We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byMolly Roy
Modified over 3 years ago
Inventory Management IV Safety Stock Lecture 7 ESD.260 Fall 2003 Caplice
Assumptions: Basic EOQ Model Demand Constant vs Variable Known vs Random Continuous vs Discrete Lead time Instantaneous Constant or Variable (deterministic/stochastic) Dependence of items Independent Correlated Indentured Review Time Continuous vs Periodic Number of Echelons One vs Many Capacity / Resources Unlimited vs Limited Discounts None All Units or Incremental Excess Demand None All orders are backordered Lost orders Substitution Perishability None Uniform with time Planning Horizon Single Period Finite Period Infinite Number of Items One Many MIT Center for Transportation & Logistics - ESD.260 2 © Chris Caplice, MIT
Fundamental Purpose of Inventory To buffer uncertainties in: -supply, -demand, and/or -transportation the firm carries safety stocks. To capture scale economies in: -purchasing, -production, and/or -transportation the firm carries cycle stocks. MIT Center for Transportation & Logistics - ESD.260 3 © Chris Caplice, MIT
Cycle Stock and Safety Stock MIT Center for Transportation & Logistics - ESD.260 4 © Chris Caplice, MIT Cycle Stock Cycle Stock Cycle Stock Safety Stock On Hand What should my inventory policy be? (how much to order when) What should my safety stock be? What are my relevant costs? Time
Preview: Safety Stock Logic MIT Center for Transportation & Logistics - ESD.260 5 © Chris Caplice, MIT P[SO] CbCb SLK N[K] E[US] TC[R] RFR
Determining the Reorder Point MIT Center for Transportation & Logistics - ESD.260 6 © Chris Caplice, MIT R = d' + kσ Reorder Point Estimated demand over the lead time (F t ) Safety Stock k = SS factor σ= RMSE Note 1.We usually pick k for desired stock out probability 2.2. Safety Stock = R –d
Define Some Terms MIT Center for Transportation & Logistics - ESD.260 7 © Chris Caplice, MIT Safety Stock Factor (k) Amount of inventory required in terms of standard deviations worth of forecast error Stockout Probability = P[d> R] The probability of running out of inventory during lead time Service Level = P[dR] = 1-P[SO] The probability of NOT running out of inventory during lead time
Service Level and Stockout Probability MIT Center for Transportation & Logistics - ESD.260 8 © Chris Caplice, MIT Where d ~ iidN(d=10,σ=25) SS = kσ Probability of Stockout Service Level Demand Forecasted Demand (d) Reorder Point Prob (x)
Cumulative Normal Distribution MIT Center for Transportation & Logistics - ESD.260 9 © Chris Caplice, MIT Where d ~ iidN(d=10,σ=25) Prob (x) Demand Probability of Stockout = 1-SL Service Level Reorder Point
Finding SL from a Given K MIT Center for Transportation & Logistics - ESD.260 10 © Chris Caplice, MIT Using a Table of Cumulative Normal Probabilities... K0.000.010.020.030.04 0.00.50000.50400.50800.51200.5160 0.10.53980.54380.54780.55170.5557 0.20.57930.58320.58710.59100.5948 0.30.61790.62170.62550.62930.6331 0.40.65540.65910.66280.66640.6700 0.50.69150.69500.69850.70190.7054 0.60.72570.72910.73240.73570.7389 0.70.75800.76110.76420.76730.7704 0.80.78810.79100.79390.79670.7995 0.90.81590.81860.82120.82380.8264 1.00.84130.84380.84610.84850.8508 If I select a K = 0.42... then my Service Level is this value. Or, in Excel, use the function: SL=NORMDIST(kσ+d, d, σ, TRUE)
K Factor versus Service Level MIT Center for Transportation & Logistics - ESD.260 11 © Chris Caplice, MIT K Factor versus Service Level Service Level [%] K Factor
Safety Stock and Service Level MIT Center for Transportation & Logistics - ESD.260 12 © Chris Caplice, MIT Example: if d ~ iidNormal (d=100,σ=10) What should my SS & R be? P[SO]SLk Safety Stock Reorder Point.50 00100.10.901.2813113.05.951.6517117.01.992.3323123
