Operations Planning: Mixed Integer Optimization Models, 1st Edition (Paperback) book cover

Operations Planning

Mixed Integer Optimization Models, 1st Edition

By Joseph Geunes

CRC Press

218 pages | 39 B/W Illus.

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A reference for those working at the interface of operations planning and optimization modeling, Operations Planning: Mixed Integer Optimization Models blends essential theory and powerful approaches to practical operations planning problems. It presents a set of classical optimization models with widespread application in operations planning. The discussion of each of these classical models begins with the motivation for studying the problem as well as examples of the problem’s application in operations planning contexts. The book explores special structural results and properties of optimal solutions that have led to effective algorithmic solution approaches for each problem class.

Each of the models and solution methods presented is the result of high-impact research that has been published in the scholarly literature, with appropriate references cited throughout the book. The author highlights the close relationships among the models, examining those situations in which a particular model results as a special case of other related models or how one model generalizes another. Understanding these relationships allows you to more easily characterize new models being developed through their relationships to classical models.

The models and methods presented in the book have widespread application in operations planning. It enables you to recognize the structural similarities between models and to recognize these structural elements within other contexts. It also gives you an understanding of various critical operations research techniques and classical operations planning models, without the need to consult numerous sources.


"The book under review gathers several of the most useful models for optimization with widespread applicability in operation planning. … With the exception of Chapter 1, each chapter contains several numerical examples and ends with a set of exercises. This approach makes the book very helpful for a graduate course on mixed integer optimization models for non-mathematically oriented, business administration students. With its precise references to a bibliography of 120 titles ranging from 1954 to 2010, the book can serve well as a reference for researchers in the domain of operations planning."

—Mihai Cipu (Bucuresti), Zentralblatt MATH, 1327

"The book provides a technically sound, yet very readable, description of various state-of-the-art mathematical programming techniques that can be used to tackle relevant operations planning problems. In early chapters, important mathematical programming concepts are introduced in the context of archetypical optimization problems, such as the knapsack and the set covering problem. In later chapters, the book covers all classical operations planning problems; i.e., problems in production planning (single and multi-stage), distribution planning, location, and routing. Although none of the material is really new, it is nice to have it well-presented in a single book instead of scattered among various journal papers. Where appropriate, the material is illustrated with meaningful numerical examples and figures. Moreover, every chapter is concluded with challenging exercises, making this book suitable for courses at the advanced undergraduate or graduat level. Because it covers a wide range of techniques, the book can also be used to introduce readers to various concepts in mathematical programming, even if they don’t have a particular interest in operations planning. In that case, the specific operations planning problems merely serve to illustrate the techniques."

—Albert P.M. Wagelmans, Erasmus University Rotterdam, The Netherlands

Table of Contents

Introduction and Purpose

Operations Planning

Mixed Integer Optimization

Optimization Models in Operations Planning

The Knapsack Problem


Knapsack Problem 0-1 Programming Formulation

Relation to the subset sum problem

Linear Relaxation of the 0-1 Knapsack Problem

Asymptotically Optimal Heuristic

Fast Approximation Algorithm

Valid Inequalities


Set Covering, Packing, and Partitioning


Problem Definition and Formulation

Solution Methods

Bin packing heuristics

Column generation and the set partitioning problem

Branch-and-price for the set partitioning problem


The Generalized Assignment Problem


GAP Problem Definition and Formulation

Lagrangian Relaxation Technique

Lagrangian Relaxation for the GAP

Branch-and-Price for the GAP

Greedy Algorithms and Asymptotic Optimality


Uncapacitated Economic Lot Sizing


The basic UELSP Model

Fixed-charge network flow interpretation

Dynamic programming solution method

Tight Reformulation of UELSP

Lagrangian relaxation shows a tight formulation

An O(T log T) Algorithm for the UELSP

Implications of Backordering


Capacitated Lot Sizing


Capacitated Lot Sizing Formulation

Relation to the (J-1 Knapsack Problem

Fixed-charge network flow interpretation

Dynamic programming approach

The Equal-Capacity Case

FPTAS for Capacitated Lot Sizing

Structure of the dynamic programming approach

Approximation of the dynamic program

Valid Inequalities for the CELSP

(S,1) inequalities

Facets for the equal-capacity CELSP

Generalized flow-cover inequalities


Multistage Production and Distribution Planning


Models with Dynamic Demand

Serial systems with dynamic demand

Production networks with non-speculative costs

Constrant-factor approximations for special cases

Models with Constant Demand Rates

Stationary, nested, power-of-two policies

The joint replenishment problem

The one-warehouse multi-retailer problem


Discrete Facility Location Problems


Relation to Previous Models in this Book

Cost-minimizing version of the FLP

Relationship of the FLP to lot sizing problems

Single-sourcing version of the FLP and the GAP

Set covering and FLP complexity

Dual-Ascent Method for the Uncapacitated FLP

Approximation Algorithms for the Metric UFLP

Randomization and derandomization

Solution Methods for the General FLP

Lagrangian relazation for the FLP

Valid inequalities for the FLP

Approximation algorithms for the FLP


Vehicle Routing and Traveling Salesman Problems


The TSP Graph and Complexity

Formulating the TSP as an Optimization Problem

Comb Inequalities

Heuristic Solutions for the TSP

Nearest neighbor heuristic

The sweep method

Minimum spanning tree based methods

Local improvement methods

The Vehicle Routing Problem

Exact solution of the VRP via branch-and-price

A GAP-based heuristic solution approach for the VRP

The Clarke-Wright savings heuristic method

Additional heuristic methods for the VRP




About the Author

Joseph Geunes has been on the faculty of the Industrial and Systems Engineering Department at the University of Florida since 1998. His research focuses on applying operations research techniques to large-scale production and logistics planning problems. Professor Geunes serves as Co-Director of the Supply Chain And Logistics Engineering (SCALE) Research Center and as Director of the Outreach Engineering Management professional Master’s Degree program at the University of Florida. He has co-authored more than 30 peer-reviewed journal articles, which have appeared in journals such as Operations Research, Manufacturing & Service Operations Management, IIE Transactions, and Naval Research Logistics. He also serves as an Associate Editor for OMEGA, Computers & IE, and Decision Sciences, and is on the editorial boards of Production and Operations Management and the International Journal of Inventory Research. Professor Geunes received a Ph.D. (1999) and MBA (1993) from Penn State University, as well as a B.S. in Electrical Engineering (1990) from Drexel University.

About the Series

Operations Research Series

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Subject Categories

BISAC Subject Codes/Headings:
BUSINESS & ECONOMICS / Operations Research
BUSINESS & ECONOMICS / Purchasing & Buying
TECHNOLOGY & ENGINEERING / Industrial Engineering
TECHNOLOGY & ENGINEERING / Operations Research