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**OPSM 501: Operations Management**

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

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**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

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**Levers for Managing Inventories**

Seasonal Inventory Use pricing and incentive tactics to smooth demand Increase resource flexibility Safety inventory-this is next!

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**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

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**Set Up: Simple Supply Chain**

orders Pipeline stock Supply On-hand inventory Inventory position Three key questions: How often to review? When to place an order? How much to order?

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**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

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**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. Newsvendor Order up-to Inventory obsolescence After one period Never Number of replenishments One (maybe two or three with some reactive capacity) Unlimited Demand occurs during replenishment No Yes 13-7

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**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.

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**Periodic review with no demand variability**

Inventory Level time (p+l) p l l p+l 2p+l 3p+l p 2p 3p 4p On-hand inventory Inventory position

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**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)

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**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

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**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 = ?

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**Determination of the Safety Stock**

Inventory Level p+ss l+ss ss time On-hand inventory Inventory position p+l+ss l p+l 2p+l 3p+l p 2p 3p 4p

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**Probabilistic Models + = S**

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

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**Designing for a target CSL**

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

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**Example #1 Given: p = 2 weeks l = 3 weeks = 1.5 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

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**Example #2 Given: p = 2 weeks l = 1 week = 1.5 units per week**

Target service level, CSL=95% Solve: Safety stock = Base stock level = so from table, z = 1.64

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**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?

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

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**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%

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**Example #4 Compute EOQ h= (3000x0.2)/52weeks/yr=$11.5 K=15+25=40**

p = Q*/m=3.2/1.5=2.15

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**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

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**DPD- Standardization Using common components or processes Examples:**

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

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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

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**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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**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

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**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)

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**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)

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**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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