Operations planning. Mixed integer optimization models (Q2879081)

Business administration requires decisions for achieving specific goals on long, medium or short term. Designing short-range activities is referred to as operation planning. The mathematical formulation of these plans requires various levels of abstraction and sophistication. The book under review gathers several of the most useful models for optimization with widespread applicability in operation planning.NEWLINENEWLINEThe cornerstone of the book is the knapsack problem presented in Chapter 2 along with effective solution methods. The discussion includes an overview of computational complexity and a brief encounter with techniques such as asymptotic heuristic analysis and fully polynomial time approximation schemes. The same problem is considered from a different perspective in Chapter 3, devoted to set cover, packing, and partitioning problems. Here new solution methods are introduced, viz., column-generation and branch-and-price. The generalized assignment problem is studied in Chapter 4. Determining good lower bounds on the optimal solution or high-quality is possible by applying Lagrangean relaxation or greedy heuristics. Chapter 5 contains an intuitive explanation of many results proved for the uncapacitated economic lot sizing problems. Besides the classical approach based on dynamic programming, a very effective concave cost network flow representation is presented. The next chapter considers the class of NP-hard capacitated lot sizing problems. Connexions with the binary knapsack problem and solving methods based on techniques introduced in previous chapters are included. Chapter 7, entitled `Multistage production and distribution planning problems', focuses on centralized systems, as the analysis of the optimal solution for this class of problems serves in the study of decentralized systems. The discrete facility location problems, to which Chapter 8 is devoted, have close relationships with most of the other models covered in the book. Therefore, many of the techniques introduced in previous chapters can be used to solve problems in this class. A different approach, based on randomization/derandomization, is also summarized. The difficult problem known as the travelling salesman problem is touched upon in the last chapter. Its generalization referred to as vehicle routing is also discussed. An overview of the most successful heuristic approaches to obtain high-quality solutions is provided here.NEWLINENEWLINEAt first sight, the selected problems have two features in common: they are deterministic and some of their variables are restricted to take integer values. The author pinpoints less visible connections between various problem classes in a convincing and appealing way. The efforts made to maintain the mathematical formalism as non-invasive as possible should be also emphasized. The presentation successfully avoids the dry definition-theorem-proof-corollary style. Each problem, along with several commonly encountered instances, is stated succinctly in plain English. The mathematical model is then formulated and the main ideas for obtaining a suitable/acceptable solution are described, mostly informally. For technical details, the reader is referred to the relevant bibliography. 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.NEWLINENEWLINEWith its precise references to a bibliography of 120 titles ranging from 1954 to 2010, the book can serve as well as a reference for researchers in the domain of operations planning.