On the rate of convergence to optimality of the LPT rule - postscript

This postscript contains the proofs of two results listed in the paper 'On the rate of convergence to optimality of the LPT rule'

Methods and models for the construction of weakly parallel tests

Several methods are proposed for the construction of weakly parallel tests [i.e., tests with the same test information function (TIF)]. A mathematical programming model that constructs tests containing a prespecified TIF and a heuristic that assigns items to tests with information functions that are equal are important components of these methods. Numerical examples demonstrate that tests can be constructed quickly and that the heuristic produces good results. However, the heuristic is not applicable for every set of practical constraints (e.g., constraints with respect to test administration time, test composition, or dependencies between items). Index terms: item banking, heuristics, mathematical programming, test construction, weakly parallel tests

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

Concurrent stochastic methods for global optimization

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

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005

Identical parallel machine scheduling problems: structural patterns, bounding techniques and solution procedures

The work is about fundamental parallel machine scheduling problems which occur in manufacturing systems where a set of jobs with individual processing times has to be assigned to a set of machines with respect to several workload objective functions like makespan minimization, machine covering or workload balancing. In the first chapter of the work an up-to-date survey on the most relevant literature for these problems is given, since the last review dealing with these problems has been published almost 20 years ago. We also give an insight into the relevant literature contributed by the Artificial Intelligence community, where the problem is known as number partitioning. The core of the work is a universally valid characterization of optimal makespan and machine-covering solutions where schedules are evaluated independently from the processing times of the jobs. Based on these novel structural insights we derive several strong dominance criteria. Implemented in a branch-and-bound algorithm these criteria have proved to be effective in limiting the solution space, particularly in the case of small ratios of the number of jobs to the number of machines. Further, we provide a counter-example to a central result by Ho et al. (2009) who proved that a schedule which minimizes the normalized sum of squared workload deviations is necessarily a makespan-optimal one. We explain why their proof is incorrect and present computational results revealing the difference between workload balancing and makespan minimization. The last chapter of the work is about the minimum cardinality bin covering problem which is a dual problem of machine-covering with respect to bounding techniques. We discuss reduction criteria, derive several lower bound arguments and propose construction heuristics as well as a subset sum-based improvement algorithm. Moreover, we present a tailored branch-and-bound method which is able to solve instances with up to 20 bins