We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the…
Mathematical Programming
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In this paper, some of the main known algorithms for the traveling salesman problem are surveyed. The paper is organized as follows: 1) definition; 2) applications; 3) complexity analysis; 4) exact algorithms; 5) heuristic algorithms; 6) conclusion.…

We present a unified heuristic which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multidepot vehicle routing…

The emergence of metaheuristics for solving difficult combinatorial optimization problems is one of the most notable achievements of the last two decades in operations research. This paper provides an account of the most recent developments in the…

A robust approach to solving linear optimization problems with uncertain data has been proposed in the early 1970s, and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the…

This paper proposes a stochastic programming model and solution algorithm for solving supply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only…

The availability of effective exact or heuristic solution methods for general MixedInteger Programs (MIPs) is of paramount importance for practical applications. In the present paper we investigate the use of a generic MIP solver as a blackbox…

This article introduces a new family of Cayley graphs, called kdegree Cayley graphs, for building interconnection networks. The kdegree Cayley graph possesses many valuable topological properties, such as regularity with degree k, logarithmic…

(This article originally appeared in Management Science, January 1981, Volume 27, Number 1, pp. 1–18, published by The Institute of Management Sciences.) One of the most computationally useful ideas of the 1970s is the observation that many hard…

DantzigWolfe decomposition and column generation, devised for linear programs, is a success story in largescale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not yet found in textbooks. We…

This paper presents a review of staff scheduling and rostering, an area that has become increasingly important as business becomes more service oriented and cost conscious in a global environment. Optimised staff schedules can provide enormous…

This paper surveys the research on the metaheuristics for the Vehicle Routing Problem with Time Windows (VRPTW).The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The…

This book's introduction features a humorous story of a man with a line of people behind him, who explains to his boss, "I can't find an efficient algorithm, but neither can all these famous people." This man illustrates an important quality of a…

Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, a literature review of facility location models in the context of supply chain management is given. We identify basic features that…

GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization. GRASP usually is implemented as a multistart procedure, where each iteration is made up of a construction phase, where a randomized greedy…

Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION "This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial…

Many revenue management problems have a network aspect. In this paper, we argue that a network can be thought of as a system of substitutable and complementary products, and the value of a revenue management model should be supermodular or…

The optimum routing of a fleet of trucks of varying capacities from a central depot to a number of delivery points may require a selection from a very large number of possible routes, if the number of delivery points is also large. This paper, after…

This paper presents a survey of the research on the vehicle routing problem with time windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes…

This paper provides a tutorial on column generation and branchandprice for vehicle routing problems. The main principles and the basic theory of the methods are first outlined. Some additional issues, including reinforcement of the relaxation or…
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