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.

[Book Review] Noel Starkey (ed), Connectionist Natural Language Processing: Readings from 'Connection Science'

Review of: Noel Starkey (ed), Connectionist Natural Language Processing: Readings from 'Connection Science'

Proportionate flow shop with controllable processing times

This paper considers a special class of flow-shop problems, known as the proportionate flow shop. In such a shop, each job flows through the machines in the same order and has equal processing times on the machines. The processing times of different jobs may be different. It is assumed that all operations of a job may be compressed by the same amount which will incur an additional cost. The objective is to minimize the makespan of the schedule together with a compression cost function which is non-decreasing with respect to the amount of compression. For a bicriterion problem of minimizing the makespan and a linear cost function, an O(n log n) algorithm is developed to construct the Pareto optimal set. For a single criterion problem, an O(n2) algorithm is developed to minimize the sum of the makespan and compression cost. Copyright © 1999 John Wiley & Sons, Ltd.

Scheduling batches with sequential job processing for two-machine flow and open shops

In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only on the machine, is required before a batch is processed on a machine, and all jobs in a batch remain at the machine until the entire batch is processed. The aim is to make batching and sequencing decisions, which specify a partition of the jobs into batches on each machine, and a processing order of the batches on each machine, respectively, so that the makespan is minimized. The flow-shop problem is shown to be strongly NP-hard. We demonstrate that there is an optimal solution with the same batches on the two machines; we refer to these as consistent batches. A heuristic is developed that selects the best schedule among several with one, two, or three consistent batches, and is shown to have a worst-case performance ratio of 4/3. For the open-shop, we show that the problem is NP-hard in the ordinary sense. By proving the existence of an optimal solution with one, two or three consistent batches, a close relationship is established with the problem of scheduling two or three identical parallel machines to minimize the makespan. This allows a pseudo-polynomial algorithm to be derived, and various heuristic methods to be suggested.

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.

Three-machine shop scheduling with partially ordered processing routes

This paper considers the problem of sequencing n jobs in a three-machine shop with the objective of minimising the maximum completion time. The shop consists of three machines, M1,M2 and M_{3}. A job is first processed on M1 and then is assigned either the route (M2,M_{3}) or the route (M_{3},M2). Thus, for our model the processing route is given by a partial order of machines, as opposed to the linear order of machines for a job shop, or to an arbitrary sequence of machines for an open shop. The main result is on O(nlog n) time heuristic, which generates a schedule with the makespan that is at most 5/3 times the optimum value.

Computational modelling-a key component in materials processing

Computational analysis software is now widely accepted as a key industrial tool for plant design and process analysis. This is due in part to increased accuracy in the models, larger and faster computer systems and better graphical interfaces that allow easy use of the technology by engineers. The use of computational modelling to test new ideas and analyse current processes helps to take the guesswork out of industrial process design and offers attractive cost savings. An overview of computer-based modelling techniques as applied to the materials processing industry is presented and examples of their application are provided in the contexts of the mixing and refining of lead bullion and the manufacture of lead ingots.

Pre-emptive scheduling problems with controllable processing times

We consider a range of single machine and identical parallel machine pre-emptive scheduling models with controllable processing times. For each model we study a single criterion problem to minimize the compression cost of the processing times subject to the constraint that all due dates should be met. We demonstrate that each single criterion problem can be formulated in terms of minimizing a linear function over a polymatroid, and this justifies the greedy approach to its solution. A unified technique allows us to develop fast algorithms for solving both single criterion problems and bicriteria counterparts.

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan.

Modelling of a dosator: an analytical approach based on measured powder flow properties

[No abstract is available for this article.]