9.16 Economic Ordering Quantity (EOQ) Model Inventory Optimal Order Quantities Model

Objective:  Optimize inventory level. The company may experience a saw-tooth pattern of inventory levels. (Other assumptions shall also remain as they were in the cash model example).


As (average) inventory and order quantity increases so do:

  • Financing costs: inventory needs to be paid from either short-term borrowings or the opportunity cost of cash invested in the short-term. (We shall, disingenuously, assume that borrowing and lending rates are the same.)
  • Other carrying costs:
    • Storage & handling
    • Labor, electricity, etc.
    • Insurance
    • Perishability / (Demurrage “on the docks”)
    • Obsolescence
  • To summarize: “Carrying” costs rise with inventory size


As inventory increases, the following decreases:

  • Ordering costs – administrative
  • Price/cost due to quantity discounts
  • Cost of stock-out, i.e., not being able to fulfill customer orders
  • “Ordering” costs decrease with inventory size


Total Cost = Carrying + Ordering Costs
Carrying Costs = (Q / 2) (P) (C)

Q / 2 = Average inventory Carried

P = Price paid per unit

C = All carrying costs including financing costs

(expressed as percent of cost)

Ordering Costs = (F) (S / Q)

F = Fixed cost per order

S = Annual unit sales projected

Q = Periodic ordering quantity (units)

(Q / 2) (P) (C) = (F) (S / Q)

(Q / S) (Q / 2) = F / PC)

Q2 = (2 F S) / (P C)

Q* = [(2 F S) ÷ (C P)] 0.5



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