Question

The Manhattan Shoe Co. maintains an inventory of shoes in a warehouse they rent locally. The monthly demand for shoes is 930 units. The shoes cost $35 per pair and the replenishment order is placed when the inventory reaches a certain level. The cost of placing the replenishment order is estimated to be $21. The annual inventory holding cost for each pair of shoes is 28% of the cost of the item.

a. Based on the above data, calculate the EOQ for the All Star Shoe Co.
b. Based on the above data, calculate the corresponding total cost purchase lot (TCp).
c. How valid are the assumptions for the simple EOQ model?

Answer 1

Answer:

a) EOQ = √[(2 x S x D) / H]

• S = order cost = $21
• D = annual demand = 930 x 12 = 11,160
• H = annual holding cost = $35 x 28% = $9.80

EOQ = √[(2 x $21 x 11,160) / $9.80] = 218.7 ≈ 219 shoes

b) total ordering costs = (11,160 / 219) x $21 = $1,070.14

total holding costs = $9.80 x (219 / 2) = $1,073.10

total purchases = $35 x 11,160 = $390,600

total inventory costs = $392,743.24

c) The EOQ model faces two main problems:

1. first, it assumes that the demand is constant and can be predicted with 100% accuracy and that is not usually the case. Also, demand might be seasonal which makes the EOQ model useless.
2. second, it assumes costs are constant and they are generally not, e.g. the price of shoes might change