Pricing and inventory

Question

A retail shop sells 500 pairs of shoes each year. Each pair of shoes is priced at $50. Suppose that the shop can get each pair of shoes from their supplier at $20 and the ordering cost, regardless of quantity, is $50. The lead time for each order is 7 calendar days. The annual holding cost of each pair of shoes is $2. Assuming that the demand is uniform across the year:

a) Compute the economic order quantity. b) Compute the reorder point.

Answer 1

Note:  an even demand across the year is important.

 

a) Compute the economic order quantity.

 

First, the formula:

    EOC = √(2DK/h)

  where

    EOC = Economic Order Quantity

     D = annual demand quantity

     K = fixed cost per order (not the cost of goods)

     h = annual holding cost per unit

 

Plug in the values:

   D = 500

   K = 50

   h = 2

 

  EOC = √(2(500)(50)/2) = 158.11

 

  EOC=158 shoes

 

 

b) Compute the reorder point.

 

First, the formula:

  R = DL     [note: does not allow for basic stock or safety stock]

 where

    R = Reorder point

    D = Demand rate per period - convert to days

    L = Lead time - in days

 

Plug in the values:

    D = 500/365   per day

    L = 7         calendar days

 

     R = (500/365)*7 = 9.59

   R = 10 shoes      [reorder when inventory gets down to 10 shoes]