A company manufactures two different products: Alpha and Beta. Each of this prod

Question

A company manufactures two different products: Alpha and Beta. Each of this product must be processed by machine K. The company has several identical machines K. The company uses a 15 percent capacity cushion. The unit processing time (minutes per unit), lot size (units per lot), and the setup time (hours per lot) are shown below. Product Alpha; 18 minutes per unit; 150 units per lot; 5.6 hours per lot; Product Beta; 24 minutes per unit; 110 units per lot; 4.4 hours per lot; The company operates two 8-hour shifts per day, 248 days per year. How many machines are required to meet the yearly demand of 46200 units of Alpha and 28160 units of Beta? Use at least 4 decimals in your calculation and answer. Do not use any comma in your answer You must show your calculation steps on your spreadsheet. The required total setup time is 99 x hours per year The required number of machines K is 7.0502 X

Explanation / Answer

Number of lots required for Alpha = 46200/150 = 308 lots

Therefore ,

Total time required for 46200 units of alpha

= Total processing time + Total set up time

= Processing time/ unit x Total number of units + Number of minutes/ lot x Number of lots

= 18 x 46200 + 5.6 hours /lot x 60 minutes/ hour x 308 minutes

= 831600 + 103488

= 935088 minutes

Number of lots required Beta = 28160 / 110 = 256

Total time required for 28160 units of Beta

= Processing time / unit x Total number of units + Number of minutes / lot x Number of lots

= 24 x 28160 + 4.4 x 60 x 256

= 675840 + 67584

= 743424 minutes

Therefore , Total time required for alpha plus beta = 935088 minutes + 743424 minutes = 167852 minutes = 27975.20

Yearly available hours for each machine K = 365 x 24 hours

Therefore , number of machines required without capacity cushion = 27975.20 /( 365 x 24) = 3.1935

Taking into account capacity cushion of 15 percent, total number of machines required

= Number of machines required without capacity cushion ( 1 + Capacity cushion %/100)

= 3.1935 x ( 1 + 15/100)

= 3.1935 x 1.15

= 3.6725

Total set up time required for product alpha = 5.6 x 308 hours = 1724.80 hours

Total set up time required for product beta = 4.4 x 256 hour = 1126.40 hours

Therefore , required total   set up time = 1724.80 + 1126.40 hours = 2851.20 hours

REQUIRED TOTAL SET UP TIME IS 2851.20 HOURS

REQUIRED NUMBER OF MACHINE K IS = 3.6725

REQUIRED TOTAL SET UP TIME IS 2851.20 HOURS

REQUIRED NUMBER OF MACHINE K IS = 3.6725

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