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 2 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 © 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 © Chris Caplice, MIT
Cycle Stock and Safety Stock MIT Center for Transportation & Logistics - ESD © 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 © Chris Caplice, MIT P[SO] CbCb SLK N[K] E[US] TC[R] RFR
Determining the Reorder Point MIT Center for Transportation & Logistics - ESD © 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 © 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 © 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 © 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 © Chris Caplice, MIT Using a Table of Cumulative Normal Probabilities... K If I select a K = 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 © Chris Caplice, MIT K Factor versus Service Level Service Level [%] K Factor
Safety Stock and Service Level MIT Center for Transportation & Logistics - ESD © Chris Caplice, MIT Example: if d ~ iidNormal (d=100,σ=10) What should my SS & R be? P[SO]SLk Safety Stock Reorder Point
Service Level What is exactly is Service Level? MIT Center for Transportation & Logistics - ESD © 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 © 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 © Chris Caplice, MIT Looking for expected units short per replenishment cycle 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 © Chris Caplice, MIT A Table of Unit Normal Loss Integrals K
Item Fill Rate MIT Center for Transportation & Logistics - ESD © 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 © Chris Caplice, MIT RkSLP[SO]N[k]N[k]sFR 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
Inventory Management II Lot Sizing Lecture 5 ESD.260 Fall 2003 Caplice.
Inventory Management Distribution Requirements Planning Lecture 11 ESD.260 Fall2003 Caplice.
Inventory Management III EOQ Notes & Some Extensions Lecture 6 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 1. Inventory Firms ultimately want to sell consumers output in the hopes of generating a profit. Along the way to having.
Independent Demand Inventory Systems 1. Inventory Inventory: a store of goods held for future use Types of inventory: raw materials, work-in- process,
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 Chapter 11. Order Point Inventory Control Methods Homework problems: 1, 2, 3, 5.
Irwin/McGraw-Hill 1 What is Inventory? Definition--The stock of any item or resource used in an organization Raw materials Finished products Component.
Inventory Management V Finite Planning Horizon Lecture 9 ESD.260 Fall 2003 Caplice.
Inventory Management. Learning Objectives You should be able to: 1.Define the term inventory, list the major reasons for holding inventories, and list.
an inventory is a stock or store of goods and inventory management focuses on the planning and control of finished goods, raw materials, purchased.
Managing Inventory throughout the Supply Chain Chapter 11.
Inventory Management Henry C. Co Technology and Operations Management, California Polytechnic and State University.
1 Logistics Systems Engineering Inventory - Requirements, Planning and Management NTU SY-521-N SMU SYS 7340 Dr. Jerrell T. Stracener, SAE Fellow.
1 1 Slide © 2001 South-Western College Publishing/Thomson Learning Anderson Sweeney Williams Anderson Sweeney Williams Slides Prepared by JOHN LOUCKS QUANTITATIVE.
Role of Inventory in the Supply Chain Overstocking: Amount available exceeds demand –Liquidation, Obsolescence, Holding Understocking: Demand exceeds amount.
1 EMBA-2, BUP EO Inventory Control. EO M. AsadEMBA-2 Inventory Control Inventory – The longer it sits, the harder it is to move Purposes of.
Statistical Inventory control models I (Q, r) model.
1 Inventory Management and Control. 2 Inventory Defined Inventory is the stock of any item or resource held to meet future demand and can include: raw.
1 Inventory Control Models. 2 Chapter Learning Objectives Students will be able to: –Use the economic order quantity (EOQ) to determine how much to order.
1 1 Slide © 2006 Thomson South-Western. All Rights Reserved. Slides prepared by JOHN LOUCKS St. Edwards University.
1 Inventory BA 339 Mellie Pullman. 2 3 Inventory Definitions Inventory vs. Inventory system Dependent vs. Independent environments Types Safety Stock.
12 – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Inventory Management 12 For Operations Management, 9e by Krajewski/Ritzman/Malhotra.
1 IE&M Shanghai Jiao Tong University Supply Chain Management One's work may be finished some day, but one's education never. – Alexandre Dumas.
ARE 511 CONSTRUCTION AND MAINTAINANCE MODELLING BY DR. SADI AL ASSAF INVENTORY ANALYSIS.
Bus 301: Business Logistics Inventory Strategies-Overview.
Inventory Management V Lecture 8 ESD.260 Fall 2003 Caplice Inventory Policy Single Item w/Probabilistic Demand.
© 2016 SlidePlayer.com Inc. All rights reserved.