Supply Chain Inventory Management. Multi-period Problems. Read: Chap Chap 11.

Transcription

1 Supply Chain Inventory Management Multi-period Problems Read: Chap Chap 11.

2 Push vs. Pull Processes PUSH: Order decision initiated in anticipation to customer orders A newspaper vendor orders first, then sells Bossini decided quantity of men s pants 3 mos before the season PULL: Order decision initiated in response to customer orders/demand A restaurant first takes orders, then makes Park n Shop replenishes a detergent item, cos stock level is low Push-Pull Boundary The restaurant must buy materials first -- push

3 Pull/Push SC Processes A push/pull boundary in a SC separates push from pull processes Typically upper stream push while down stream pull Examples Park n Shop (stores: pull ) Campbell s soup (procurement & production -- push) Textbook 1.5

4 Defining concepts put aside Assemble-to-order (build-to-order) You start assembly operations only after you have received the order Often, you have the materials/subassemblies ready Dell has all the materials made ready by its suppliers, then batch assembles to the orders Make-to-order (build-to-order) You start processing the order after you receive it Typically, you do not have materials ready until the order arrives Most apparel subcontract manufacturers run in this mode Which mode takes a longer lead time to finish the order?

5 Decisions When to order? In what quantity? How to get the order delivered? From whom? Prices? SKU: Stock keeping unit the decision unit

6 Two Inventory Decisions/Replenishment Rules How much to order / produce? Order quantity -- e.g., OUT, EOQ, When to order / produce? Reorder points, time periods Use Safety Stock to cope with uncertainty

7 Multiple Period Problems Inventory may be sold/used and replenished in multiple periods - multiple period inventory problem What is the major difference between this and the newsboy problem? You can carry inventory from one period to the next Backlogging your demand is possible (but at some intangible cost) Two popular types of systems: periodic review and continuous replenishment

8 Periodic v.s. Continuous Review Periodic review model Common for B & C items Economy of scales Continuous review model Slow moving items or Important items When periodic/continuous review? Inventory policy: when and how much to order - tactical level

9 Two Inventory Decisions How much to order / produce? Order quantity -- e.g., OUT, EOQ, When to order / produce? Reorder points, time periods Use Safety Stock to cope with uncertainty

10 Inventory Costs Order/Set-up costs Trucking, receiving, inspection, calls, faxes, GE estimated the cost of processing a typical replenishment order is about $50 Trucking cost a major part Diminishing over time Holding costs Stock-out / shortage /underage cost Salvage value

11 Inventory Holding Costs Category % of Inventory Value Housing (building) cost 6% Material handling costs 3% Labor cost 3% Inventory investment costs 11% Pilferage, scrap, & obsolescence 3% Total holding cost 26%

12 EOQ Assumptions Known & constant demand Known & constant lead time Instantaneous receipt of material (or constant leadtime) No quantity discounts Only order (setup) cost & holding cost No stockouts Price is pre-fixed

13 Annual Cost EOQ Model: How Much to Order? Total Cost Curve Holding Cost Order (Setup) Cost Optimal Order Quantity (Q*) Order Quantity

14 Inventory Level Optimal Order Quantity (Q*) EOQ Model: When to Order? Cycle Inventory! Average Inventory (Q*/2) Reorder Point (ROP) Lead Time Time

15 The EOQ Formula Economic order quantity EOQ Q* 2DK hc Where: D = annual demand (units) K = setup cost/order h = carrying charge ($/unit/year) c = unit cost ($/unit) Total cost = order cost + carrying cost TC = c D +(D/Q)K+ (Q/2 ) h c Optimal fixed order quantity

16 The Key Insight of EOQ 1. There is a tradeoff between lot size and inventory 2. Holding and setup costs are fairly insensitive to lot size Q TC(Q*) = cd +(D/Q)K+ (Q/2 ) h c => Sqrt (2 D*K*h*c) Q -> TC(Q )/TC(Q*) = [Q /Q* + Q*/Q ]/2 e.g., Q = 2Q*, TC(Q )/TC(Q*) = 1.25

17 Textbook Economic order quantity lot size EOQ 2DK hc EOQ 2???? - The model is insensitive to parameter values and robust!

18 Example: Broadway Consider inventory management for a certain SKU at Broadway. Supply lead time is 4 days. Daily demand for the item is variable with a mean of 30 units and a coefficient of variation of 20%. Assume that fixed ordering cost is estimated at $50 per order, and inventory holding costs are 15% of the product cost ($80) per year. Also, assume that the store is open 360 days a year. Propose an inventory policy for this SKU. L = 4, AVG D d = 30 per day K = 50, hc = (0.15)(80)/360 = (converted to daily cost) Use EOQ to calculate order quantity: Q = sqrt[2(k)(avg)/(hc)] = sqrt[2(50)(30)/0.0333] = sqrt(90000) = 300

19 Multiple Products/Items The setup cost can be shared among different products/items Replenish all jointly Replenish a subset each time

20 Order qu ty All jointly together Time Subset jointly together

21 Problems with EOQ? Deterministic demand? Moving to random/uncertain demand What will happen to the above EOQ charts? First consider a single product/item

22 Shortage/Underage Costs Emergency ordering, loss of goodwill, lost sales, hurting return buz. In multiple periods, they are notoriously difficulty to estimate Shortage/stockout occurs, what ll happen? Lost-sales or backlogging/backordering Throughout, we assume backordering

23 Performance Evaluation of Material/Dist Mgt Imagine you are a distribution manager, you re responsible for delivery of products to sales outlets - mkting gets customer & you deliver. How should you be evaluated? Costs are clearly most relevant. But how to estimate shortage costs?

