# 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:

• 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