Principles of Inventory Management: When You Are Down to Four, Order More

1 Inventories Are Everywhere.- 1.1 The Roles of Inventory.- 1.2 Fundamental Questions.- 1.3 Factors Affecting Inventory Policy Decisions.- 1.3.1 System Structure.- 1.3.2 The Items.- 1.3.3 Market Characteristics.- 1.3.4 Lead Times.- 1.3.5 Costs.- 1.4 Measuring Performance.- 2 EOQ Model.- 2.1 Model Development: Economic Order Quantity (EOQ) Model.- 2.1.1 Robustness of the EOQ Model.- 2.1.2 Reorder Point and Reorder Interval.- 2.2 EOQ Model with Backordering Allowed.- 2.2.1 The Optimal Cost.- 2.3 Quantity Discount Model.- 2.3.1 All Units Discount.- 2.3.2 An Algorithm to Determine the Optimal Order Quantity for the All Units Discount Case.- 2.3.3 Incremental Quantity Discounts.- 2.3.4 An Algorithm to Determine the Optimal Order Quantity for the Incremental Quantity Discount Case.- 2.4 Lot Sizing When Constraints Exist.- 2.5 Exercises.- 3 Power-of-Two Policies.- 3.1 Basic Framework.- 3.1.1 Power-of-Two Policies.- 3.1.2 PO2 Policy for a Single-Stage System.- 3.1.2.1 Cost for the Optimal PO2 Policy.- 3.2 Serial Systems.- 3.2.1 Assumptions and Nomenclature.- 3.2.2 A Mathematical Model for Serial Systems.- 3.2.3 Algorithm to Obtain an Optimal Solution to (RP).- 3.3 Multi-Echelon Distribution Systems.- 3.3.1 A Mathematical Model for Distribution Systems.- 3.3.1.1 Relaxed Problem.- 3.3.2 Powers-of-Two Solution.- 3.4 Joint Replenishment Problem (JRP).- 3.4.1 A Mathematical Model for Joint Replenishment Systems.- 3.4.2 Rounding the Solution to the Relaxed Problem.- 3.5 Exercises.- Dynamic Lot Sizing with Deterministic Demand.- 4.1 The Wagner-Whitin (WW) Algorithm.- 4.1.1 Solution Approach.- 4.1.2 Algorithm.- 4.1.3 Shortest-Path Representation of the Dynamic Lot Sizing Problem.- 4.1.4 Technical Appendix for the Wagner-Whitin Algorithm.- 4.2 Wagelmans-Hoesel-Kolen (WHK) Algorithm.- 4.2.1 Model Formulation.- 4.2.2 An Order T logT Algorithm for Solving Problem (4.5).- 4.2.3 Algorithm.- 4.3 Heuristic Methods.- 4.3.1 Silver-Meal Heuristic.- 4.3.2 Least UnitCost Heuristic.- 4.4 A Comment on the Planning Horizon.- 4.5 Exercises.- 5 Single-Period Models.- 5.1 Making Decisions in the Presence of Uncertainty.- 5.2 An Example.- 5.2.1 The Data.- 5.2.2 The Decision Model.- 5.3 Another Example.- 5.4 Multiple Items.- 5.4.1 A General Model.- 5.4.2 Multiple Constraints.- 5.5 Exercises.- 6 Inventory Planning over Multiple Time Periods: Linear-Cost Case.- 6.1 Optimal Policies.- 6.1.1 The Single-Unit, Single-Customer Approach: Single-Location Case.- 6.1.1.1 Notation and Definitions.- 6.1.1.2 Optimality of Base-Stock Policies.- 6.1.1.3 Stochastic Lead Times.- 6.1.1.4 The Serial Systems Case.- 6.1.1.5 Generalized of Demand Model.- 6.1.1.6 Capacity Limitations.- 6.2 Finding Optimal Stock Levels.- 6.2.1 Finite Planning Horizon Analysis.- 6.2.2 Constant, Positive Lead Time Case.- 6.2.3 End-of-Horizon Effects.- 6.2.4 Infinite-Horizon Analysis.- 6.2.5 Lost Sales.- 6.3 Capacity Limited Systems.- 6.3.1 The Shortfall Distribution.- 6.3.1.1 General Properties.- 6.3.2 Discrete Demand Case.- 6.3.3 An Example.- 6.4 A Serial System.- 6.4.1 An Echelon-Based Approach for Managing Inventories in Serial Systems.- 6.4.1.1 A Decision Model.- 6.4.1.2 A Dynamic Programming Formulation of the Decision Problem.- 6.4.1.3 An Algorithm for Computing Optimal Echelon Stock Levels.- 6.4.1.4 Solving the Oil Rig Problem: The Stationary Demand Case.- 6.5 Exercises.- 7 Background Concepts: An Introduction to the (s-1, s) Policy under Poisson Demand.- 7.1 Steady State.- 7.1.1 Backorder Case.- 7.1.2 Lost Sales Case.- 7.2 Performance Measures.- 7.3 Properties of the Performance Measures.- 7.4 Finding Stock Levels in (s-1, s) Policy Managed Systems: Optimization Problem Formulations and Solution Algorithms.- 7.4.1 First Example: Minimize Expected Backorders Subject to an Inventory Investment Constraint.- 7.4.2 Second Example: Maximize Expected System Average Fill Rate Subject to an Inventory Investment Constraint.- 7.5 Exercises.- 8 A Tactical Planning Model f