Question

Torrance Refinery produces approximately 20.0 Million barrels of gasoline per year. A California distributor sources its gasoline from the Torrance refinery. The annual demand for gasoline at the California distributor is 11.1 Million barrels. The cost of storing gasoline is approximately $21 per barrel (per year). The cost of placing an order to the Torrance refinery (including shipping) is $4400 per order. Orders will be received gradually instead of delivered all at once (hence EPQ).

At what quantity will the total cost of procurement be the lowest?

Answer 1

Given values:

Annual Production (P) = 20.0 Million barrels

Annual Demand (D) = 11.1 Million barrels

Cost of Holding (H) = $21 per barrel (per year)

Cost of Ordering (Co) = $4400 per order

Number of days in a year = 365 days

Daily demand (d) = Annual demand / Number of days = (11.1 x 1000000) / 365 = 30,136.99 barrels (1 Million = 1,000,000)

Daily production (p) = Annual production / Number of days = (20.0 x 1000000) / 365 = 54,794.52 barrels

Economic Production Quantity (EPQ):

EPQ = SQRT [(2 x D x Co) / H x (1 - d/p)]

EPQ = SQRT [(2 x 11.1 x 1000000 x $4400) / $21 x (1 - 30,136.99/54,794.52)]

EPQ = 102,238.19 or 102,238 (Rounding off to the nearest whole number)

Economic Production Quantity (EPQ) = 102,238 barrels or 0.102 Million barrels