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OPSM 501: Operations Management Week 12: Inventory Management Order-up-to model Koç University Graduate School of Business MBA Program Zeynep Aksin

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Presentation on theme: "OPSM 501: Operations Management Week 12: Inventory Management Order-up-to model Koç University Graduate School of Business MBA Program Zeynep Aksin"— Presentation transcript:

1 OPSM 501: Operations Management Week 12: Inventory Management Order-up-to model Koç University Graduate School of Business MBA Program Zeynep Aksin

2 Levers for Managing Inventories  Theoretical Inventory I th =R x T th –Reduce critical activity times –Eliminate non-value added work –Move work from critical to non-critical –Redesign process to replace serial with parallel processing  Cycle inventory –Average inventory per cycle=Q/2 –Reduce set-up to reduce cycle inventory

3 Levers for Managing Inventories  Seasonal Inventory –Use pricing and incentive tactics to smooth demand –Increase resource flexibility  Safety inventory-this is next!

4 4 A Multi-Period Inventory Model  Often, there are multiple reorder opportunities  Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory

5 5 Set Up: Simple Supply Chain  Three key questions: –How often to review? –When to place an order? –How much to order? orders Pipeline stock Supply On-hand inventory Inventory position

6 Timing in the order up-to model  Time is divided into periods of equal length, e.g., one hour, one month.  During a period the following sequence of events occurs: –A replenishment order can be submitted. –Inventory is received. –Random demand occurs.  Lead times: –An order is received after a fixed number of periods, called the lead time. –Let l represent the length of the lead time. An example with l =

7 Order up-to model vs. newsvendor model  Both models have uncertain future demand, but there are differences… –Newsvendor applies to short life cycle products with uncertain demand and the order up-to applies to long life cycle products with uncertain, but stable, demand. NewsvendorOrder up-to Inventory obsolescenceAfter one periodNever Number of replenishments One (maybe two or three with some reactive capacity) Unlimited Demand occurs during replenishment NoYes 13-7

8 8 Periodic Review, Order-up-to Policy Inventory Position = Quantity + Quantity on hand on order S - Base stock level/Order-up-to Point p - Review period; l - Replenishment lead time  - Demand per unit time ss - Safety stock Ordering Rule: Place an order every p periods so as to bring your inventory position to the Base Stock Level, S.

9 9 Periodic review with no demand variability Inventory Level time  (p+ l ) pp ll lp+l2p+l3p+l p2p3p4p On-hand inventory Inventory position 0

10 10 Periodic review with no demand variability Order Quantity, Q =  p Average Cycle stock = Q/2 =  p / 2 Pipeline stock =  l Order-up-to point, S =  (p + l )

11 11 Why hold Safety Inventory?  Demand uncertainty  Supply uncertainty Measures of product availability –Product fill rate (f): fraction of demand that is satisfied from product in inventory –Cycle service level (CSL): fraction of replenishment cycles that end with all the customer demand being met

12 12 Periodic review with variable demand Order-up-to point (S) =  ( p+l ) + Safety Stock (ss) Average Order Quantity (Q) =  p Average Pipeline stock =  l Average Cycle stock = Q/2 =  p / 2 Safety Stock = ss = ?

13 13 Determination of the Safety Stock Inventory Level  p+ss  l + ss ss time On-hand inventory Inventory position  p+  l+ss l p+l2p+l3p+l p2p3p 4p 0

14 14 Probabilistic Models X + = S Key idea:Order-up-to target covers demand over time period of p+l

15 15 Designing for a target CSL Safety Stock (ss) = Choosing z:  =CSL= P(demand during p+l <= S) z= F s -1 (CSL)

16 16 Example #1 Given:p = 2 weeks l = 3 weeks  = 1.5 units per week   = 4 units per week Target service level, CSL=95% Solve: Safety stock = Base stock level = so from table, z = 1.64 Average on-hand inv= 1.5x2/2 + safety stock= =8.86

17 17 Example #2 Given:p = 2 weeks l = 1 week  = 1.5 units per week   = 4 units per week Target service level, CSL=95% Solve: Safety stock = Base stock level = so from table, z = 1.64

18 18 Computer example continued  Suppose we do not know the base-stock level S  We know the company uses a periodic-review, order-up-to policy  From company data we know that average on- hand inventory is 12.6 units  What service level is the store providing?

19 19 Example #3 12.6= (1.5 x 2)/2 + z x 2 x z =2.48 F(2.48)=0.993

20 20 Computer store: determining policy parameters  Store wants to re-evaluate order frequency  Retain service level of 95%  Apple charges a fixed fee of $25 for shipping and handling of order  Store’s order processing cost is $15  The model being considered has wholesale price of $3000  Holding cost rate is estimated to be 20%

21 21 Example #4  Compute EOQ –h= (3000x0.2)/52weeks/yr=$11.5 –K=15+25=40 –Q*=3.2 –p = Q*/  =3.2/1.5=2.15

22 22 Delayed Product Differentiation  Products start off undifferentiated; at some point, product variety explodes  Trade-off between product variety vs. inventory and service levels  Design the product so the point of differentiation is delayed as much as possible  Don’t commit to FGI early on

23 23 DPD- Standardization  Using common components or processes –Reduces complexity of manufacturing –Increases “flexibility” of work-in-process –Improves service level  Examples: –standardizing head driver board & print mechanism interface in b&w and color printers –generic printer for Mac and Windows users

24 24 DPD-Modular Design  Decomposing the complete product into submodules that are easily assembled; delay assembly of product specific modules –Can increase no. of modules –Same benefits as standardization  Examples: –Power supply module in the HP Deskjet printer –Inserting plastic color panel to generic products –Channel assembly in PC industry

25 25 DPD – Process Restructuring Postponing (if necessary) reverse operations  Operation divided into two steps, first step common to all products  Reverse the order of two operations with first operation common to all products  Example: –Benetton (dye & knit  knit & dye)

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29 29 When is DPD appropriate?  High uncertainty in demand mix  Long lead times  Short product life cycle  High inventory /stock out costs  Not too costly/time consuming to customize  High value to core component  Low variable cost of differentiating components

30 Announcement 1  Next week field trip to Mercedes coach plant  Departure from campus 8:10-visit 9:30  Bus info: MUHAMMET GÜLER ZP 4194  Intermediate stop at Ataturk Oto Sanayi: 8:35  HOŞDERE OTOBÜS FABRİKASI-check web site for directions  Sanayi Mah. Mercedes Bulvarı No. 5, Esenyurt / İstanbul Tel: (0 212) Pbx Fax: (0 212)

31 Announcement 2  Read the Temsa case before the trip  Bonus assignment-can be done in pairs (5%):  Take notes-ask questions-take photos if allowed to –Strategy: Comment on the 4 product attributes for Mercedes: PQTV –Process documentation: Provide a high level process flow chart –Process Selection: Analyze volume, variety level and its fit with the type of process (position the plant on the product-process matrix based on this analysis)

32 Announcement 3  Last session: will play the beer game in-class –Need to read the handout that I will distribute before coming to class –Need to be on time since we will start at 11:00 sharp- aim for arrival at 10:45.  Final exam on January 10:00  Room will be announced


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