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.

Two-stage open shop scheduling with a bottleneck machine

It is known that for the open shop scheduling problem to minimize the makespan there exists no polynomial-time heuristic algorithm that guarantees a worst-case performance ratio better than 5/4, unless P6≠NP. However, this result holds only if the instance of the problem contains jobs consisting of at least three operations. This paper considers the open shop scheduling problem, provided that each job consists of at most two operations, one of which is to be processed on one of the m⩾2 machines, while the other operation must be performed on the bottleneck machine, the same for all jobs. For this NP-hard problem we present a heuristic algorithm and show that its worst-case performance ratio is 5/4.

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.

Non-preemptive two-machine open shop scheduling with non-availability constraints

We study a two-machine open shop scheduling problem, in which the machines are not continuously available for processing. No preemption is allowed in the processing of any operation. The objective is to minimize the makespan. We consider approximability issues of the problem with more than one non-availability intervals and present an approximation algorithm with a worst-case ratio of 4/3 for the problem with a single non-availability interval.

Two-machine flowshop scheduling problems with no-wait jobs

We study a two-machine flow shop scheduling problem with no-wait in process, in which one of the machines is not available during a specified time interval. We consider three scenarios of handing the operation affected by the nonavailability interval. Its processing may (i) start from scratch after the interval, or (ii) be resumed from the point of interruption, or (iii) be partially restarted after the interval. The objective is to minimize the makespan. We present an approximation algorithm that for all these scenarios delivers a worst-case ratio of 3/2. For the second scenario, we offer a 4/3-approximation algorithm.

Flow shop scheduling problems under machine–dependent precedence constraints

The paper considers the flow shop scheduling problems to minimize the makespan, provided that an individual precedence relation is specified on each machine. A fairly complete complexity classification of problems with two and three machines is obtained.

Batching decisions for assembly production systems

The two-stage assembly scheduling problem is a model for production processes that involve the assembly of final or intermediate products from basic components. In our model, there are m machines at the first stage that work in parallel, and each produces a component of a job. When all components of a job are ready, an assembly machine at the second stage completes the job by assembling the components. We study problems with the objective of minimizing the makespan, under two different types of batching that occur in some manufacturing environments. For one type, the time to process a batch on a machine is equal to the maximum of the processing times of its operations. For the other type, the batch processing time is defined as the sum of the processing times of its operations, and a setup time is required on a machine before each batch. For both models, we assume a batch availability policy, i.e., the completion times of the operations in a batch are defined to be equal to the batch completion time. We provide a fairly comprehensive complexity classification of the problems under the first type of batching, and we present a heuristic and its worst-case analysis under the second type of batching.

Two-Machine Shop Scheduling with an Uncapacitated Interstage Transporter

In this paper we study the two-machine flow shop and open shop problems to minimize the makespan with a single interstage transporter that may carry any number of jobs between the machines at a time. For each of these problems we present a best possible approximation algorithm within a class of schedules with at most two shipments. As a by-product of this research, for the problem of minimizing the makespan on parallel identical machines we analyze the ratio of the makespan for a non-preemptive schedule over the makespan of a preemptive schedule.

Optimising the wave soldering process for lead free solders

Nitrogen is now used in wave soldering machines to help lower the amount of dross that can be formed on the solder bath surface. The paper provides details on the use of computational fluid dynamics in helping understand the flow profiles of nitrogen in a wave soldering machine and to predict the concentration of nitrogen and oxygen around the solder bath.

Matching search in fractal video compression and its parallel implementation in distributed computing environments

Fractal video compression is a relatively new video compression method. Its attraction is due to the high compression ratio and the simple decompression algorithm. But its computational complexity is high and as a result parallel algorithms on high performance machines become one way out. In this study we partition the matching search, which occupies the majority of the work in a fractal video compression process, into small tasks and implement them in two distributed computing environments, one using DCOM and the other using .NET Remoting technology, based on a local area network consists of loosely coupled PCs. Experimental results show that the parallel algorithm is able to achieve a high speedup in these distributed environments.

From sudoku to DNA in six steps

Tony Valsamidis, senior lecturer in information systems, Greenwich University reviews Genesis Machines: The New Science of Biocomputing by Martyn Amos - Atlantic Books ISBN - 184354 224 2. What do encryption, the double helix and sudoku have in common? They are all bound together by the newish science of biocomputing in rather surprising ways, as Martyn Amos masterfully shows in this compendious volume.

Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times - a polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in $ \O({\rm T}_{\rm feas}(n) \times\log n)$ time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper.

Transporting jobs through a two-machine open shop

We consider the two-machine open shop scheduling problem in which the jobs are brought to the system by a single transporter and moved between the processing machines by the same transporter. The purpose is to split the jobs into batches and to find the sequence of moves of the transporter so that the time by which the completed jobs are collected together on board the transporter is minimal. We present a 7/5-approximation algorithm. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009

Multicomponent gas-mixture measurements using an array of gas sensors and an artificial neural-network

An Electronic Nose is being jointly developed between the University of Greenwich and the Institute of Intelligent Machines to detect the gases given off from an oil filled transformer when it begins to break down. The gas sensors being used are very simple, consisting of a layer of Tin Oxide (SnO2) which is heated to approximately 640 K and the conductivity varies with the gas concentrations. Some of the shortcomings introduced by the commercial gas sensors available are being overcome by the use of an integrated array of gas sensors and the use of artificial neural networks which can be 'taught' to recognize when the gas contains several components. At present simulated results have achieved up to a 94% success rate of recognizing two component gases and future work will investigate alternative neural network configurations to maintain this success rate with practical measurements.