Inventory Management – Economic Order Quantity
A local artisan uses supplies purchased from an overseas supplier. The owner believes the
assumptions of the EOQ model are met reasonably well. Minimization of inventory costs
is her
objective. Relevant data, from the files of the craft firm, are annual demand (D) =2500
units, ordering
cost (S) = $18.75 per order, and holding cost (H) = $1.50 per unit per year. The company
has 250
working days per year and order lead time is 3 days.
a) Given the information, what would be the economic order quantity (EOQ)?
b) Given the EOQ, what is the total annual cost of managing the inventory?
c) What is the daily demand? Calculate the reorder point.
g) The company has a problem of stock out; and the expected service level is 95% and
the standard
deviation of demand during lead time is =4 units, what will be the safety stock and new
reorder point?
Introduction
Economic Order Quantity (EOD) is one of the oldest production scheduling cost models. It was
developed by Ford, W.H. in the year 1913 and later refined by Wilson, a consultant in
Inventory Management – Economic Order Quantity 2
management. EOD is the material order quantity that actually minimizes the total cost of holding
inventory and the ordering costs. (Hax and Candea, 1984)
a) Annual demand, D = $ 2500, ordering Cost (S) = $18.75, holding Cost (H) = $1.5
The working days of the company are 250 days in a year while the lead time is 3days.
EOD = √2DCo/Ck = √2(2500)18.75/1.5 = √62500 = 250 tones. b) TC = DC+ D/QCo + Q/2 *Ch =46875 + 46825/250 (18.75) + 250/2 *1.5
= 46875 + 3515.63 +187.5 = $398,625.5
c) Daily demand = Annual demand 2500/360 = 6.94
Reorder quantity(R) = d’L = 2500/250 *3days = 30 units.
d) Safety stock = Z = 1.65 (95%) * average demand (6.94) * 4 = 45.8 units and also the
new reorder quantity.
To conclude, several other factors must also prevail for the above calculations to reflect the true
position of the EOQ. These are the cost ordering and the purchase price must be constant, the
lead time must be fixed, the rate of demand must also be known and only one product is
involved.
Reference
Inventory Management – Economic Order Quantity 3
Hax, A.C. and Candea, D. (1984), Production and Operations Management , Prentice-Hall,
Englewood Cliffs, NJ, p. 135
