An m-partition of a set is a way to distribute the members into m parts. Given a set of positive numbers, an optimal m-partition problem asks for an m-partition optimizing some objective function. List scheduling is an on-line algorithm that has been widely used in scheduling problems. In this paper, we show the tight bounds on the performances of list scheduling for partition problems with the...

Minimizing a convex function over a convex region is probably the core problem in the Nonlinear Programming literature. Under the assumption of the function of a differentiable function of interest, several methods have been proposed and successively studied. For example, the Steepest Descent Method consists of performing a line search along a descent direction given by minus the gradient of th...

Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2 − ε for the problem of minimizing the total weighted completion time in concurrent open shops. We also obtain a hardness of 2 − ε for minimizing the makespan in the assembly line problem. These results follow from a new inapproximability result for...

In this article, we address a variant of the rolling stock (RS) problem in dense railway systems within a metropolitan context. It consists in determining every train composition and scheduling empty trains to efficiently fit the demand. By empty trains we refer to scheduled trips where trains travel along the system without carrying passengers. A heuristic is presented to generate eligible slo...

This paper deals with the Assembly Line Balancing Problem considering incompatibilities between the tasks with the aim of, first, minimizing the number of workstations and, then, minimizing the cycle time for the minimum number of workstations. In order to solve the problem we propose the use of a Greedy Randomized Adaptive Search Procedure (GRASP) obtained from the application of some classic ...

The line sum optimization problem asks for a ( 0 , 1 ) -matrix minimizing the of given functions evaluated at its row and column sums. We show that uniform problem, with identical functions, monotone over matrices nonincreasing sums, are polynomial time solvable.