Deterministic Inventory Theory Professor Stephen R. Lawrence Leeds School of Business University of Colorado at Boulder Boulder, CO

EOQ Economic Order Quantity

EOQ Assumptions Demand rate deterministic and constant (no variation); No quantity discounts; Cost factors do not change appreciably with time; All items treated independently of other items; Constant replenishment leadtime; No shortages/backorders allowed; Entire order quantity is delivered at same time.

EOQ Inventory Pattern time Inventory Level tttt Q Q /2 average inventory

EOQ Problem Structure  Each order is for quantity Q  A stocking cost of S is incurred every time an order (outside vendor) or setup (internal production) is incurred  Cost of a single item is C  The annual holding cost fraction is h  The holding cost per unit is H=hC  Annual demand is D

EOQ Costs  Annual holding costs: (Q/2)H  Annual stocking costs: D S / Q  Total inventory costs: holding + stocking costs

EOQ Cost Trade-offs Total Costs Stocking Costs Holding Costs min TC Q* Costs Quantity Q QH /2 DS /Q TC

EOQ Cost Trade-offs  Trade-off between stocking and holding costs  Minimum cost where holding = stocking cost  Note that Total Cost curve is “flat” near Q*  Lesson! total cost is relatively insensitive to small errors in optimal order quantity Q*.

Intuitive Solution for Q* Total costs minimized when holding costs = stocking costs Solving for Q gives optimal order quantity Q*

Exact Determination of Q* Total costs minimized when Solving for Q gives optimal order quantity Q*

EOQ Example  Consider a product with the following parameters: D = 10,000 units per year h = 24% per year S = $2,500 C = $1,000  What is the Economic Order Quantity?

Other EOQ-type Models  Economic Production Quantity (EPQ)  EOQ with quantity discounts  Backorder and stockout (lost sales)  Special sale price  Known price increase  Multiple item  Maximum order size  Inflation  Quality deterioration

Inventory Spreadsheet

Utility of EOQ Models  Offer good insights  Conceptually elegant  Robust Good results even when assumptions are violated  Very useful despite shortcomings