Supply Chain Inventory Management. Multi-period Problems. Read: Chap Chap (except materials for fill rate)

Transcription

1 Supply Chain Inventory Management Multi-period Problems Read: Chap Chap (except materials for fill rate)

2 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?

3 Inventory Decisions/Rules Imagine you re a manager for a store/dc Park n Shop: for shampoo, you can buy from Procter & Gamble ( 寶潔 ), Johnson & Johnson ( 强生 ) P&G, J&J, may have their own DRPs for stock mgmt But Park n Shop orders/replenishes by its own way Assume after you order, sometime later you will get it delivered Then, the decisions are

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

5 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

6 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 review/replenishment

7 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

8 The ABC Classification Close examination of multi-sku inventory systems reveals a statistical regularity in the usage rate of diff items ($) A class, B class, C class: 80/20 rule Policies based on ABC analysis Develop class A suppliers more... Give tighter physical control of A items Forecast A items more carefully

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

14 EOQ Model: Inventory Level Optimal Order Quantity (Q*) 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 Total cost = order cost + carrying cost TC = c D +(D/Q)K+ (Q/2 ) h c Optimal fixed order quantity Where: D = annual demand (units) K = setup cost/order h = carrying charge ($/unit/year) c = unit cost ($/unit)

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. Is that all? 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? What will happen if we ignore 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), also known as In-Stock Rate. Cycle-Service-Level = In-Stock Rate Item/Line-based service levels WalMart: 95%-98%; Dell s DC: 98.80%

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 Using Service Level Specification to Determine Orderup-to Level What would you do, as a dist. Manager, if you are evaluated only by service performances, say, fill rate: the higher fill rate, the higher your bonus? Or Supply chain planner Trade-off between service and costs - holding & ordering

30 How to Set a Service Level? E.g., Cycle-Service-Level = In-Stock Rate: Item Gross Margin x 52 weeks x (1 In-Stock Rate) = The Cost of carrying an item for a yr In -Stock Rate [52 x item gross (1- cost of margin] ) carrying an item for one yr/ If review/replenishment is made at a frequency other than weekly, we simply replace 52 in the formula with the number of replenishment cycles in a yr. Say, monthly, 12.

31 An example: cost of holding an item for a year = 30% its value (at cost) 1) Item gross margin = 10 % its value (at cost) Then, in-stock rate = 1-30%/(52*10%) =94% 2) If gross margin = 20% (50%), then it is 97% (99%) If monthly (instead of weekly): 1) at margin 10%, it is 75% 2) at margin 20% (50%): the rate = 87.5% (95%) Now, are we lowing the service and letting more stock out?

32 APPROPRIATE LEVEL $ TC SALES CSL

33 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

34 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.

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

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

37 Ave. Inventory Q CYCLE SAFETY TIME

38 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

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

40 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?

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

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

43 Evaluating In-stock Rate (Cycle Service Level) Given an (R, Q) Replenishment Policy (Ex. 11-2) Weekly demand for Palms: N(2,500, 500^2) LT = 2 wks. What the In-stock rate if R=6,000, Q=10,000? R = Aver DDLT+ S.S., Aver DDLT = 2x2500=5,000 S.S. = 6,000-5,000 = 1,000, Sigma_L = Sqr (2)*500 =707, S.S. = z*sigma_l z = 1000/707 = : the rate or CSL = 92 %

44 Normal Dist. Table z R = Aver DDLT+ S.S., Aver DDLT = 2x2500=5,000 S.S. = 6,000-5,000 = 1,000, Sigma_L = Sqr (2)*500 =707, S.S. = z*sigma_l -> z = 1000/707 = : the rate or CSL = 92 % F(z) 0 z

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

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

47 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

48 When and how much is ordered? Economy of scale? Inventory Level Target maximum Aver. Demand SS Period Period Period Time

49 Ordering every period Periodic Review SS = Reorder point (level) Aver. DDLT Can (r, Q) policy work properly? Min Max policy (system) For your reference: Review interval is reduced from monthly to weekly. Will inventory level to be lowered?

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

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

52 Realism All models (stylized systems) assume stable markets When they are not, these are just approximations!

53 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

54 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?

55 Homework 2 Part 1 (Due date: Nov. 9, 7:pm) 1. What are some strategic, planning, and operational decisions that must be made by an apparel retailer like Giordano 佐丹奴? (Chapter 1) 2. Why does ZARA source products with uncertain demand (in EU) from local manufacturers and products with predictable demand from Asian contractors? 3. Offer an explain why Sasa s inventory turns (3 times/yr) is so much slower than Circle-K (~20/yr)? 4. Speculate how different in their supply chains between Watsons (health and beauty products part) and Fortress, both belonging to Each answer is at most 2 pages long! Try to apply the framework/theory learnt.

56 (continued) 5. The following table shows financial data (yr 2007) for two major retailers Retailer A ($mil) Retailer B ($mil) Inventories $3, 643 $29,447 Sales $48,106 $286,103 Cost of Goods Sold (COGS) $41,651 $215,493 Assume both retailers have an average annual holding cost rate of 30% (i.e., costs both $3 hold an item that they procured for $10 for one entire yr). a.how many days, on average, does a product stay in Retailer A before it is sold? (Hint: inventory turns.) Assume that stores are operated 365 days a yr. b.how much lower is, on average, the inventory cost for Retailer A compared to Retailer B of a household cleaner valued at $100 COGS? Assume the unit costs of the cleaner is the same for both.

57 6. Chap. 12, Discussion Question 1 7. Chap. 12, Discussion Question 2 8 Chap 12, Ex. 8. [Note, for Part a, you just calculate the underage cost Cu as the foregone profit.] 9. Chap 12, Exercise 9. [Note: salvage value = 75-15=60) 10. Chap 12, Ex. 10. parts a & d only. (Note that in a, the salvage value = $70- $10; in d, the salvage value $75 is the net after deducting the holding-transport costs already) All questions are in the handout pages.

58 HW 2 Part 2 (due date:., Nov. 23, 7: 00 pm) Exercises (Ch. 11) -- see your handout. You need to hand-in this part after the Midterm exam. 1. Exercise (Ch. 11) 1. (Best Buy/Motorola) 2. Exercise (Ch. 11) 2. (Best Buy/Motorola) 3. Exercise (Ch. 11) 3 4. Exercise (Ch. 11) 4 (HP Printers at Sam s Club): Skip the last question regarding fill rate 5-6. Discussion Q. (Ch. 11), 7 (Amazon.com) & 9 (Bookstore Borders) Remember: HP Case questions hand in Nov. 2 nd (in class, hard copy, better before the class stars and in any case no later than 7:30 )