Service Level What is exactly is Service Level? MIT Center for Transportation & Logistics - ESD.260 13 © Chris Caplice, MIT Service Level.... IS IS NOT Probability that a stockout does not occur during lead time The fraction of demand satisfied from stock Probability that stock is available Fraction of order cycles during which no SO soccur Probability that all demand will be satisfied from on hand stock w/in any given replenishment cycle Fraction of time that stock is available in the system Fill rate for or availability of an item
So, how do I find Item Fill Rate? MIT Center for Transportation & Logistics - ESD.260 14 © Chris Caplice, MIT Fill Rate Fraction of demand met with on-hand inventory Based on each replenishment cycle OrderQuantity E [ UnitsShort ] FillRate OrderQuantity = But, how do I find Expected Units Short? More difficult Need to calculate a partial expectation:
Expected Units Short Consider both continuous and discrete cases MIT Center for Transportation & Logistics - ESD.260 15 © Chris Caplice, MIT Looking for expected units short per replenishment cycle. 1 2 3 4 5 6 7 8 X What is E[US] if R=5? 1/8 P[x] For normal distribution we have a nice result: E[US] = σN[k] Where N[k] = Normal Unit Loss Function Found in tables or formula
The N[k] Table MIT Center for Transportation & Logistics - ESD.260 16 © Chris Caplice, MIT A Table of Unit Normal Loss Integrals K.00.01.02.03.04 0.0.3989.3940.3890.3841.3793 0.1.3509.3464.3418.3373.3328 0.2.3069.3027.2986.2944.2904 0.3.2668.2630.2592.2555.2518 0.4.2304.2270.2236.2203.2169 0.5.1978.1947.1917.1887.1857 0.6.1687.1659.1633.1606.1580 0.7.1429.1405.1381.1358.1334 0.8.1202.1181.1160.1140.1120 0.9.1004.09860.09680.09503.09328 1.0.08332.08174.08019.07866.07716
Item Fill Rate MIT Center for Transportation & Logistics - ESD.260 17 © Chris Caplice, MIT OrderQuantity E [ UnitsShort ] FillRate OrderQuantity = = FR So, now we can look for the k that achieves our desired fill rate.
Item Fill Rate Example Find fill rate for R=250, 300, 350, and 500 where, Q = 500 units and demand ~ N(d =200, σ=100) MIT Center for Transportation & Logistics - ESD.260 18 © Chris Caplice, MIT RkSLP[SO]N[k]N[k]sFR 2500.5.69.31.197819.78.9604 3001.0.84.16.08338.33.9833 3501.5.93.07.02932.93.9941 5003.0.999.001.0003.03.9999 Note: Fill rate is usually much higher than service level Fill rate depends on both R and Q Q determines the number of exposures for an item
Normal Curve Area Problems involving only z (not x yet) To accompany Hawkes lesson 6.2 A few slides are from Hawkes Plus much original content by D.R.S.
Inventory Management II Lot Sizing Lecture 5 ESD.260 Fall 2003 Caplice.
Inventory Management III EOQ Notes & Some Extensions Lecture 6 ESD.260 Fall 2003 Caplice.
1 Inventory Management Lecture 4 ESD.260 Fall 2003 Caplic e.
Inventory Management Distribution Requirements Planning Lecture 11 ESD.260 Fall2003 Caplice.
Inventory Management V Finite Planning Horizon Lecture 9 ESD.260 Fall 2003 Caplice.
Re-Order Point Problems Set 1: General. 2 Ardavan Asef-Vaziri Sep-2012Flow Variability; Safety Inventory Notations.
Independent Demand Inventory Systems 1. Inventory Inventory: a store of goods held for future use Types of inventory: raw materials, work-in- process,
Independent Demand Inventory 1. Inventory Firms ultimately want to sell consumers output in the hopes of generating a profit. Along the way to having.
1 Managing Inventory under Risks Leadtime and reorder point Uncertainty and its impact Safety stock and service level The lot-size reorder point system.
1 1 Slide © 2006 Thomson South-Western. All Rights Reserved. Slides prepared by JOHN LOUCKS St. Edwards University.
Inventory Control Models.
Irwin/McGraw-Hill 1 What is Inventory? Definition--The stock of any item or resource used in an organization Raw materials Finished products Component.
Chapter 8 Inventory Management. Learning Objectives To learn about the ways that inventory can be classified To discuss inventory costs and the trade-offs.
1 Inventory Control. 2 Week 1Introduction to Production Planning and Inventory Control Week 2Inventory Control – Deterministic Demand Week 3Inventory.
