A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run

Question

A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. Determine the

a. Optimal run size

b. Minimum total annual cost for carrying and setup.

c. Cycle time for the optimal run size.

d. Run time.

a. Optimal run size

b. Minimum total annual cost for carrying and setup.

c. Cycle time for the optimal run size.

d. Run time.

Accepted Answer

D = 48 000 wheels per year

S =$45

H =$1 per wheel per year

P = 800 wheels per day

u =48 ,000 wheels per 240 days, or 200 wheels per day

a. [latex]Q_p = \sqrt{\frac{2DS}{H} }= \sqrt{\frac{p}{p-u} } =\sqrt{\frac{2(48,000) 45}{1} }\sqrt{\frac{800}{800 - 200} } = 2,400[/latex] wheels

b. [latex]TC_{min} =[/latex] Carrying cost + Setup cost= [latex]\left\lgroup\frac{I_{\max}}{2} ight group H + (D /Q_p)S[/latex]

Thus, first compute [latex]I_{\max}[/latex]:

[latex]I_{\max}= \frac{Q_p}{p}(p - u)= \frac{2,400}{800}(800 - 200) = 1,800[/latex] wheels

[latex]TC = \frac{1,800}{2} imes \$ 1 + \frac{48,000}{2,400} imes \$ 45 = \$ 900 + \$ 900 = \$ 1,800 [/latex]

Note again the equality of cost (in this example, setup and carrying costs) at the EOQ.

c. Cycle time =[latex]\frac{Q_p}{u}= \frac{2,400 wheels}{200 wheels per day} = 12 days [/latex]

Thus, a run of wheels will be made every 12 days.

d. Run time =[latex]\frac{Q_p}{u}= \frac{2,400 wheels}{800 wheels per day} = 3 days[/latex]

Thus, each run will require three days to complete.

Question 13.4: A toy manufacturer uses 48,000 rubber wheels per year for it...

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