1. Deterministic Inventory Theory Professor Stephen R. Lawrence Leeds School of Business University of Colorado at Boulder Boulder, CO 80309-7058

2. EOQ Economic Order Quantity

3. 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.

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

5. 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

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

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

8. 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*.

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

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

11. 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?

12. 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

13. Inventory Spreadsheet

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