Chapter 9 Inventory Management. Learning Objectives To determine the costs of holding inventory To identify the costs associated with a stockout To understand.
1 Inventory BA 339 Mellie Pullman. 2 3 Inventory Definitions Inventory vs. Inventory system Dependent vs. Independent environments Types Safety Stock.
Managing Inventory throughout the Supply Chain Chapter 11.
Inventory Control IME 451, Lecture 3. Economic Order Quantity Harris (1913) developed this basic, widely used model to find economic lot sizes Balancing.
Managing Uncertainty in Supply Chain: Safety Inventory Spring, 2014 Supply Chain Management: Strategy, Planning, and Operation Chapter 11 Byung-Hyun Ha.
1 Logistics Systems Engineering Inventory - Requirements, Planning and Management NTU SY-521-N SMU SYS 7340 Dr. Jerrell T. Stracener, SAE Fellow.
Inventory Control Models Ch 5 (Uncertainty of Demand) R. R. Lindeke IE 3265, Production And Operations Management.
Graduate Program in Business Information Systems Inventory Decisions with Uncertain Factors Aslı Sencer.
Chapter 6: Probability. Flow of inferential statistics and probability SamplePopulation Inferential Statistics Probability.
ISEN 315 Spring 2011 Dr. Gary Gaukler. Lot Size Reorder Point Systems Assumptions –Inventory levels are reviewed continuously (the level of on-hand inventory.
Simulations The basics for simulations. Simulation is a way to model random events, such that simulated outcomes closely match real-world outcomes. By.
© 2006 Prentice Hall, Inc.12 – 1 Operations Management Chapter 12 – Inventory Management © 2006 Prentice Hall, Inc. PowerPoint presentation to accompany.
© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J Operations Management Inventory Management Chapter 12.
1 Lecture 6 Inventory Management Chapter Economic production quantity (EPQ) model: variant of basic EOQ model Production done in batches or lots.
Chris Morgan, MATH G160 March 19, 2011 Lecture 23 Chapter 7.3, 7.4, & 7.5: Point Estimation, Sampling Distribution of x-bar and p-bar.
11-1Inventory Management William J. Stevenson Operations Management 8 th edition.
Economic Order Quantity The economic order quantity (EOQ) is the fixed order quantity (Q) that minimizes the total annual costs of placing orders and holding.
Fill in missing numbers or operations
CHAPTER 6 Inventory Management. Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 6-2 Purposes of Inventory Enables.
1 Chapter 11. Order Point Inventory Control Methods Homework problems: 1, 2, 3, 5.
£1 Million £500,000 £250,000 £125,000 £64,000 £32,000 £16,000 £8,000 £4,000 £2,000 £1,000 £500 £300 £200 £100 Welcome.
Role of Inventory in the Supply Chain Overstocking: Amount available exceeds demand –Liquidation, Obsolescence, Holding Understocking: Demand exceeds amount.
INVENTORY IS BAD. DIRECT FINANCIAL EFFECTS Pay money to get Place to Store Equipment to move DAMAGE - OBSOLESCENCE INCREASED CYCLE TIME Less flexibility.
Cost-Volume-Profit Relationships Chapter LEARNING OBJECTIVES 1.Explain how changes in activity affect contribution margin. 2.Compute the contribution.
1 Inventory Control with Stochastic Demand. 2 Week 1Introduction to Production Planning and Inventory Control Week 2Inventory Control – Deterministic.
Number bonds to 10, = = = = = = = = 10 Making 10, 20 and 100 Adding can be a lot easier.
1 S7 Capacity and Constraint Management PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management,
1 Chapter 16 When demands are unknown, expected values are the keys for deciding how much to order and how often. Inventory Decisions with Uncertain Factors.
Fundamentals of Cost Analysis for Decision Making Chapter 4 Acc
1 Copyright © 2013 Elsevier Inc. All rights reserved. Appendix 01.
$100 $200 $300 $400 $100 $200 $300 $400 $100 $200 $300 $400 $100 $200 $300 $400 $100 $200 $300 $400.
___________________________________________________________________________ Operations Research Jan Fábry Probabilistic Inventory Models.
1 Material Management Class Note # 3-A ( In review ) ~ Inventory control, analysis, and management ~ Prof. Yuan-Shyi Peter Chiu Feb
© 2017 SlidePlayer.com Inc. All rights reserved.