The metropolitan bus company (mbc) purchases diesel fuel from american petroleum supply. in addition to the fuel cost, american petroleum supply charges mbc $300 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 $0.03 per month, or $0.36 per year; and annual fuel usage is 240,000 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 240,000 gallons. should mbc consider expanding the capacity of its storage tanks? d. what is the recorder point?

The MBC data is given below:

Demand Rate, D = 240000 gallons per year

Setup cost, S = $300 per order  

Holding cost, H = 0.36 per year  

Number of operating days = 300 days a year

Lead time, L = 10 days

a)  Calculate the optimal quantity for MBC as follows:

EOQ =  

EOQ =  

EOQ =  

EOQ = 20000

Therefore, the optimal order quantity for MBC is 20000 gallons.

b)  Calculate the order frequency MBC should order to replenish the gasoline supply as follows:

Order frequency = Demand rate/EOQ

Order frequency = 240000/20000

Order frequency = 12

Therefore, the order frequency MBC should order to replenish the gasoline supply is 12 orders per year.

c)  Should MBC consider expanding the capacity of its storage tanks

The quantity ordered in intervals at EOQ level i.e., 20,000 gallons is less than the tank capacity that is 240,000 gallons. The tank capacity is sufficiently large enough to hold the 20,000 gallons of gasoline order each month.

Therefor the MBC should not consider expanding the capacity of its storage tank.

d)  Calculate the order point as follows:

Reorder point = Average daily demand × Lead time

Reorder point = (Demand rate / Number of operating days) × Lead time

Reorder point = (240000/300) × 10

Reorder point = 800 × 10

Reorder point = 8000

Therefore, the reorder point is 8000 gallons.

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