Sensitivity Analysis of List Scheduling Heuristics

When jobs have to be processed on a set of identical parallel machines so as to minimize the makespan of the schedule, list scheduling rules form a popular class of heuristics. The order in which jobs appear on the list is assumed here to be determined by the relative size of their processing times; well known special cases are the LPT rule and the SPT rule, in which the jobs are ordered according to non-increasing and non-decreasing processing time respectively. When one of the job processing times is gradually increased, the schedule produced by a list scheduling rule will be affected in a manner reflecting its sensitivity to data perturbations. We analyze this phenomenon and obtain analytical support for the intuitively plausible notion that the sensitivity of a list scheduling rule increases with the quality of the schedule produced

Order statistics and the linear assignment problem

Under mild conditions on the distribution functionF, we analyze the asymptotic behavior in expectation of the smallest order statistic, both for the case thatF is defined on (–, +) and for the case thatF is defined on (0, ). These results yield asymptotic estimates of the expected optiml value of the linear assignment problem under the assumption that the cost coefficients are independent random variables with distribution functionF

The asymptotic behaviour of a distributive sorting method

In the distributive sorting method of Dobosiewicz, both the interval between the minimum and the median of the numbers to be sorted and the interval between the median and the maximum are partitioned inton/2 subintervals of equal length; the procedure is then applied recursively on each subinterval containing more than three numbers. We refine and extend previous analyses of this method, e.g., by establishing its asymptotic linear behaviour under various probabilistic assumptions

Integrale bedrijfsmodellen

Integrale bedrijfsmodelle

THE AGGREGATION OF FUNCTIONAL MODELS: TECHNICAL ASPECTS

The standard approach to corporate model building is through a modular design in which various decision making units in the organization appear as components. This raises the technical issue of how to aggregate the results of the corresponding submodels

PROBABILISTIC ANALYSIS OF ALGORITHMS

An introductory and selective review is presented of results obtained through a probabilistic analysis of combinatorial algorithms. The emphasis is on asymptotic characteristics of optimal solution values, and on the relative and absolute error analysis for simple heuristics

STOCHASTIC GLOBAL OPTIMIZATION METHODS PART I: CLUSTERING METHODS

In this stochastic approach to global optimization, clustering techniques are applied to identify local minima of a real valued objective function that are potentially global. Three different methods of this type are described; their accuracy and efficiency are analyzed in detail

STOCHASTIC GLOBAL OPTIMIZATION METHODS PART II: MULTI LEVEL METHODS

In Part II of this paper, two stochastic methods for global optimization are described that, with probability 1, find all relevant local minima of the objective function with the smallest possible number of local searches. The computational performance of these methods is examined both analytically and empirically