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**Operations Management Inventory Management Chapter 12**

© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**What is Inventory? Stock of materials Stored capacity**

© 1995 Corel Corp. While most students recognize inventory as a “stock of material,” the notion of inventory as a “stored capacity” probably merits explicit discussion. © T/Maker Co. © T/Maker Co. © 1995 Corel Corp. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Types of Inventory Raw material Work-in-progress**

Maintenance / repair / operating supplies Finished goods It might be useful here to explicitly discuss the purpose of each type of inventory. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**The Material Flow Cycle**

This slide illustrates the overall material flow cycle. You should stress the proportion of time material spends as inventory as opposed to being actually worked on; and note that this suggests effective inventory management and materials movement can reduce overall cycle time significantly. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**The Functions of Inventory**

To ”decouple” or separate various parts of the production process To provide a stock of goods that will provide a selection for customers To take advantage of quantity discounts To hedge against inflation and upward price changes If this course is the first exposure of students to manufacturing, it might be useful to discuss the decoupling function. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Disadvantages of Inventory**

Higher costs Interest or opportunity costs Holding (or carrying) costs – storage, handling, taxes, insurance, shrinkage Ordering (or setup) costs Risk of deterioration or obsolescence Hides production problems Yield / scrap variations Unscheduled downtime Of the items listed on this slide, the least obvious to most students is the manner in which inventory can be used to hide production problems. Total cost = 20% - 40% of inventory value / year © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Pressures on inventory**

Pressure for lower inventory Inventory investment Inventory holding cost Pressure for higher inventory Customer service Other costs related to inventory © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Different Views of Inventory**

Demand Type Independent Dependent Types of Inventory Cycle Pipeline Safety Stock Anticipation Annual $ Volume A B C Process stage Raw Material Work in Process Finished Goods Other Maintenance / Repair Operating Supplies © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**How Is Inventory Created?**

Cycle Inventory – result of lot size Pipeline Inventory – in transit Safety Stock Anticipation Inventory Average cycle inventory = Q + 0 2 Pipeline inventory = DL = dL Types of Inventory Cycle Pipeline Safety Stock Anticipation © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Calculations**

We use 70 hypodermic needles a week. We buy them in lots of It takes three weeks for order handling and shipment. Cycle inventory = Q/2 = 280/2 = 140 needles Pipeline inventory = DL = dL = (70 needles/week)(3 weeks) = 210 drills Inventory Worksheets © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Reduction Tactics**

Cycle inventory Pipeline inventory Safety Stock Anticipation inventory Reduce lot size Reduce lead time Reduce uncertainties Various © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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ABC Analysis Divides on-hand inventory into three classes on the basis of annual dollar volume – A, B, and C $ volume = Annual demand x Unit cost Policies based on ABC analysis Develop class A suppliers more Maintain tighter physical control of A items Forecast A items more carefully Annual $ Volume A B C It might be helpful here to discuss some of the differences in the ways we would manage items in the three different levels. What actions would we actually take in managing A versus in managing C? © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**ABC Analysis A B C Class % $ Vol % Items A 80 20 B 15 30 C 5 50**

% of Inventory Items 20 40 60 80 100 50 % Annual $ Usage A B C Are we back to Pareto analysis? © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Models for Independent Demand**

Fixed order-quantity models Economic order quantity Production order quantity Quantity discount Probabilistic models Fixed order-period models Help answer the inventory planning questions! This slide simply introduces some of the available models. Additional details are provided in subsequent slides. © T/Maker Co. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**EOQ – Economic Order Quantity**

Objective: minimize (ordering cost + holding cost) Assumptions: Known and constant demand Known and constant lead time Instantaneous receipt of material No quantity discounts Only ordering / setup cost and holding cost No stockouts Students should be asked to consider the degree to which each of these assumptions is accurate. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Usage Over Time**

Inventory Level Average Cycle Inventory Q Usage Rate Q 2 One should link this model to the assumptions. You should also explore, at least briefly, how this picture would change if the assumptions were not met. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**EOQ Model How Much to Order?**

Order quantity (Q) Annual Cost Holding Cost Total Cost Ordering (Setup) Cost Optimal Order Quantity (Q*) Minimum total cost © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Why Holding Costs Increase**

More units must be stored if more are ordered Purchase Order Description Qty. Microwave 1 Order quantity 1000 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Why Ordering Costs Decrease**

Cost is spread over more units Example: You need 1000 microwave ovens Purchase Order Description Qty. Microwave 1 1 Order (Postage $ 0.33) 1000 Orders (Postage $330) Order quantity 1000 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**EOQ Model – When to Order**

