Costs involved in Inventory Models

1. Costs involved in Inventory Models • Ordering (Setup) cost • Unit purchasing (Production) cost • Holding (Carrying) cost • Shortage (Penalty) cost • Revenue (Selling price)

2. Basic EOQ Model • EOQ: Economic Order Quantity • Assumptions of EOQ models: • Demand is constant (unvarying ), expressed as annual demand (units per year ). • Models use continuous review, not periodic review. • Lead time is constant & known. • Quantity discounts are not possible. • 2 variable costs: setup cost and holding cost.

3. Inventory Levels Usage rate (D) • Inventory vs. time. Inventory ( Q ) Reorder Point (ROP) time Cycle time (T) Lead time ( L, l )

4. Symbols in EOQ models • Order quantity: Q • Optimal order quantity: Q* • Annual demand (units): D • Setup cost per order: K • Holding cost (per unit): H

5. Total Cost vs. Order Quantity. Combined curve: holding & setup. Annual Cost Minimum annual cost Holding cost curve We’ll find an equation for this amount Setup cost curve Optimal order quantity Order Quantity

6. D Q Annual setup cost = K * Annual setup cost: equation Q, K, & D demand / quantity per order = # of orders. # of orders * K = annual setup cost. • What is related to it?

7. Q/2 Constant slope Q time Annual holding cost: equation. • Q: order quantity Q & H. • inventory is replenished precisely when no inventory remains. • Average inventory =

8. Q time Annual holding cost: equation. Q 2 Annual holding cost = H *

9. Finding where they are equal. • The minimum cost of the system will be found where ASC = AHC. Q 2 D Q ASC = AHC = H K * *

10. Solve for Q • The minimum cost of the system will be found where ASC = AHC. D Q Q 2 K H = * *

11. Solve for Q • The minimum cost of the system will be found where ASC = AHC. 2DK = Q2 H

12. Solve for Q • The optimal order quantity that results in the lowest system cost is called Q* 2DK = Q* H

13. Holding costs • Total annual holding cost: inc. monetary value of inventory,annual cost of capital, storage costs: cQ 2 Hc =

14. Holding costs • Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs: i * cQ 2 Hf =

15. Holding costs • Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs: sQ 2 Hs =

16. Total holding costs • Total annual holding cost: inc. monetary value of inventory, annual cost of capital, storage costs: ( s + i c ) Q 2 Ht =

17. Other factors (lurking in the shadows) • Unit cost (production cost): cost per unit to buy the inventory: symbol “c” • Annual unit cost = cD

18. Other factors (lurking in the shadows) • Revenue: profit per unit of inventory sold: symbol “r” • Annual revenue = rD

19. Total Cost of the System DK Q ( s + i c ) Q 2 Total cost = cD + + Cost of inventory Cost of the products Cost of ordering

20. ROP Q L T = Q ROP L time Determine reorder point • Demand is constant. Lead time is known.

21. MS Excel example • (Go to it)

22. Homework: due Thursday Preview of Thurs.: 2 other models (ind. D) • p. 470, #1, 2, 4 - turn in ON PAPER (preferably computer printouts, each on 1 sheet of paper that can be understood by someone who WASN’T there when you set it up.) • Production Order Quantity Model • Quantity Discount Model