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A set of items has to be assigned to a set of bins with different sizes. If necessary the size of each bin can be extended. The objective is to minimize the total size, i.e. the sum of the sixs of the bins. In this paper we study both the oll-line case and the on-line variant of this problem under the assumption that each item is smaller than any bin. For… (More)

In this paper we propose a method for integrating constraint propagation algorithms into an optimization procedure for vertex coloring with the goal of finding improved lower bounds. The key point we address is how to get instances of Constraint Satisfaction Problems (CSPs) from a graph coloring problem in order to give rise to new lower bounds… (More)

A set of tasks has to be scheduled on three processors and each task requires that a set of the processors be available for a given processing time. The objective of the problem is to determine a nonpreemptive schedule with minimum makespan. The problem is known to be NP-hard in the strong sense. A normal schedule is such that all tasks requiring the same… (More)