1. EOQ Answers the Question “How Much to Order?” Assumptions: zInstantaneous production zImmediate delivery zDeterministic demand zConstant demand: D units/year zConstant setup cost: A $/setup zIndependent products

2. EOQ view of Inventory Time Inventory Order Quantity Q

3. Costs Setup Costs –A $/setup –How many setups if we make Q each time? Why not just make D units in one setup?

4. Inventory Cost zUsually billed as a “holding cost” zEssentially interest on the money tied up in inventory yh $/unit/year zExample: Holding 100 units for 6 months costs: ? zInventory holding Cost yh*Average Inventory

5. A Model Lot Size or Order Quantity: Q units Average Inventory Level: Q/2units Annual Demand: D units/year Order Frequency: every D/Q times per year Average Variable Cost/Year: TVC = h*Q/2 +A*D/Q

6. The EOQ zUse Calculus to find the value of Q that minimizes TVC(Q) zOr...

11. The Economic Order Quantity h Q/2 = A D/Q Q 2 = 2 A D/h Q = SQRT(2 A D/h) CAVEAT: Make sure you use commensurate units!

12. An Example zRaw Material X yQuarterly demand: 6,000 units yCost per unit: ~ $25/unit yHolding Cost: say 10% per year yTransaction Cost: $100/order EOQ = SQRT(2 C T D/ C I ) = SQRT(2 * 100 * 6,000/(0.025*25)) ~ 1,385 units per shipment

13. Robustness of the EOQ

14. Robustness

15. EPQ Answers the Question “How Much to Produce?” Assumptions: zInstantaneous production zConstant production rate: P > D units/year zImmediate delivery zDeterministic demand zConstant demand: D units/year zConstant setup cost: A$/setup zIndependent products

16. EPQ view of Inventory Time Inventory Production Quantity Q Max Inv. Level Length of Prod. Run

17. A Model Lot Size or Production Quantity: Q units Average Inventory Level zProduction run lasts: Q/P zInventory grows at rate: (P-Q) zSo, max inventory is: (P-D)Q/P = (1-D/P)Q zAverage inventory is: (1-D/P)Q/2 Order Frequency: every D/Q times per year Average Variable Cost/Year: TVC = h*(1-D/P)Q/2 +A*D/Q

18. The EPQ zUse Calculus to find the value of Q that minimizes TVC(Q) zOr use the previous answer... yTVC = h*(1-D/P)Q/2 +A*D/Q = h’Q/2 +A*D/Q So, Q = SQRT(2 A D/h’) = SQRT(2AD/h(1-D/P))

19. An Example zRaw Material X yQuarterly demand: 6,000 units yCost per unit: ~ $25/unit yHolding Cost: say 10% per year yTransaction Cost: $100/order yQuarterly Production Rate: 8,000 units EOQ = SQRT(2 C T D/ C I ) = SQRT(2*100*6,000/(0.025*25*(1-6/8))) ~ 2,771 units per run

20. A Model zDivide the planning horizon into time buckets t = 1, 2,..., T zD t = units of demand in period t zc t = unit production cost in period t zA t = setup cost in period t zh t = inventory holding cost in period t zQ t = the lot size in period t zI t = units in inventory at the end of period t

21. Heuristics zLot-for-lot: Make what is required each period. zFixed Order Quantity: Order the EOQ zPeriod Order Quantity: Calculate the EOQ, Q. Convert to order frequency: T = Q/D. Orders sized to last for time T.