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 greedy open shop heuristic with job priorities

The paper presents an improved version of the greedy open shop approximation algorithm with pre-ordering of jobs. It is shown that the algorithm compares favorably with the greedy algorithm with no pre-ordering by reducing either its absolute or relative error. In the case of three machines, the new algorithm creates a schedule with the makespan that is at most 3/2 times the optimal value.

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.

A polynomial algorithm for the three-machine open shop with a bottleneck machine

The paper considers the three‐machine open shop scheduling problem to minimize themakespan. It is assumed that each job consists of at most two operations, one of which is tobe processed on the bottleneck machine, the same for all jobs. A new lower bound on theoptimal makespan is derived, and a linear‐time algorithm for finding an optimalnon‐preemptive schedule is presented.

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.

An open shop scheduling problem with a non-bottleneck machine

This paper considers the problem of processing n jobs in a two-machine non-preemptive open shop to minimize the makespan, i.e., the maximum completion time. One of the machines is assumed to be non-bottleneck. It is shown that, unlike its flow shop counterpart, the problem is NP-hard in the ordinary sense. On the other hand, the problem is shown to be solvable by a dynamic programming algorithm that requires pseudopolynomial time. The latter algorithm can be converted into a fully polynomial approximation scheme that runs in time. An O(n log n) approximation algorithm is also designed whi finds a schedule with makespan at most 5/4 times the optimal value, and this bound is tight.

Two-machine open shop scheduling with special transportation times

The paper considers a problem of scheduling n jobs in a two-machine open shop to minimise the makespan, provided that preemption is not allowed and the interstage transportation times are involved. In general, this problem is known to be NP-hard. We present a linear time algorithm that finds an optimal schedule if no transportation time exceeds the smallest of the processing times. We also describe an algorithm that creates a heuristic solution to the problem with job-independent transportation times. Our algorithm provides a worst-case performance ratio of 8/5 if the transportation time of a job depends on the assigned processing route. The ratio reduces to 3/2 if all transportation times are equal.

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.

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-machine open shop scheduling with an availability constraint

We study a two-machine open shop scheduling problem, in which one machine is not available for processing during a given time interval. The objective is to minimize the makespan. We show that the problem is NP-hard and present an approximation algorithm with a worst-case ratio of 4/3.

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.

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.

Open ended microwave oven for flip-chip assembly

A novel open-ended waveguide cavity resonator for the microwave curing of bumps, underfills and encapsulants is described. The open oven has the potential to provide fast alignment of devices during flip-chip assembly, direct chip attach, surface mount assembly or wafer-scale level packaging. The prototype microwave oven was designed to operate at X-band for ease of testing, although a higher frequency version is planned. The device described in the paper takes the form of a waveguide cavity resonator. It is approximately square in cross-section and is filled with a low-loss dielectric with a relative permittivity of 6. It is excited by end-fed probes in order to couple power preferentially into the TM3,3,k mode with the object of forming nine 'hot-spots' in the open end. Low power tests using heat sensitive film demonstrate clearly that selective heating in multiple locations in the open end of the oven is achievable

Microwave curing for high density package

Summary form only given. Currently the vast majority of adhesive materials in electronic products are bonded using convection heating or infra-red as well as UV-curing. These thermal processing steps can take several hours to perform, slowing throughput and contributing a significant portion of the cost of manufacturing. With the demand for lighter, faster, and smaller electronic devices, there is a need for innovative material processing techniques and control methodologies. The increasing demand for smaller and cheaper devices pose engineering challenges in designing a curing systems that minimize the time required between the curing of devices in a production line, allowing access to the components during curing for alignment and testing. Microwave radiation exhibits several favorable characteristics and over the past few years has attracted increased academic and industrial attention as an alternative solution to curing of flip-chip underfills, bumps, glob top and potting cure, structural bonding, die attach, wafer processing, opto-electronics assembly as well as RF-ID tag bonding. Microwave energy fundamentally accelerates the cure kinetics of polymer adhesives. It provides a route to focus heat into the polymer materials penetrating the substrates that typically remain transparent. Therefore microwave energy can be used to minimise the temperature increase in the surrounding materials. The short path between the energy source and the cured material ensures a rapid heating rate and an overall low thermal budget. In this keynote talk, we will review the principles of microwave curing of materials for high density packing. Emphasis will be placed on recent advances within ongoing research in the UK on the realization of "open-oven" cavities, tailored to address existing challenges. Open-ovens do not require positioning of the device into the cavity through a movable door, hence being more suitable for fully automated processing. Further potential advantages of op- - en-oven curing include the possibility for simultaneous fine placement and curing of the device into a larger assembly. These capabilities promise productivity gains by combining assembly, placement and bonding into a single processing step. Moreover, the proposed design allows for selective heating within a large substrate, which can be useful particularly when the latter includes parts sensitive to increased temperatures.