A machine tool is used to machine parts in batches In one ba

A machine tool is used to machine parts in batches. In one batch of interest, the starting piece is a casting that costs = $5.00 each. Batch quantity = 40. The actual machining time in the operation = 6.86 min. Time to load and unload each workpiece = 2.0 min. Cost of the cutting tool = $3.00, and each tool must be changed every 10 pieces. Tool change time = 1.5 min. Setup time for the batch = 1.75 hr. Hourly wage rate of the operator = $16.00/hr, and the applicable labor overhead rate = 50%. Hourly equipment cost rate = $22.00/hr, which includes overhead. Assume availability = 100% and scrap rate = 0. Determine: The cycle time for the piece Average hourly production rate when setup time is figured in; and Cost per piece.

Solution

Given:- C_c = Cost of casting= $5.00

C_t = Initial cost of the tool = $3.00; p= No. of parts produced per batch = 40

T_m= Machining Time = 6.86 min; t_l= time to load and unload = 2.0min;  

p_g= No of pieces produced between tool changing = 10; t_c = Tool changing time = 1.5min

t_o= Set up time for a batch = 1.75 hr; C_L= Manpower cost = $16.00; C_m= Machine tool operating cost = $22.00

R= Labor overhead rate = 50%

a) Cycle time for the peice = T_m + t_l + Set up time per peice

Set up time per piece = (1.75x60/40) =2.625 min

Hence Cycle time for the peice = 11.485 min

b) Average hourly production rate = 60/11.485 = 5.224 pieces /hr

c) C_o = overall overhead cost =  C_L + C_m(1+R) = $49.00/60= $0.8167/min

Cost of all overheads per piece = C₁ = C_o(t_l+t_o/p) = $3.77

Total cost of the tool C₂ = Cost of tool replacement +Cost of the tool

C₂ = ((C₀xt_c)+ C_t ) / p_g = $0.422

Machining Cost = C₃ = C_oT_m = $5.602

therefore total cost per piece is

C= C_c+C₁+C₂+C₃ = $14.794