1. Independent demand inventory models PUSH INVENT. SYSTEM PULL INVENT.(EOQ,ROP)

2. Learning objectives Push Inventory Control Pull inventory control Reorder Point System

3. Pull vs. Push Systems Pull: – Treat each stocking point independent of others. – Each orders independently and “pulls” items in. – Common in retail. Push: – Set inventory levels collectively. – Allows purchasing, production and transportation economies of scale. – May be required if large amounts are acquired at one time. 3

4. Push Inventory Control Acquire a large amount. Allocate amount among stocking points (warehouses) based on: – Forecasted demand and standard deviation. – Current stock on hand. – Service levels. Locations with larger demand or higher service levels are allocated more. Locations with more inventory on hand are allocated less. 4

5. Push Inventory Control TR i = Total requirements for warehouse i NR i = Net requirements at i Total excess = Amount available - NR for all warehouses Demand % = (Forecast demand at i)/(Total forecast demand) Allocation for i = NR i + (Total excess) x (Demand %) 5 = Forecast demand at i + Safety stock at i = Forecast demand at i + z x Forecast error at i = TR i - Current inventory at i z is from Appendix A

6. Push Inventory Control Example Allocate 60,000 cases of product among two warehouses based on the following data. CurrentForecast Forecast WarehouseInventoryDemandError SL 1 10,000 20,0005,000 0.90 2 5,000 15,0003,000 0.98 35,000 6

7. Push Inventory Control Example Current Forecast Forecast Demand z WarehouseInventory Demand Error SL % 1 10,000 20,000 5,000 0.90 0.5714 1.28 2 5,000 15,000 3,000 0.98 0.4286 2.05 35,000 7 TR 1 = 20,000 + 1.28 x 5,000 = 26,400 TR 2 = 15,000 + 2.05 x 3,000 = 21,150 NR 1 = 26,400 - 10,000 = 16,400 NR 2 = 21,150 - 5,000 = 16,150 Total Excess = 60,000 - 16,400 - 16,150 = 27,450 Allocation for 1 = 16,400 + 27,450 x (0.5714) = 32,086 cases Allocation for 2 = 16,150 + 27,450 x (0.4286) = 27,914 cases

8. Learning objectives Push Inventory Control Pull inventory control Reorder Point System

9. Pull inventory control Reorder Point System(continous review sys.) – quantity ordered is constant – the time between orders varies Periodic Review System – the time between orders is constant – the order quantity varies

10. Learning objectives Push Inventory Control Pull inventory control Reorder Point System

11. Two Fundamental Inventory Decisions How much to order of each material when orders are placed with either outside suppliers or production departments within organizations When to place the orders

12. Inventory Costs Costs associated with ordering too much (represented by carrying costs) Costs associated with ordering too little (represented by ordering costs) These costs are opposing costs, i.e., as one increases the other decreases

13. Inventory Costs (continued) The sum of the two costs is the total stocking cost (TSC) When plotted against order quantity, the TSC decreases to a minimum cost and then increases This cost behavior is the basis for answering the first fundamental question: how much to order It is known as the economic order quantity (EOQ)

14. Balancing Carrying against Ordering Costs Annual Cost ($) Order Quantity Minimum Total Annual Stocking Costs Annual Carrying Costs Annual Ordering Costs Total Annual Stocking Costs SmallerLarger Lower Higher EOQ

15. Fixed Order Quantity Systems Behavior of Economic Order Quantity (EOQ) Systems Determining Order Quantities Determining Order Points

16. Behavior of EOQ Systems As demand for the inventoried item occurs, the inventory level drops When the inventory level drops to a critical point, the order point, the ordering process is triggered The amount ordered each time an order is placed is fixed or constant When the ordered quantity is received, the inventory level increases... more

17. كمية الطلب الإقتصادي EOQ دورة طلب المخزون : Demand rate Time Order receipt Inventory Level Order quantity, Q 0

18. Behavior of EOQ Systems An application of this type system is the two- bin system A perpetual inventory accounting system is usually associated with this type of system

19. Determining Order Quantities Basic EOQ EOQ for Production Lots EOQ with Quantity Discounts

20. Model I: Basic EOQ Typical assumptions made – annual demand (D), carrying cost (C) and ordering cost (S) can be estimated – average inventory level is the fixed order quantity (Q) divided by 2 which implies no safety stock orders are received all at once demand occurs at a uniform rate no inventory when an order arrives –... more

21. Model I: Basic EOQ Assumptions (continued) – Stockout, customer responsiveness, and other costs are inconsequential – acquisition cost is fixed, i.e., no quantity discounts Annual carrying cost = (average inventory level) x (carrying cost) = (Q/2)C Annual ordering cost = (average number of orders per year) x (ordering cost) = (D/Q)S... more

22. Model I: Basic EOQ Total annual stocking cost (TSC) = annual carrying cost + annual ordering cost = (Q/2)C + (D/Q)S The order quantity where the TSC is at a minimum (EOQ) can be found using calculus (take the first derivative, set it equal to zero and solve for Q)

23. كمية الطلب الإقتصادي EOQ TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = SoDQSoDQ CcQ2CcQ2 Q 2 = 2SoDCc2SoDCc Q opt = 2SoDCc2SoDCc

24. Example: Basic EOQ Zartex Co. produces fertilizer to sell to wholesalers. One raw material – calcium nitrate – is purchased from a nearby supplier at $22.50 per ton. Zartex estimates it will need 5,750,000 tons of calcium nitrate next year. The annual carrying cost for this material is 40% of the acquisition cost, and the ordering cost is $595. a) What is the most economical order quantity? b) How many orders will be placed per year? c) How much time will elapse between orders?

25. Example: Basic EOQ Economical Order Quantity (EOQ) D = 5,750,000 tons/year C =.40(22.50) = $9.00/ton/year S = $595/order = 27,573.135 tons per order

26. Example: Basic EOQ Total Annual Stocking Cost (TSC) TSC = (Q/2)C + (D/Q)S = (27,573.135/2)(9.00) + (5,750,000/27,573.135)(595) = 124,079.11 + 124,079.11 = $248,158.22 Note: Total Carrying Cost equals Total Ordering Cost

27. Example: Basic EOQ Number of Orders Per Year = D/Q = 5,750,000/27,573.135 = 208.5 orders/year Time Between Orders = Q/D = 1/208.5 =.004796 years/order =.004796(365 days/year) = 1.75 days/order Note: This is the inverse of the formula above. of the formula above.

28. Sensitivity analysis Annual Cost ($) Order Quantity Minimum Total Annual Stocking Costs Annual Carrying Costs Annual Ordering Costs Total Annual Stocking Costs SmallerLarger Lower Higher EOQ

29. Reorder Point System Order amount Q when inventory falls to level ROP. Constant order amount (Q). Variable order interval. 29

30. Reorder Point System Place 1st order 30 Receive 1st order Receive 2nd order Place 2nd order Receive 3rd order Place 3rd order LT1 LT2LT3 Each increase in inventory is size Q.

31. Reorder Point System Place 1st order 31 Receive 1st order Receive 2nd order Place 2nd order Receive 3rd order Place 3rd order LT1 LT2LT3 Time between 1st & 2nd order Time between 2nd & 3rd order

32. Reorder Point Quantity to which inventory is allowed to drop before replenishment order is made Need to order EOQ at the Reorder Point: ROP = d X LT d = Demand rate per period LT = lead time in periods