CEE6100 HW9

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Western Michigan University *

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6100

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Civil Engineering

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Apr 3, 2024

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WESTERN MICHIGAN UNIVERSITY CCE-6100-100 - Civil Systems Analysis HW.9 Done by: Aws Tarawneh
1. The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $250 per order to cover the expenses of delivering and transferring the fuel to MBC’s storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is $0.04 per month, or $0.48 per year; and annual fuel usage is 150,000 gallons. MBC buses operate 300 days a year. a. What is the optimal order quantity for MBC? b. How frequently should MBC order to replenish the gasoline supply? c. The MBC storage tanks have a capacity of 15,000 gallons. Should MBC consider expanding the capacity of its storage tanks? d. What is the reorder point? 2. Suppose that Westside Auto of Problem 4, with D 5 12,000 units per year, Ch 5 (2.50) (0.20) 5 $0.50, and Co 5 $25, decided to operate with a backorder inventory policy. Back- order costs are estimated to be $5 per unit per year. Identify the following: a. Minimum cost order quantity Q * = 2 D c o c h . ( c h + c b c h ) = 2 12000 25 0.5 . ( 0.5 + 5 0.5 ) =1148.91 b. Maximum number of backorders S * = Q * . ( c h c h + c b ) = 1148.91* ( 0.5 0.5 + 5 ) =104.45 c. Maximum inventory Q * - S * =1148.91-104.45=1044.46 d. Cycle time T= 250 Q ¿ D = 250 1148.91 12000 =23.94 e. Total annual cost TC= ¿¿ =237.37+261.12+23.74=522.24
3. The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 40 cars per month. The cars cost $60 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%. a. Determine the economic order quantity and total annual cost under the assumption that no backorders are permitted. Q * = 2 D c o c h . = 2 4 0 12 15 0.2 60 = 34.64 TC= 1 2 Q c h + D Q c o =207.85+207.85=415.70 b. Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost for the model racing cars. Q * = 2 D c o c h . ( c h + c b c b ) = 2 480 15 0.2 60 . ( 0.2 60 + 45 45 ) =39 S * = Q * . ( c h c h + c b ) =8.21 TC= ¿¿ =145.80+184.68+38.88=369.36 c. What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year. Length of backorder period = S d = 8.21 480 / 300 = 5.13 days d. Would you recommend a no-backorder or a backorder inventory policy for this product? Explain. Backorder case since the maximum wait is only 5.13 and the cost savings is 415.70-369.36=46.34 (11.1%) e. If the lead time is six days, what is the reorder point for both the no-backorder and backorder inventory policies? EQQ: r=dm= 480 300 6 = 9.6 Backorder: r=dm-S=1.39
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4. Apply the EOQ model to the following quantity discount situation for which D=500units per year, Co=$40, and the annual holding cost rate is 20%. What order quantity do you recommend? Q 1 = 2 D c o c h = 2 500 40 0.2 10 =141.42 Q 2 = 2 D c o c h = 2 500 40 0.2 9.7 = 143.59 Use Q 2 as the optimal order quantity TC=139.28+139.28+4,850=5,128.56