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