24 Service Levels Inventory related service performance measurements Fill rate: fraction of demand being filled right away e.g., over past 52 wks, customer orders: 120,500 units, filled upon arriving: 110,050 units => customer backorders = 10,450. Fill rate = Ready rate: % of periods (or times) that there is no stock out - filling all the demand arriving in the periods (or upon arriving); e.g., among the past 52 wks (or orders), in 47 wks (or orders), no stockout, ready rate = 90%. In your textbook, it is called Cycle Service Level (CSL). Item/Line-based service levels

25 Line and Order Based Service Levels Line/item based or item based service level: for only one SKU or similar SKUs. Order based: a customer order may request a number of different SKUs - lines - with varying #. Throughout this course, we mean item/line service level. Several Cases mention both types of service levels.

26 Multi-Product Availability Service level = fill rate <= suitable? Item-based = Line-based <=> order based Order fulfillment rate : % times of filling orders completely (prob. being fully fulfilled)

27 More about Fill/Ready Rate Off-shelf v.s. Time-window Off-shelf : instant availability Time-window : available or delivered within a certain time - ready rate within TW We confine ourselves within off-shelf fill /ready rates, item-based

28 Service Level Line/Item Based Order Based In-stock %, Cycle Service Level Fill rate Off-shelf Window Based

29 APPROPRIATE LEVEL $ TC SALES CSL

30 Demands are uncertain! Order point system (R,Q) Inventory position (effective inventory level = on hand + on order backorders (or allocated) Rule: Whenever the inventory position goes below the reorder point R then order a fixed quantity Q. Best known as Reorder Point & Batch Size Policy

31 Order point system (R,Q) Two bin system... A B Rule: when the big bin is empty, open the small bin and place an order.

32 Inventory Level Freq Max. X Place order Lead Time Receive order Time

33 DDLT=demand during leadtime Inventory Level Freq Max. SS X Aver. DDLT Place order Lead Time Safety Stock (SS) Receive order Time

34 Ave. Inventory Q CYCLE SAFETY TIME

35 How to determine (ROP, Q)? Lot size Q by EOQ ROP by a service level specification Key assumption here is the same demand pattern over many periods or long time

36 Inventory Level Freq Max. SS X ROP Aver. DDLT Place order Lead Time Safety Stock (SS) Receive order Time

37 An Example You re a buyer for General Hospital. The demand for hospital ER kits is normally distributed. The mean demand during the reorder period is 350 kits, with = 10 kits. The hospital wants stockouts no more than 5% of the time. What are the safety stock & ROP?

38 Solution Frequency = 10 Svc Level =.95 P(Stockout) =.05 = = 350 x =? X Safety Stock = x -

39 Safety stock Safety stock ROP Solution x From statistics, z Safety stock Therefore, z & Safety stock From normal table, z 1.65 x z Safety stock If sigma is bigger or leadtime longer, then SS? z

40 Other Continuous Systems Sell one then replenish one ( 賣一補一 ) Extended reorder-point, lot-size system (r, nq): r=rop Min Max policy (system )

41 Eff. Inventory Level Max. =ROP+Q ROP Place order Lead Time Receive order Time

42 Periodic Review Systems Order up-to model definitions On-order inventory / pipeline inventory = the number of units that have been ordered but have not been received. On-hand inventory = the number of units physically in inventory ready to serve demand. Backorder = the total amount of demand that has has not been satisfied: All backordered demand is eventually filled, i.e., there are no lost sales. Inventory level = On-hand inventory - Backorder. Inventory position = On-order inventory + Inventory level. Order up-to level, S the maximum inventory position we allow. sometimes called the base stock level

43 When and how much is ordered? Inventory Level Target maximum Aver. Demand SS Period Period Period Time

44 Ordering every period Periodic Review SS = Reorder point (level) Aver. DDLT Can (r, Q) policy work properly? Min Max policy (system)

45 Multi-Item System Control Coordination is required for multiple product ordering. Why? One policy is (Min, c, Max) : can-order

46 Item A Item B Max Max c Can-order ROP - MIN c Can-order ROP - MIN

47 What learnt here? Two review/auditing systems Several ordering rules/policies How are the question of when and how much to order in each of this systems-policies answered? Reorder point/level can be determined by a service level requirement/specification The concept of safety stock

48 Managerial Insights Insight 1: the higher variability of demand, the higher SS. Insight 2: Shorter leadtime will result in lower SS Insight 3: When supply and/or leadtime is uncertain, SS?