McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 1 Independent Demand Inventory Management Systems

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 2 Module Objectives Explain the concept of marginal analysis and its application to inventory management Understand the differences between continuous and periodic review policies Articulate the different ways of defining service levels for a single inventory item Identify ways to “optimize” inventory policies Explain the trade-off between customer service and inventory investment Explain the effect of order frequency on inventory levels and customer service Understand basic inventory models for managing independent-demand inventory

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 3 Independent Demand Inventory Models Review Method Framework Basic Model Special Case When How Much Continuous Review Regular demand Inventory reaches a certain level Fixed quantity to order each time an order is placed Regular demand On some periodic basis Enough to cover demand over the next period Periodic Review One-time buys Prior to an event Enough to cover demand for the one- time event

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 4 Independent Demand Inventory Models Time Framework Time Periods Review Method Model Alternative Name Single Periodic based on events Single Period Newsboy Model Continuous Continuous Review Re-Order Point Model Multiple Periodic based on the calendar Periodic Review Fixed Period Model

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 5 Measuring Inventory Policy Costs Ordering costs Holding costs Stock out costs Product price Management system costs

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 6 Measuring Customer Service Cycle fill rate Cfr = (1 – P us ) X 100% Unit fill rate Ufr = 100% - Expected percentage of demand missed

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 7 Single Period Inventory Model Discrete demand analysis Marginal analysis approach Continuous demand analysis

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 8 Discrete Demand Analysis - Example Replacement Part History for Aladea and others (per 1000 monitors)

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 9 Frequency Distribution of Demand

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 10 Aladea – Inventory Decision Tree d=50 d=60 d=70 d=50 d=60 d=70 d=50 d=60 d=70 Order 50 Order 60 Order 70 Decision Outcomes 50($80) = $4000 Situation Cost 50($80) + 10($100) = $ ($80) + 20($100) = $6000 Probability Expected Cost 60($80) = $ ($80) = $ ($80) - 10($10) = $ ($80) + 10($100) = $ ($80) - 20($10) = $ ($80) - 10($10) = $ $1000 $5000 $2500 $1500 $1175 $5025 $2400 $1450 $1350 $5500 $2750 $1400

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 11 Marginal Analysis Approach If P us (C us )  (1 – P us ) C os, then stock one more unit Stock out probability that balances costs: Pus  C os / (C us + C os ) Desirable fill rate: cfr = C us / (C us + C os )

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 12 Continuous Demand - Example

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 13

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 14 Multiperiod Models Continuous review –Inventory is continuously monitored until it reaches a certain level, the ReOrder Point, after which an order is placed. Periodic review –Inventory is reviewed and replenished at specified points in time. With a PR policy, there is no control over inventory levels on hand when an order is placed.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 15 Continuous Review System

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 16 Periodic Review System

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 17 Measuring Customer Service – Setting Safety Stocks ROP = d L + z  dL   d L = 2 where:

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 18 Normal Distribution z values and Probabilities

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 19 Costing Multiperiod Policies TAC* = Ordering + Holding + Stockout = S X D/Q + H (SS + Q/2) + D/Q X P us X C s * Ignoring price and management system costs

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 20 Holding / Order Cost Tradeoff Holding + Order Holding Costs Order Costs Order Quantity Q or Order Period T Costs

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 21 Optimizing Multiperiod Policies Economic Order Quantity (EOQ) TAC = H Q/2 + S D/Q Q* = (2DS/H) 1/2 Economic Order Period (EOP) T* = Q*/D

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 22 Price Discounts - Example Suzy buys aluminum by the pound for Ford Motor Co. Alcoa has offered Suzy the following price schedule. How much should she order each time? Quantity (in pounds)Price / pound 0 - 9,999$12 10, ,999$10 100,000 +$8 Holding cost per pound per year = 20% of unit cost Cost to place an order = $450 Annual demand for aluminum = 400,000 pounds What if the holding cost were 90% of unit cost?

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 23 Holding / Shortage Cost Tradeoff Holding + Shortage Holding Costs Shortage Costs Safety Stock Inventory Level Costs

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 24 Safety Stock Levels

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 25 Trade-off Example

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 26 Combining Order Quantity and SS Decisions

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 27 Production Order Quantity Inventory Level Q Inventory Used during Production Run Time t T POQ* = (2DS / H(1-D/R) 1/2

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc., All Rights Reserved. 28 Calculating Expected Units Short