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Homework answers / question archive / A bicycle production company receives a demand for 15,000 bikes each year, and needs to produce one frame for each bike
A bicycle production company receives a demand for 15,000 bikes each year, and needs to produce one frame for each bike. The production setup cost for the company is $500, and per unit production cost is $10. The company can produce 1,500 frames per month. (There are 12 months in one year.) The yearly interest rate is estimated to be 30%.
a. [10 points] What is the optimal production quantity for frames and maximum inventory level that can be achieved in any order cycle?
b. [5 points] What is the annual total cost of setup, ordering, and inventory holding?
c. [5 points] Suppose that the warehouse for the frames has a capacity for 3,000 frames only. Would this warehouse capacity restriction change the decision of the company made in Part (a)? Why?
Answer :
(a)
Annual demand (D) = 15,000 bikes
Average monthly demand (d) = 15,000 ÷ 12 = 1,250
Production rate (p) = 1500
Annual holding cost (H) = 30% × unit cost = 30% × 10 = $3
Ordering cost (S) = $500
1)Optimal production quantity (Q) = square root (2DS / H(1- d/p))
= Square root {(2 × 15,000 × 500) / 3 (1 - 1,250/1500)}
= 5,477 units
2) maximum inventory level = Q × (1 - d/p)
= 5,477 × (1 - 1,250/1500)
= 913 units
(b)
Total annual cost = Q/2 × H × (1 - d/p) + D/Q × S
= 5,477/2 × 3 × (1 - 1,250/1,500) + 15000/5,477 × 500
= 1369.25 + 1,369.36
= 2,738.61
(c)
Maximum inventory level is 913 which is less than capacity of warehouse. Therefore, there would be no change in decision made in part (a).
