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Problem 5. Use EOQ model to solve following problem. The item is demanded 50 weeks a year. Item c...

Problem 5.

Use EOQ model to solve following problem. The item is demanded 50 weeks a year.

Item cost: $10

Fixed Order cost: $250

Annual holding cost: 33% of item cost

Average demand: 515 per week, constant rate

a. Calculate the optimal order quantity and the total inventory cost.

b. If your purchase quantity is equal to or above 2000, the fixed ordering cost is reduced to $200. Would you take advantage of it? How much would you save annually?

business   Operations-Management   
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Answer #1

(a) Annual Demand = D = 515*50 = 25750/year

Ordering Cost = Co = $250

Holding Cost = Cc = 33% of $10 = $3.33/year

Economic Order Quantity Q* = √(2DCo/Cc) = √(2*25750*250/3.33) = 1966.31

Annual Inventory cost = average inventory * unit carrying cost = (Q*/2)*Cc = (1966.31/2)*3.33 = $3273.91

(b) Annual Order cost = Number of orders * cost/order = (D/Q*) Co = (25750/1966.31)*250 = $3273.90

Total Cost with Q* = 3273.91 + 3273.90 = $6547.81

If order quantity = 2000,

Total Cost = Inventory Cost + Order Cost = (Q*/2)*Cc + (D/Q*) Co = (2000/2)*3.33 + (25750/2000)*200 =  $5905

Hence, Annual Savings = 6547.81 - 5905 = $642.81

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