Non-approximability results for scheduling problems with minsum criteria

We provide several non-approximability results for determin- istic scheduling problems whose objective is to minimize the total job completion time. Unless P = NP, none of the problems under consid- eration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by Max SNP hardness proofs. Among the investigated problems are: scheduling unrelated machines with some additional features like job release dates, deadlines and weights, scheduling flow shops, and scheduling open shops

Solving a linear diophantine equation with lower and upper bounds on the variables

We develop an algorithm for solving a linear diophantine equation with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction, and first finds short vectors satisfying the diophantine equation. The next step is to branch on linear combi- nations of these vectors, which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists. The research was motivated by the need for solving constrained linear dio- phantine equations as subproblems when designing integrated circuits for video signal processing. Our algorithm is tested with good result on real-life data

The maximum traveling salesman problem under polyhedral norms

We consider the traveling salesman problem when the cities are points in Rd for some fixed d and distances are computed according to a polyhedral norm. We show that for any such norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(n f-2 log n), where f is the number of facets of the polyhedron determining the polyhedral norm. Thus for example we have O(n 2 log n) algorithms for the cases of points in the plane under the Rectilinear and Sup norms. This is in contrast to the fact that finding a minimum length tour in each case is NP-hard

Uma propriedade estrutural do problema de programação da produção flow shop permutacional com tempos de setup

Neste artigo apresenta-se uma propriedade estrutural do problema de programação da produção flow shop permutacional com tempos de setup das máquinas separados dos tempos de processamento das tarefas, a qual foi identificada a partir de investigações que foram realizadas sobre as características do problema. Tal propriedade fornece um limitante superior do tempo de máquina parada entre a sua preparação e o início de execução das tarefas. Utilizando a propriedade, o problema original de programação da produção com minimização do makespan pode ser resolvido de maneira heurística por meio de uma analogia com o problema assimétrico do caixeiro-viajante.<br>This paper deals with the permutation flow shop scheduling problem with separated machine setup times. As a result of an investigation on the problem characteristics a structural property is introduced. Such a property provides an upper bound on the idle time of the machines between the setup task and the job processing. As an application of this property, the original scheduling problem with the makespan criterion can be heuristically solved by an analogy with the asymmetric traveling salesman problem