Shop scheduling problems under precedence constraints

The paper considers a scheduling model that generalizes the well-known open shop, flow shop, and job shop models. For that model, called the super shop, we study the complexity of finding a time-optimal schedule in both preemptive and non-preemptive cases assuming that precedence constraints are imposed over the set of jobs. Two types of precedence rela-tions are considered. Most of the arising problems are proved to be NP-hard, while for some of them polynomial-time algorithms are presented.

An application of quasi-Newton methods for the numerical solution of interface problems

Quasi-Newton methods are applied to solve interface problems which arise from domain decomposition methods. These interface problems are usually sparse systems of linear or nonlinear equations. We are interested in applying these methods to systems of linear equations where we are not able or willing to calculate the Jacobian matrices as well as to systems of nonlinear equations resulting from nonlinear elliptic problems in the context of domain decomposition. Suitability for parallel implementation of these algorithms on coarse-grained parallel computers is discussed.

Heuristics for short route job shop scheduling problems

We consider two “minimum”NP-hard job shop scheduling problems to minimize the makespan. In one of the problems every job has to be processed on at most two out of three available machines. In the other problem there are two machines, and a job may visit one of the machines twice. For each problem, we define a class of heuristic schedules in which certain subsets of operations are kept as blocks on the corresponding machines. We show that for each problem the value of the makespan of the best schedule in that class cannot be less than 3/2 times the optimal value, and present algorithms that guarantee a worst-case ratio of 3/2.

Shop-scheduling problems with fixed and non-fixed machine orders of the jobs

The paper deals with the determination of an optimal schedule for the so-called mixed shop problem when the makespan has to be minimized. In such a problem, some jobs have fixed machine orders (as in the job-shop), while the operations of the other jobs may be processed in arbitrary order (as in the open-shop). We prove binary NP-hardness of the preemptive problem with three machines and three jobs (two jobs have fixed machine orders and one may have an arbitrary machine order). We answer all other remaining open questions on the complexity status of mixed-shop problems with the makespan criterion by presenting different polynomial and pseudopolynomial algorithms.

Complexity of mixed shop scheduling problems: A survey

We survey recent results on the computational complexity of mixed shop scheduling problems. In a mixed shop, some jobs have fixed machine orders (as in the job shop), while the operations of the other jobs may be processed in arbitrary order (as in the open shop). The main attention is devoted to establishing the boundary between polynomially solvable and NP-hard problems. When the number of operations per job is unlimited, we focus on problems with a fixed number of jobs.

Scheduling batches with simultaneous job processing for two-machine shop problems

We consider the problem of scheduling independent jobs on two machines in an open shop, a job shop and a flow shop environment. Both machines are batching machines, which means that several operations can be combined into a batch and processed simultaneously on a machine. The batch processing time is the maximum processing time of operations in the batch, and all operations in a batch complete at the same time. Such a situation may occur, for instance, during the final testing stage of circuit board manufacturing, where burn-in operations are performed in ovens. We consider cases in which there is no restriction on the size of a batch on a machine, and in which a machine can process only a bounded number of operations in one batch. For most of the possible combinations of restrictions, we establish the complexity status of the problem.

A domain decomposition algorithm for inverse welding problems

A mathematical model and a numerical scheme for the inverse determination of heat sources generated by means of a welding process is presented in this paper. The accuracy of the heat source retrieval is discussed.

Scheduling problems for parallel dedicated machines under multiple resource constraints

The paper considers scheduling problems for parallel dedicated machines subject to resource constraints. A fairly complete computational complexity classification is obtained, a number of polynomial-time algorithms are designed. For the problem with a fixed number of machines in which a job uses at most one resource of unit size a polynomial-time approximation scheme is offered.

A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and threedimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted.

A generic time and space accurate numerical approach to closely coupled fluid-structure interaction problems

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, flow in elastic pipes and blood vessels and extrusion of metals through dies. However a comprehensive computational model of these multi-physics phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply even to the extent in metal forming, for example, that the deformation of the die is totally ignored. More recently, strategies for solving the full coupling between the fluid and soild mechanics behaviour have developed. Conventionally, the computational modelling of fluid structure interaction is problematical since computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. In the past the concurrent, but rather disparate, development paths for the finite element and finite volume methods have resulted in numerical software tools for CFD and CSM that are different in almost every respect. Hence, progress is frustrated in modelling the emerging multi-physics problem of fluid structure interaction in a consistent manner. Unless the fluid-structure coupling is either one way, very weak or both, transferring and filtering data from one mesh and solution procedure to another may lead to significant problems in computational convergence. Using a novel three phase technique the full interaction between the fluid and the dynamic structural response are represented. The procedure is demonstrated on some challenging applications in complex three dimensional geometries involving aircraft flutter, metal forming and blood flow in arteries.