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OPSM 501: Operations Management

Ko ç Un iversity Graduate School of Business MBA Program. OPSM 501: Operations Management. Week 12: Inventory Management Order-up-to model. Zeynep Aksin zaksin @ku.edu.tr. Levers for Managing Inventories. Theoretical Inventory I th =R x T th Reduce critical activity times

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OPSM 501: Operations Management

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

  2. Levers for Managing Inventories • Theoretical Inventory Ith=R x Tth • 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. 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. orders Pipeline stock On-hand inventory Supply Inventory position Set Up: Simple Supply Chain • Three key questions: • How often to review? • When to place an order? • How much to order?

  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 = 1 13-6

  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. 13-7

  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. Inventory position On-hand inventory Inventory Level (p+l) p l time 0 p 2p 3p 4p l p+l 2p+l 3p+l Periodic review with no demand variability

  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. 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. 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. Inventory position Inventory Level On-hand inventory p+l+ss p+ss l+ss ss 0 p 2p 3p 4p time l p+l 2p+l 3p+l Determination of the Safety Stock

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

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

  16. Given: p = 2 weeks l = 3 weeks  = 1.5 units per week 2 = 4 units per week Target service level, CSL=95% Solve: so from table, z = 1.64 Safety stock = Base stock level = Example #1 Average on-hand inv= 1.5x2/2 + safety stock=1.5+7.36=8.86

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

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

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

  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. 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. 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. 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)

  26. 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

  27. Announcement 1 • Next week field trip to Mercedes coach plant • Departure from campus 8:10-visit starts @ 9:30 • Bus info: MUHAMMET GÜLER 05392294281 34 ZP 4194 • Intermediate stop at Ataturk Oto Sanayi: 8:35 • HOŞDERE OTOBÜS FABRİKASI-check web site for directions • Sanayi Mah. Mercedes Bulvarı No. 5, 34500 Esenyurt / İstanbulTel: (0 212) 622 70 00 PbxFax: (0 212) 622 84 00

  28. 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)

  29. 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 4 @ 10:00 • Room will be announced

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