1. OMG 402 - Operations Management Spring 1997 CLASS 8: Process and Inventory Control (1) Harry Groenevelt

2. 2 Agenda Introduction Production and cost: the EOQ Production and time: JIT Summary of Insights

3. 3 Introduction to Production Control We’ll seek answers to such questions as: –when should we order supplies or produce products? –how much should be ordered/produced at a time? –what are the advantages and costs of flexibility in production? –how do we ensure quality?

4. 4 Production and cost: the EOQ Examples: –retail replenishment –surgery or office supplies –raw material purchasing at Donner Tension between fixed cost of production (ordering) and variable holding costs Note: we’ll use terms interchangeably: set-up cost and ordering cost

5. 5 orders received Assemble PC processors memory cache case monitorkeyboard manuals Pack finished Product shipment to customer Production and Cost Gateway 2000’s Assemble-to-Order Production

6. 6 Focus on Vivitron 17" Monitor Inventory –How frequently to order from Sony? –How much to order at a time? –How much is spent on holding and ordering? Ship to customer Vivitron 17 Pack finished Product Supplier (Sony) (shipment from Sony Manufacturing is by boat and then truck) Production and Cost

7. 7 Set-up Costs and Inventory Vivitron Monitor Example – Data weekly demand (D = 7,000 monitors) variable cost (C = $120 / monitor) fixed ordering cost (S = $500) annual cost of capital = 20% (approx. 0.4%/week) variable storage cost = $0.10/monitor/week

8. 8 Set-up Costs and Inventory Calculating Inventory Holding Costs H= variable holding cost for one monitor per week. In this case, H= (variable cost of capital) + (variable storage cost) = Reminder: The weekly cost of capital is the expected return forgone by investing in one monitor. To calculate, include all variable costs incurred to purchase and bring the monitor to the warehouse. How should we calculate the cost of capital? What other costs should be considered when calculating H?

9. 9 The ‘Economic Order Quantity’ (EOQ) Assume: –Constant, deterministic demand (D units/week) –Known fixed cost per order placed ($S) –Fixed unit price ($C/unit), independent of order size –Holding cost associated with each unit of stock on hand ($H/unit/week) –Fixed order quantity: Q units –Instantaneous receipt of the ordered quantity

10. 10 Set-up Costs and Inventory Holding and ordering costs for order size Q average inventory: holding cost per week: # of orders per week needed to fill demand D: ordering cost per week:

11. 11 How ordering and inventory costs vary with order size Q

12. 12 # Orders per week = Costs Minimized by Q* = ‘EOQ’ This formula can be derived by plugging Q* into the cost formula

13. 13 EOQ in Practice In practice, demand is not constant, so we’ll have trouble if we order the same amount each week Need to continually adjust the ordering pattern to actual demand: –Keep order frequency constant and vary order quantity (e.g., ‘periodic’ or ‘base stock’ system) –Keep order quantity constant and vary order frequency (e.g., ‘order point / order quantity’ or ‘Kanban’ system) In practice, order quantity or frequency will be rounded to some convenient value

14. 14 Base stock system Order periodically to bring inventory on hand + on order back to the base stock level; period length matches EOQ order frequency Base stock level and period length together determine stockouts

15. 15 Order point / order quantity (OP/OQ) system Order the EOQ when inventory on hand + on order drops to the order point Order point and order quantity together determine stockouts

16. 16 Qualitative Behavior of the EOQ Ordering Cost (S) Q* Holding Cost (H) Q*

17. 17 EOQ: Economies of Scale If the EOQ is used,every time demand doubles, ordering plus holding costs increase by about 40%!

18. 18 see: Principles of Corporate Finance, Brearly and Myers, pp. 774-779 Another EOQ Application Management of cash balances: keep cash on hand to pay bills and replenish by selling Treasury bills. –What does the ‘inventory’ of cash look like? –What is Q*? –What is S? –What is H?

19. 19 EOQ Generalizations Quantity discounts and price breaks Multiple products Discounting cash flows Variability in demand Finite production rate (EOQ assumes that the goods arrive all at once)

20. 20 Production and Time What was Jonah’s attitude towards batching? (see pg. 232 of The Goal) “reduce batch sizes by 1/2” on non-bottlenecks –reduce queue by 1/2 –reduce wait by 1/2 –reduce lead time by 1/2 –more responsive to the customer Why not batch sizes of ‘1’?

21. 21 What production plan should be used to meet demand for 1000 cars of each type per week? Demand for 600 cars of each type? For 100? Flexible Production two types of cars: moon roof ( ) ) and standard ( * ) time to produce a batch is proportional to batch size large batch production plan 500 cars ) setup 1 week 150 ) setup 150 * setup 500 cars * setup 500 cars ) setup 500 cars * setup 150 ) setup 150 * setup 150 ) setup 150 * setup 150 ) setup 150 * setup small batch production plan

22. 22 Flexible Production Danger of small batches (short product cycles): demand not fulfilled (stoplight at Mt. Hope and Elmwood). Solution: –larger batch sizes or… –setup time reduction use standardized fixtures, tools, and procedures distinguish between on-line and off-line setup use teams and training

23. 23 Production and Time: JIT Philosophy of JIT: “produce only when products are needed, in the quantities needed” Goals: –small batch sizes / short cycles / low inventories –‘balance’ flow in all parts of the production network (internal and external suppliers) with the demand for the final product –continuous improvement –elimination of waste

24. 24 JIT: Level Production (Heijunka) production with almost instantaneous setups models mixed and proportional to demand. Example: two standard cars sold for every one moon roof sold. Therefore, produce only two standard, one moon: **)**)**)**)**)**)**)

25. 25 JIT: Level Production (Heijunka) also called ‘balanced’ or ‘mixed-model’ production quick setups small inventories balanced flow throughout production process But how short do setups have to be? A mathematical model will tell us

26. 26 Summary of Insights Inventory Models: –tradeoff between ordering and inventory costs –economies of scale Flexible Production: –long set-up times necessitate large batches; short set- ups allow flexibility –flexibility both requires, and encourages, the elimination of ‘waste’ Seek to “change the rules”: don’t take costs as given!