Question

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 $0.06 per month, or $0.72 per year; and annual fuel usage is 120,000 gallons. MBC buses operate 300 days a year.

1. What is the optimal order quantity for MBC?
   
   Q* =
   
2. How frequently should MBC order to replenish the gasoline supply?
   
   __________ orders per year
   
3. The MBC storage tanks have a capacity of 15,000 gallons. Should MBC consider expending the capacity of its storage tanks?
   
   Metropolitan Bus Company (Needs to expand / does not need to expand) the capacity of its storage tanks.
   
4. What is the reorder point?
   
   r = ______ gallons

Answer 1

Given: Annual Demand = D = 120,000 gallons

Ordering cost = S = $300

Lead time = LT = 10 days

Annual Holding cost = H = $0.72

No. of working days = N = 300 days

a) Optimal Order quantity = EOQ = = = 10,000 gallons

b) No. of orders per year = D / EOQ = 120,000 / 10,000 = 12 orders per year

c) Demand during lead time = Daily demand * Lead time = (D / N) * LT = (120,000 / 300 ) * 10 = 4000 gallons

Total storage required = EOQ + Demand during lead time = 10000 + 4000 = 14000 gallons

Since capacity = 15000 gallons > 14000 gallons, Metropolitan Bus Company does not need to expand the capacity of its storage tanks.

d) Reorder point = Demand during lead time + safety stock = 4000 + 0 = 4000 gallons

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