A parametric critical path problem and an application for cyclic scheduling

Levner, Eugene; Kats, Vladimir

doi:10.1016/s0166-218x(98)00054-7

Cited by 60 publications

(58 citation statements)

References 11 publications

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“…These two inequalities naturally lead to two different arcs, one from to and the other from to , in a program evaluation and review technique (PERT)-like directed graph. Similar ideas for robot scheduling based or the associated directed graphs can be more or less found in the literature [2], [3], [6]. In such a graph, the arc from to denotes that event can occur time units after event occurs.…”

Section: Negative Event Graphmentioning

confidence: 99%

“…Examples include chemical processing systems such as hoist-based production systems for printed circuit board manufacturing, robot-based cluster tools for chemical vapor deposition in semiconductor manufacturing, and other robot cells [1]- [3]. There have been attempts to model and investigate scheduling problems of automated manufacturing systems with time window constraints [2]- [6].…”

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confidence: 99%

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An Extended Event Graph With Negative Places and Tokens for Time Window Constraints

Lee

Park

2005

IEEE Trans. Automat. Sci. Eng.

138

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Abstract-We introduce places with negative holding times and tokens with negative token counts into a timed event graph in order to model and analyze time window constraints. We extend the enabling and firing rules for such an extended event graph named a negative event graph (NEG). We develop necessary and sufficient conditions based on the circuits for which the NEG is live, that is, an infinite sequence of feasible firing epochs exist for each transition. We prove that the minimum cycle time is the same as the maximum circuit ratio of the circuits with positive token counts. We also show that when there exists circuits with negative token counts, the maximum cycle time is bounded and the same as the minimum circuit ratio of such circuits. A scheduling example for a robot-based cluster tool with wafer residency time constraints for semiconductor manufacturing is explained.Note to Practitioners-Scheduling and control problems for modern man-made systems, including automated manufacturing systems such as cluster tools for semiconductor manufacturing, microcircuits, and real-time software systems, are usually modeled as discrete event systems. Such systems often have strict time constraints on timings of some events. Our results can be used for identifying whether there can be a feasible schedule that satisfies all time constraints, computing the range of the feasible cycle times, and determining a steady schedule with the minimum cycle time. By using the feasibility condition, we also can accommodate the system configuration, the task times, and the task sequence so that the system can satisfy the time constraints while meeting the target cycle time. Such practice is already used for real cluster tool engineering. We have more results on implementing a real-time scheduler and controller for time constrained systems. Index Terms-Discrete event system, negative place, negative token, Petri net, time window constraint.

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Section: Negative Event Graphmentioning

confidence: 99%

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confidence: 99%

An Extended Event Graph With Negative Places and Tokens for Time Window Constraints

Lee

Park

2005

IEEE Trans. Automat. Sci. Eng.

138

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“…Lee 2000;Seo and Lee 2002) or algorithms with polynomial complexity (e.g. Lee and Posner 1997;Levner and Kats 1998). If batches do not overlap on any single resource, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…all activities of a batch are finished on a resource prior to the start of the first activity of the following batch (no overtaking), the problem of scheduling is reduced to fixing the optimal sequence and timing such that the single batch can be processed and repeated as fast as possible (e.g. Hall et al 2002;Lee and Posner 1997;Levner and Kats 1998). Many of the cyclic scheduling methods in the literature address cycle shop problems (Middendorf and Timkovsky 2002), which do not cover the case of a general precedence network structure.…”

Section: Introductionmentioning

confidence: 99%

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Throughput-Optimal Sequences for Cyclically Operated Plants

Mayer

Haus

Raisch

et al. 2008

Discrete Event Dyn Syst

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In this paper, we present a method to determine globally optimal schedules for cyclically operated plants where activities have to be scheduled on limited resources. In cyclic operation, a large number of entities is processed in an identical time scheme. For strictly cyclic operation, where the time offset between entities is also identical for all entities, the objective of maximizing throughput is equivalent to the minimization of the cycle time. The resulting scheduling problem is solved by deriving a mixed integer optimization problem from a discrete event model. The model includes timing constraints as well as open sequence decisions for the activities on the resources. In an extension, hierarchical nesting of cycles is considered, which often allows for schedules with improved throughput. The method is motivated by the application to high throughput screening plants, where a specific combination of requirements has to be obeyed (e.g. revisited resources, absence of buffers, or time window constraints).

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Cyclic scheduling in a robotic production line

Kats

Levner

2002

J. Sched.

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SUMMARYThe solution of cyclic scheduling problems is part of the classical repertoire on scheduling algorithms. We consider a problem of cyclic scheduling of identical parts in a production line where transportation of the parts between machines is performed by several robots. The problem is to ÿnd co-ordinated movements of the parts and robots in the line with the no-wait constraints imported; the objective is to maximize the throughput rate. Unlike many previous algorithms which are either heuristic or at best solve the single-robot version of the problem in O(m 4 log m) time, the proposed algorithm provides an exact solution for the more complicated case of multiple robots and solves the problem in O(m 3 log m) time, where m denotes the number of machines in the line.

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A parametric critical path problem and an application for cyclic scheduling

Cited by 60 publications

References 11 publications

An Extended Event Graph With Negative Places and Tokens for Time Window Constraints

An Extended Event Graph With Negative Places and Tokens for Time Window Constraints

Throughput-Optimal Sequences for Cyclically Operated Plants

Cyclic scheduling in a robotic production line

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