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Dive into the research topics where Alexander H. G. Rinnooy Kan is active.

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Featured researches published by Alexander H. G. Rinnooy Kan.


Handbooks in Operations Research and Management Science | 1993

Chapter 9 Sequencing and scheduling: Algorithms and complexity

Eugene L. Lawler; Jan Karel Lenstra; Alexander H. G. Rinnooy Kan; David B. Shmoys

Publisher Summary This chapter discusses different types of sequencing and scheduling problems, and describes different types of algorithms and the concepts of complexity theory. A class of deterministic machine scheduling problems has been introduced in the chapter. The chapter also deals with the single machine, parallel machine and multi-operation problems in this class, respectively. The two generalizations of the deterministic machine-scheduling model have been presented in the chapter. A deterministic scheduling model may give rise to various stochastic counterparts, as there is a choice in the parameters that are randomized, in their distributions, and in the classes of policies that can be applied. A characteristic feature of these models is that the stochastic parameters are regarded as independent random variables with a given distribution and that their realization occurs only after the scheduling decision has been made. In the deterministic model, one has perfect information, and capitalizing on it in minimizing the realization of a performance measure may require exponential time.


Mathematical Programming | 1990

Concurrent stochastic methods for global optimization

Richard H. Byrd; Cornelius L. Dert; Alexander H. G. Rinnooy Kan; Robert B. Schnabel

The global optimization problem, finding the lowest minimizer of a nonlinear function of several variables that has multiple local minimizers, appears well suited to concurrent computation. This paper presents a new parallel algorithm for the global optimization problem. The algorithm is a stochastic method related to the multi-level single-linkage methods of Rinnooy Kan and Timmer for sequential computers. Concurrency is achieved by partitioning the work of each of the three main parts of the algorithm, sampling, local minimization start point selection, and multiple local minimizations, among the processors. This parallelism is of a coarse grain type and is especially well suited to a local memory multiprocessing environment. The paper presents test results of a distributed implementation of this algorithm on a local area network of computer workstations. It also summarizes the theoretical properties of the algorithm.


European Journal of Operational Research | 1992

The stochastic vehicle routing problem revisited

Cock Bastian; Alexander H. G. Rinnooy Kan

Abstract The stochastic vehicle routing problem is a problem of growing importance. Introduction of stochastic element in classical routing problems may change the structure of those problems. This property has not been fully recognized in the literature. We present modifications of existing models and introduce more realistic ones. Under certain assumptions, these models turn out to exhibit the structure of the time-dependent traveling salesman problem.


Mathematical Programming | 1993

Decomposition in general mathematical programming

Olaf E. Flippo; Alexander H. G. Rinnooy Kan

In this paper a unifying framework is presented for the generalization of the decomposition methods originally developed by Benders (1962) and Dantzig and Wolfe (1960). These generalizations, calledVariable Decomposition andConstraint Decomposition respectively, are based on the general duality theory developed by Tind and Wolsey. The framework presented is of a general nature since there are no restrictive conditions imposed on problem structure; moreover, inaccuracies and duality gaps that are encountered during computations are accounted for. The two decomposition methods are proven not to cycle if certain (fairly general) conditions are met. Furthermore, finite convergence can be ensured under the traditional finiteness conditions and asymptotic convergence can be guaranteed once certain continuity conditions are met. The obvious symmetry between both types of decomposition methods is explained by establishing a duality relation between the two, which extends a similar result in Linear Programming. A remaining asymmetry in the asymptotic convergence results is argued to be a direct consequence of a fundamental asymmetry that resides in the Tind-Wolsey duality theory. It can be shown that in case the latter asymmetry disappears, the former does too. Other decomposition techniques, such as Lagrangean Decomposition and Cross Decomposition, turn out to be captured by the general framework presented here as well.


Journal of Intelligent Manufacturing | 1991

Machine allocation algorithms for job shop manufacturing

Mario van Vliet; Alexander H. G. Rinnooy Kan

In this paper we present algorithms for the solution of two server (machine) allocation problems that occur in manufacturing networks. The manufacturing network is modelled as an open network of queues with general interarrival time and service time distributions. The queueing network is analyzed by using the parametric decomposition method: a two-moment approximation scheme. The server allocation problems are solved by means of a marginal analysis scheme. Numerical results on two manufacturing networks are presented.


Mathematics of Operations Research | 1994

Average case analysis of a heuristic for the assignment problem

Richard M. Karp; Alexander H. G. Rinnooy Kan; Rakesh V. Vohra

Our main contribution is an On log n algorithm that determines with high probability a perfect matching in a random 2-out bipartite graph. We also show that this algorithm runs in On expected time. This algorithm can be used as a subroutine in an On2 heuristic for the assignment problem. When the weights in the assignment problem are independently and uniformly distributed in the interval [0, 1], we prove that the expected weight of the assignment returned by thus heuristic is bounded above by 3 + On-α, for some posrtive constant a.


Operations Research Letters | 1990

A note on benders decomposition in mixed-integer quadratic programming

Olaf E. Flippo; Alexander H. G. Rinnooy Kan

In this note two decomposition methods are improved for Mixed-Integer Quadratic Programs, developed by E. Balas and R. Lazimy.


European Journal of Operational Research | 1989

The future of operations research is bright

Alexander H. G. Rinnooy Kan

Abstract The paper discusses ways in which OR has fulfilled the hopes of the past, is achieving success in the present, and exhibits exciting and demanding challenges for the future.


North-holland Mathematics Studies | 1987

Probabilistic Analysis of Algorithms

Alexander H. G. Rinnooy Kan

Publisher Summary This chapter explores the probabilistic analysis of algorithms that has become an active research area. It reviews some representative results that are known for problems defined in the Euclidean plane. The chapter examines the fertile area of optimization problems defined on graphs and networks and presents a short digression on modes of stochastic convergence, an essential concept if one wants to analyze the notion of a random variable such as the error of a heuristic going to 0 with increasing problem size. The probabilistic analysis of heuristic method performance is quite difficult; each step in the algorithm conditions the probability distribution encountered in the succeeding steps in a complicated fashion. As the difference of two independent uniformly distributed random variables follows a triangular distribution, there is no distributional invariance throughout the steps of this method and yet such invariance is an essential prerequisite for a successful analysis. One way to overcome this kind of obstacle is to change the algorithm so that the value produced is not affected but its modified behavior is analyzed.


Archive | 1992

Formulation and a Lagrangean Relaxation Procedure for Solving Part Scheduling and Tool Loading Problems in FMS

Kannan Sethuraman; Marshall L. Fisher; Alexander H. G. Rinnooy Kan

The growth of the metal-working industry spawned improvements in computer integrated manufacturing technology. One result of such improvements was the development of Flexible Manufacturing Systems (FMS). A Flexible Manufacturing System typically consists of versatile numerically controlled machines, connected by an automated material handling system, all under a central computer control. The FMS’s achieve the enviable results of effectively combining the efficiency of transfer lines and flexibility of job shops by eliminating or reducing set-up or change over times between manufacturing operations. Although FMS’s can offer a wide variety of benefits, the flexibility of these systems has resulted in making the design and subsequent operation of FMS’s very complex.

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Jan Karel Lenstra

Eindhoven University of Technology

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Olaf E. Flippo

Erasmus University Rotterdam

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Cornelius L. Dert

University of Colorado Boulder

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Richard H. Byrd

University of Colorado Boulder

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Cock Bastian

Erasmus University Rotterdam

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Mario van Vliet

Erasmus University Rotterdam

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Kannan Sethuraman

University of Pennsylvania

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