A particular type of rubber is used in the production of tennis balls and the co
ID: 339151 • Letter: A
Question
A particular type of rubber is used in the production of tennis balls and the company must decide on three different suppliers. Supplier A will sell the rubbers for $1.50 per rubber and will not accept any orders fewer than 7,000. Supplier B will sell the rubbers for $1.40 each but wil not consider an order for greater than 8,500 rubbers, and Supplier C will sel the rubbers for $1.35 each but wil not accept an order for greater than 9,000 rubbers. Assume an order setup cost of $150 and an annual requirement of 60,000 rubbers. Assume a 20 percent annual interest rate for holding cost calculations. a. Which suppliers should be selected and what is the size of the standing order? b. What is the optimal value of the holding and setup costs for rubbers when the optimal source is used? c. If the replenishment lead time for rubbers is three months, determine the reorder point based on the on-hand level of inventory of rubbersExplanation / Answer
Annual demand, D = 60,000
Order Setup cost, S = $ 150
(a)
Supplier A
Unit price, P = $ 1.5
Holding cost, H = 1.5*20% = 0.3
EOQ = SQRT(2DS/H) = SQRT(2*60000*150/0.3) = 7746 (this satisfies the supplier requirement of order not less than 7000)
Annual cost = Ordering cost + Holding cost + Purchase cost = (D/Q)*S + (Q/2)*H + D*P
= (60000/7746)*150 + (7746/2)*0.3 + 60000*1.5
= $ 92,324
_________________________________
Supplier B
Unit price, P = $ 1.4
Holding cost, H = 1.4*20% = 0.28
EOQ = SQRT(2DS/H) = SQRT(2*60000*150/0.28) = 8018 (this satisfies the supplier requirement of order not more than 8500)
Annual cost = Ordering cost + Holding cost + Purchase cost = (D/Q)*S + (Q/2)*H + D*P
= (60000/8018)*150 + (8018/2)*0.28 + 60000*1.4
= $ 86,245
_________________________________
Supplier C
Unit price, P = $ 1.35
Holding cost, H = 1.35*20% = 0.27
EOQ = SQRT(2DS/H) = SQRT(2*60000*150/0.27) = 8165 (this satisfies the supplier requirement of order not more than 9000)
Annual cost = Ordering cost + Holding cost + Purchase cost = (D/Q)*S + (Q/2)*H + D*P
= (60000/8165)*150 + (8165/2)*0.27 + 60000*1.35
= $ 83,205
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Total cost of Supplier C is the lowest. Therefore, Supplier C should be selected.
Size of the standing order = 8165
b) Optimal value of holding cost and setup costs = (60000/8165)*150 + (8165/2)*0.27 = $ 2205
c) Reorder point = Average monthly demand * Lead time in months = (60000/12)*3 = 15,000
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