The multiple resource constrained project scheduling problem: a breadth-first approach

Article Abstract:

A simple breadth-first tree search scheme for minimizing the makespan of a project with a partially ordered network of activities under multiple resource constraints is presented. Breadth_maximal resource satisfying set (MRS) compares favorably with existing methods that use depth-first or best-first search. Results demonstrate that Breadth_MRS and Best_MRS are fast and memory-efficient algorithms and that the threshold value theta and the resource availabilities together determine the difficulty level of the problem.

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V- and inverted V-shaped properties for optimal single machine schedules for a class of non-separable penalty functions

Article Abstract:

The single-machine job scheduling problem to minimize a non-separable objective function is explored. The latter is actually a linear combination of the 'sum of the squares,' 'sum of the mean' and 'mean' functions of job completion times and a generalization of penalty functions such as the mean completion time. To obtain its optimal sequence for different values of alpha, beta and , the longest processing time, shortest processing time, V-shaped and inverted V-shaped schedules are derived.

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A direct approach for finding all efficient solutions for multiobjective programming problems

Article Abstract:

A direct strategy for determining the efficient solutions for multiobjective programming problems is proposed. The approach is based on a level set concept and uses a weighting scheme to solve the duality gap problem in the multiobjective generalized convex program. The solution obtained on the k-th step of the algorithm developed for the approach was used as basis to generate the efficient solutions.

Mathematical optimization, Vector analysis

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