Carrying costs of inventory

These are costs incurred because the firm has decided to maintain inventories. They generally consist of:

•    Stock-out costs
•    Insurance costs
•    Warehouse and storage costs
•    Material handling costs
•    costs of obsolescence

Total Ordering Cost = (Total demand for period x Ordering Costs per period) / Quantity Ordering
                             = DO/Q


Total Holding Costs  = (Quantity Ordered x Holding Costs per unit) / 2
                             = Q H/2

Therefore total relevant costs (TC) for any order quantity can be expressed as:

TC = DO/Q + Q H/2
                           

We can determine a minimum of this total cost function by:

i. Differentiating the above formula with respect to Q and setting the derivative (1st) equal to zero.

dTC/ dQ = (-DO/Q2) + H/2 = 0

                        
ii. Equating ordering costs to holding costs.

DO/Q = Q H/2