Mathematical modelling of the solidification of liquid tin with electromagnetic stirring

It is well known that during alloy solidification, convection currents close to the so-lidification front have an influence on the structure of dendrites, the local solute concentration, the pattern of solid segregation, and eventually the microstructure of the casting and hence its mechanical properties. Controlled stirring of the melt in continuous casting or in ingot solidification is thought to have a beneficial effect. Free convection currents occur naturally due to temperature differences in the melt and for any given configuration, their strength is a function of the degree of superheat present. A more controlled forced convection current can be induced using electro-magnetic stirring. The authors have applied their Control-Volume based MHD method [1, 2] to the problem of tin solidification in an annular crucible with a water-cooled inner wall and a resistance heated outer one, for both free and forced convection situations and for various degrees of superheat. This problem was studied experimentally by Vives and Perry [3] who obtained temperature measurements, front positions and maps of electro-magnetic body force for a range of superheat values. The results of the mathematical model are compared critically against the experimental ones, in order to validate the model and also to demonstrate the usefulness of the coupled solution technique followed, as a predictive tool and a design aid. Figs 6, refs 19.

The open shop scheduling problem with a given sequence of jobs on one machine

The paper considers the open shop scheduling problem to minimize the make-span, provided that one of the machines has to process the jobs according to a given sequence. We show that in the preemptive case the problem is polynomially solvable for an arbitrary number of machines. If preemption is not allowed, the problem is NP-hard in the strong sense if the number of machines is variable, and is NP-hard in the ordinary sense in the case of two machines. For the latter case we give a heuristic algorithm that runs in linear time and produces a schedule with the makespan that is at most 5/4 times the optimal value. We also show that the two-machine problem in the nonpreemptive case is solvable in pseudopolynomial time by a dynamic programming algorithm, and that the algorithm can be converted into a fully polynomial approximation scheme. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 705–731, 1998

A 3/2 algorithm for two-machine open shop with route-dependent processing times

This paper considers the problem of minimizing the schedule length of a two-machine shop in which not only can a job be assigned any of the two possible routes, but also the processing times depend on the chosen route. This problem is known to be NP-hard. We describe a simple approximation algorithm that guarantees a worst-case performance ratio of 2. We also present some modifications to this algorithm that improve its performance and guarantee a worst-case performance ratio of 3=2.

Heuristics for the two-stage job shop scheduling problem with a bottleneck machine

The paper considers the job shop scheduling problem to minimize the makespan. It is assumed that each job consists of at most two operations, one of which is to be processed on one of m⩾2 machines, while the other operation must be performed on a single bottleneck machine, the same for all jobs. For this strongly NP-hard problem we present two heuristics with improved worst-case performance. One of them guarantees a worst-case performance ratio of 3/2. The other algorithm creates a schedule with the makespan that exceeds the largest machine workload by at most the length of the largest operation.

Group technology approach to the open shop scheduling problem with batch setup times

This paper studies the problem of scheduling jobs in a two-machine open shop to minimize the makespan. Jobs are grouped into batches and are processed without preemption. A batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. For this NP-hard problem, we propose a linear-time heuristic algorithm that creates a group technology schedule, in which no batch is split into sub-batches. We demonstrate that our heuristic is a -approximation algorithm. Moreover, we show that no group technology algorithm can guarantee a worst-case performance ratio less than 5/4.

A heuristic for the two-machine open-shop scheduling problem with transportation times

The paper considers a problem of scheduling n jobs in a two-machine open shop to minimize the makespan, provided that preemption is not allowed and the interstage transportation times are involved. This problem is known to be unary NP-hard. We present an algorithm that requires O (n log n) time and provides a worst-case performance ratio of 3/2.

Magnetic modelling and magneto-hydro-dynamic simulations of an aluminium production electrolytic cell

A simulation of the motion of molten aluminium inside an electrolytic cell is presented. Since the driving term of the aluminium motion is the Lorentz (j × B) body force acting within the fluid,this problem involves the solution of the magneto-hydro-dynamic equations. Different solver modules for the magnetic field computation and for the fluid motion simulation are coupled together. The interactions of all these are presented and discussed.

Performance evaluation of a distributed algorithm for an inverse heat conduction problem

Numerical solutions of realistic 2-D and 3-D inverse problems may require a very large amount of computation. A two-level concept on parallelism is often used to solve such problems. The primary level uses the problem partitioning concept which is a decomposition based on the mathematical/physical problem. The secondary level utilizes the widely used data partitioning concept. A theoretical performance model is built based on the two-level parallelism. The observed performance results obtained from a network of general purpose Sun Sparc stations are compared with the theoretical values. Restrictions of the theoretical model are also discussed.

An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables

Multilevel refinement strategies for the capacity vehicle routing problem

We discuss the application of the multilevel (ML) refinement technique to the Vehicle Routing Problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. A SL algorithm, which uses a combination of standard VRP heuristics, is developed first to solve instances of the VRP. A ML version, which extends the global view of these heuristics, is then created, using variants of the construction and improvement heuristics at each level. Finally some multilevel enhancements are developed. Experimentation is used to find suitable parameter settings and the final version is tested on two well-known VRP benchmark suites. Results comparing both SL and ML algorithms are presented.

Scalable and efficient graph colouring in 3 dimensions using emergence engineering principles

This paper describes ways in which emergence engineering principles can be applied to the development of distributed applications. A distributed solution to the graph-colouring problem is used as a vehicle to illustrate some novel techniques. Each node acts autonomously to colour itself based only on its local view of its neighbourhood, and following a simple set of carefully tuned rules. Randomness breaks symmetry and thus enhances stability. The algorithm has been developed to enable self-configuration in wireless sensor networks, and to reflect real-world configurations the algorithm operates with 3 dimensional topologies (reflecting the propagation of radio waves and the placement of sensors in buildings, bridge structures etc.). The algorithm’s performance is evaluated and results presented. It is shown to be simultaneously highly stable and scalable whilst achieving low convergence times. The use of eavesdropping gives rise to low interaction complexity and high efficiency in terms of the communication overheads.