Principles of Inventory Management

Transcription

1 John A. Muckstadt Amar Sapra Principles of Inventory Management When You Are Down to Four, Order More fya Springer

2 Inventories Are Everywhere The Roles of Inventory Fundamental Questions Factors Affecting Inventory Policy Decisions System Structure The Items Market Characteristics Lead Times Costs Measuring Performance 15 EOQ Model Model Development: Economic Order Quantity (EOQ) Model Robustness of the EOQ Model Reorder Point and Reorder Interval EOQ Model with Backordering Allowed The Optimal Cost Quantity Discount Model All Units Discount An Algorithm to Determine the Optimal Order Quantity for the All Units Discount Case Incremental Quantity Discounts An Algorithm to Determine the Optimal Order Quantity for the Incremental Quantity Discount Case Lot Sizing When Constraints Exist Exercises 42

3 xiv Contents 3 Power-of-Two Policies Basic Framework Power-of-Two Policies PO2 Policy for a Single-Stage System Cost for the Optimal PO2 Policy Serial Systems Assumptions and Nomenclature A Mathematical Model for Serial Systems Algorithm to Obtain an Optimal Solution to (RP) Multi-Echelon Distribution Systems A Mathematical Model for Distribution Systems Relaxed Problem Powers-of-Two Solution Joint Replenishment Problem (JRP) A Mathematical Model for Joint Replenishment Systems Rounding the Solution to the Relaxed Problem Exercises 82 4 Dynamic Lot Sizing with Deterministic Demand The Wagner-Whitin (WW) Algorithm Solution Approach ' Algorithm Shortest-Path Representation of the Dynamic Lot Sizing Problem Technical Appendix for the Wagner-Whitin Algorithm Wagelmans-Hoesel-Kolen (WHK) Algorithm Model Formulation An Order T log T Algorithm for Solving Problem (4.5) Algorithm Heuristic Methods Silver-Meal Heuristic Least Unit Cost Heuristic A Comment on the Planning Horizon Exercises Single-Period Models Making Decisions in the Presence of Uncertainty An Example The Data The Decision Model 117

4 xv 5.3 Another Example Multiple Items A General Model Multiple Constraints Exercises 136 Inventory Planning over Multiple Time Periods: Linear-Cost Case Optimal Policies The Single-Unit, Single-Customer Approach: Single-Location Case : Notation and Definitions Optimality of Base-Stock Policies Stochastic Lead Times The Serial Systems Case Generalized Demand Model Capacity Limitations Finding Optimal Stock Levels Finite Planning Horizon Analysis Constant, Positive Lead Time Case End-of-Horizon Effects Infinite-Horizon Analysis ' Lost Sales Capacity Limited Systems The Shortfall Distribution General Properties Discrete Demand Case An Example A Serial System An Echelon-Based Approach for Managing Inventories in Serial Systems )1 A Decision Model A Dynamic Programming Formulation of the Decision Problem An Algorithm for Computing Optimal Echelon Stock Levels Solving the Oil Rig Problem: The Stationary Demand Case Exercises 181

5 Background Concepts: An Introduction to the (5 1,5) Policy under Poisson Demand Steady State Backorder Case Lost Sales Case Performance Measures Properties of the Performance Measures Finding Stock Levels in (s l,s) Policy Managed Systems: Optimization Problem Formulations and Solution Algorithms First Example: Minimize Expected Backorders Subject to an Inventory Investment Constraint Second Example: Maximize Expected System Average Fill Rate Subject to an Inventory Investment Constraint Exercises 208 A Tactical Planning Model for Managing Recoverable Items in Multi-Echelon Systems The METRIC System System Operation and Definitions The Optimization Problem Approximating the Stationary Probability Distribution for the Number of LRUs in Resupply Finding Depot and Base LRU Stock Levels Waiting Time Analysis Exercises 234 Reorder Point, Lot Size Models: The Continuous Review Case An Approximate Model When Backordering Is Permitted Assumptions Constructing the Model Finding Q* and r* Convexity of the Objective Function Lead Time Demand Is Normally Distributed Alternative Heuristics for Computing Lot Sizes and Reorder Points Final Comments on the Approximate Model An Exact Model Determining the Stationary Distribution of the Inventory Position Random Variable 254

6 xvii Determining the Stationary Distribution of the Net Inventory Random Variable Computing Performance Measures Average Annual Cost Expression Waiting Time Analysis Continuous Approximations: The General Case A Continuous Approximation: Normal Distribution Another Continuous Approximation: Laplace Distribution Optimization Normal Demand Model Laplace Demand Model Exact Poisson Model Additional Observations: Compound Poisson Demand Process, Uncertain Lead Times Finding the Stationary Distribution of the Inventory Position Random Variable When an (nq, r) Policy Is Followed Establishing the Probability Distribution of the Inventory Position Random Variable When an (s, S) Policy Is Employed Constructing an Objective Function' Stochastic Lead Times A Multi-Item Model Model Model Model Model Finding ft Exercises Lot Sizing Models: The Periodic Review Case Notation An Approximation Algorithm Algorithm Algorithm for Computing a Stationary Policy A Primer on Dynamic Programming with an Average Cost Criterion Formulation and Background Results Algorithm Proof of Theorem

7 xviii Contents 10.5 A Heuristic Method for Calculating s and S Exercises 316 References 319 Index 337