The Pedal Pusher Bicycle Shop operates 7 days per week, closing only on Christmas Day. The shop pays
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The Pedal Pusher Bicycle Shop operates 7 days per week, closing only on Christmas Day. The shop pays $300 for a particular bicycle purchased from the manufacturer. The annual holding cost per bicycle is estimated to be 25% of the dollar value of inventory. The shop sells an aver- age of 25 bikes per week. Frequently, the dealer does not have a bike in stock when a customer purchases it, and the bike is back-ordered. The dealer estimates his shortage cost per unit back- ordered, on an annual basis, to be $250 due to lost future sales (and profits). The ordering cost for each order is $100. Determine the optimal order quantity and shortage level and the total minimum cost.

Sep 15 2021 07:49 AM

1 Approved Answer

Tara P
answered on
September 17, 2021

3.5
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(9 Votes)

Optimal order quantity = √2RO/C R = average bike sell * number of week (52) R = 25 * 52 = 1300 units O = $100 C = 25% of per unit cost (300) = 300 * 25% = 75 = √2 * 1300 * 100 / 75 = √260000 / 75 = √3466.67 = 58.88 or 59 units Shortage = EOQ * (Holding cost / (shortage cost + holding cost)) = 59 * (75 / (250 + 75)) = 59 * (75 / 325) = 13.65...

s Total minimum cost = Annual Holding Cost + Annual Order Cost + Shortage Cost = 2213 + 2204 + 250 = $4667 Annual holding cost = (59 / 2) * C = (59 / 2) * 75 = 29.5 * 75 = $2213 Annual order cost = (R / Q) * O = (1300 / 59) * 100 = $2203.39 or 2204

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