Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management.
The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization.
"Applications of Combinatorial Optimization" is presenting a certain number among the most common and well-known applications of Combinatorial Optimization.
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Yes, you can access Applications of Combinatorial Optimization, Volume 3 by Vangelis Th. Paschos in PDF and/or ePUB format, as well as other popular books in Matematica & Matematica discreta. We have over one million books available in our catalogue for you to explore.
In the airline industry, optimizing and automating the building of crew pairings is a major financial and organizational issue. The problem consists of covering all the company’s flights, programmed in a given time window, with teams made up of Cockpit personnel (pilots, copilots) and of cabin personnel (stewardesses, Stewards) at a minimum cost. With a frequency of several days (in the order of a week), each crew leaves from the base to which it is assigned, carries out a certain number of flights, and comes back to the base. This sequence of flights with a return to the base is called a rotation, or pairing. Drawing up the pairings of an airline Company is highly constrained by international, national and internal work regulations, and by the limited availability of resources. These constraints make the problem particularly hard to solve. Besides the gains in terms of Organization, security and calculation time, the use of optimization programs and models for this problem allows big companies to make substantial financial gains. It is not unusual for a reduction of 1% in the total cost of the rosters to result in savings of several tens of millions of dollars for big companies [DES 97], which is one reason for the abundant fundamental and applied research on this subject. The general crew pairing problem with resource constraints problem (CPP-RC) can be formulated as a minimum cost multicommodity flow problem with additional variables and resource constraints. Even though in most applications the cost of a rotation is non-linear [DES 97, LAV 88], in this chapter we will restrict ourselves to the case where the cost function is a hnear approximation. The ways of constructing a network of feasible pairings, and calculating the cost of the rosters, along with the associated mathematical program, are presented in section 1.2. Section 1.3 gives an overview of classical solution techniques, with a focus on the column generation method, whose associated subproblem is studied in section 1.4. Section 1.5 concludes the chapter.
1.2. Definition of the problem
The set of flights to be covered by the crews is denoted by
= {1,…, n}. The flight program and the associated timetables are established more or less exactly for the considered period, in the order of a month or a week depending on the size of the company. The term flight associated with each e...
Table of contents
Cover
Title Page
Copyright
Preface
Chapter 1: Airline Crew Pairing Optimization
Chapter 2: The Task Allocation Problem
Chapter 3: A Comparison of Some Valid Inequality Generation Methods for General 0–1 Problems
Chapter 4: Production Planning
Chapter 5: Operations Research and Goods Transportation
Chapter 6: Optimization Models for Transportation Systems Planning
Chapter 7: A Model for the Design of a Minimum-cost Telecommunications Network
Chapter 8: Parallel Combinatorial Optimization.
Chapter 9: Network Design Problems: Fundamental Methods
Chapter 10: Network Design Problems: Models and Applications
Chapter 11: Multicriteria Task Allocation to Heterogenous Processors with Capacity and Mutual Exclusion Constraints
