottleneck operation in the shop for the upcoming fiscal year are given in the following table.

The shop works two shifts per day, 8 hours per shift, 190 days per year. Currently, the company operates four machines, and desires a 25 percent capacity cushion. How many machines should be purchased to meet the upcoming year's demand without resorting to any short-term capacity solutions?

The number of additional machines required is ??? (Enter your response rounded up to the next whole number.)

Item Kites Wind Socks Demand forecast 28,000 units/year 12,000 units/year Lot size 15 units 70 units Standard processing time 0.2 hour/unit 1.0 hour/unit Standard setup time 3.0 hours/lot 4.0 hours/lot

Explanation / Answer

Shifts per day: 2

Hours per shift: 8 hours

Days: 190

Total number of hours available = N = Days x shifts/day x hours/shift

N = 190 x 2 x 8 = 3040 Hours

C = Desired capacity Cushion = 25%

Capacity requirement or number of machines (M) required is given as:

M =(Hours required by each product for processing and setup)/(Hours available per year after deducting desired capacity cushion)

M = [(Dipi + (Di/Qi)Si]/[N(1-C/100)]

Item

Kites

Wind Socks

Demand forecast

Dk = 28,000 units/year

Dw = 12,000 units/year

Lot size

Qk = 15 units

Qw = 70 units

Standard processing time

pk = 0.2 hour/unit

pw = 1.0 hour/unit

Standard setup time

Sk = 3.0 hours/lot

Sw = 4.0 hours/lot

Processing time required (Dipi)

28000 x 0.2 = 5600 hours

12,000 x 1.0 = 12,000 hours

Setup processing time required [(Di/Qi)Si]

(28000/15) x 3 = 5600 hours

(12000/70) x 4 = 685.7 hours

Total hours required for Processing and Setup

5600 +5600 = 11200 hours

12000+685.7 = 12685.7 hours

M = [11200 + 12685.7/[3040(1-25/100)]

M = 23885.7/2280

M = 10.48

11 Machines are required with a desired capacity cushion of 25 %.

The number of additional machines required is 11.