Time Inventory Level Average Cycle Inventory Q* Reorder Point (ROP) Lead Time One should link this model to the assumptions. You should also explore, at least briefly, how this picture would change if the assumptions were not met. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**EOQ Model Equations = × N D Q* T d ROP L S H 2 Optimal Order Quantity**

Expected Number of Orders Expected Time Between Orders Working Days / Year = × N D Q* T d ROP L S H 2 D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days For some students, it is most important at this point to explain in detail the meaning and significance of each equation. It might be helpful to actually work through a numerical example. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Models for Independent Demand**

Fixed order-quantity models Economic order quantity Production order quantity Quantity discount Probabilistic models Fixed order-period models Help answer the inventory planning questions! This slide simply introduces some of the available models. Additional details are provided in subsequent slides. © T/Maker Co. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**POQ – Production Order Quantity**

Answers how much to order and when to order Allows partial receipt of material Other EOQ assumptions apply Suited for production environment Material produced, used immediately Provides production lot size Lower holding cost than EOQ model One way to approach this is as an EOQ model with the instantaneous replenishment assumption relaxed. The following slide (EOQ Model modified to show changes for POQ) allows you to do this if you wish. Otherwise, skip it and move on. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Both production and usage take place**

EOQ POQ Model Both production and usage take place Usage only takes place Maximum inventory level Inventory Level Time © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Models for Independent Demand**

Fixed order-quantity models Economic order quantity Production order quantity Quantity discount Probabilistic models Fixed order-period models Help answer the inventory planning questions! This slide simply introduces some of the available models. Additional details are provided in subsequent slides. © T/Maker Co. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Quantity Discount Model**

Answers how much to order & when to order Allows quantity discounts Other EOQ assumptions apply Trade-off is between lower price & increased holding cost Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 No discount $ 5.00 2 1,000 to 1,999 4 $ 4.80 3 2,000 and over 5 $ 4.75 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Quantity Discount – How Much to Order**

© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Models for Independent Demand**

Fixed order-quantity models Economic order quantity Production order quantity Quantity discount Probabilistic models Fixed order-period models Help answer the inventory planning questions! This slide simply introduces some of the available models. Additional details are provided in subsequent slides. © T/Maker Co. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Probabilistic Models Answer how much & when to order**

X Service Level P(Stockout) Frequency Answer how much & when to order Allow demand to vary Other EOQ assumptions apply Consider service level & safety stock Service level = 1 – Probability of stockout Higher service level means more safety stock More safety stock means higher ROP One point to stress here is that this is simply an extension of the original EOQ model where we are now allowing the demand to vary. Students should become accustomed to seeking such extensions as the need arises. The next slide presents a graphical view of this model. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Probabilistic Models - When to Order?**

Reorder Point (ROP) X Safety Stock (SS) Time Inventory Level Lead Time SS ROP Service Level P(Stockout) Place order Receive order Frequency © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J 32

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**Inventory Models for Independent Demand**

Fixed order-quantity models Economic order quantity Production order quantity Quantity discount Probabilistic models Fixed order-period models Help answer the inventory planning questions! This slide simply introduces some of the available models. Additional details are provided in subsequent slides. © T/Maker Co. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Fixed Period (P) Systems**

Answers how much to order Orders placed at fixed intervals Inventory brought up to target amount Amount ordered varies No continuous inventory count Possibility of stockout between intervals Useful when vendors visit routinely Example: Office Max representative calls every week This represents a model in which orders are based upon time, not the quantity needed. The following slide provides a graphical representation. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory in a Fixed Period System**

Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to target maximum p Q1 Q2 Q3 Q4 Target maximum Time On-Hand Inventory © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Comparison of Q and P Systems**

Continuous Review System (Q) A system designed to track the remaining inventory of an item each time a withdrawal is made, to determine whether it is time to replenish Periodic Review System (P) A system in which an item’s inventory position is reviewed periodically rather than continuously © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Comparison of Q and P Systems**

Continuous Review System (Q) Individual review frequencies Possible quantity discounts Lower, less-expensive safety stocks Periodic Review System (P) Convenient to administer Orders may be combined Inventory position only required at review © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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**Inventory Measures Average inventory = $2 million**

Cost of goods sold = $10 million 52 business weeks per year = = weeks $2 million ($10 million)/(52 weeks) Weeks of supply = Average inventory value Weekly sales (at cost) Annual sales (at cost) Average inventory value Inventory turns = $10 million $2 million = = 5 turns/year © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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Summary Functions of inventory – Inventory enables value creation for many processes Costs of inventory Different views of inventory Inventory reduction tactics ABC and EOQ are traditional tools used to manage inventory – still used in many circumstances Continuous review system (Q) for high-value parts; Periodic review system (P) for some low value parts Weeks of Supply and inventory turns are widely-used measures of inventory © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J

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