Formal Approach of FMS Cyclic Scheduling

Trouillet, Benoit; Korbaa, Ouajdi; Gentina, J.C.

doi:10.1109/tsmcc.2006.876063

Cited by 19 publications

(10 citation statements)

References 20 publications

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“…Optimization problems for particular net subclasses have also been proposed in the context of max-plus [30] and min-plus algebras [31]. In [30] linear systems are considered that are equivalent to PN marked graphs, and optimization problems are defined to express situations in which some of the system coefficients may vary within certain intervals.…”

Section: B Related Workmentioning

confidence: 99%

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A Min-Max Problem for the Computation of the Cycle Time Lower Bound in Interval-Based Time Petri Nets

Bernardi

Campos

2013

IEEE Trans. Syst. Man Cybern, Syst.

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The time Petri net with firing frequency intervals (TPNF) is a modeling formalism used to specify system behavior under timing and frequency constraints. Efficient techniques exist to evaluate the performance of TPNF models based on the computation of bounds of performance metrics (e.g., transition throughput, place marking). In this paper, we propose a min-max problem to compute the cycle time of a transition under optimistic assumptions. That is, we are interested in computing the lower bound. We will demonstrate that such a problem is related to a maximization linear programming problem (LP-max) previously stated in the literature, to compute the throughput upper bound of the transition. The main advantage of the min-max problem compared to the LP-max is that, in addition to the optimal value, the optimal solutions provide useful feedback to the analyst on the system behavior (e.g., performance bottlenecks). We have implemented two solution algorithms, using CPLEX APIs, to solve the min-max problem, and have compared their performance using a benchmark of TPNF models, several of these being case studies. Finally, we have applied the min-max technique for the vulnerability analysis of a critical infrastructure, i.e., the Saudi Arabian crude-oil distribution network.Index Terms-Lagrangian relaxation, linear programming problem (LPP), min-max problem, performance bounds, time Petri net, vulnerability analysis.

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Section: B Related Workmentioning

confidence: 99%

“…The work in [31] states a throughput optimization problem, but minimizing other criteria such as the work in process, in the framework of min-plus algebras for the particular case of marked graphs and weighted T-systems.…”

Section: B Related Workmentioning

confidence: 99%

A Min-Max Problem for the Computation of the Cycle Time Lower Bound in Interval-Based Time Petri Nets

Bernardi

Campos

2013

IEEE Trans. Syst. Man Cybern, Syst.

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“…The production lines of manufacturing system often include assembly/disassembly tasks. This can be accounted for the nature of the aimed output, which requires to assemble and/or disassemble several parts ( [13], [17], [18], [19], [20], [21]). There are also many systems with only disassembly tasks, for example disassembly lines used in recycling ( [8], [10], [15]).…”

Section: A Systems With Assembly/disassembly Tasksmentioning

confidence: 99%

A Mathematical Model for Cyclic Scheduling with Assembly Tasks and Work-In-Process Minimization

Amar

Camus

Korbaa

2010

Frontiers of Assembly and Manufacturing

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In this paper, we deal with the cyclic scheduling problem. More precisely, we consider the cyclic job shop with assembly tasks. Such a problem is made of several jobs, each job consisting of tasks (assembly/disassembly tasks and transformation tasks) being assigned to machines in a cyclic way. This kind of scheduling problem is well fitted to medium and large production demands, since the cyclic behavior can avoid the scheduling of the whole tasks by considering only a small temporal window (cycle). Thus, cyclic scheduling is a heuristic to solve the scheduling problems whose complexity is NP-hard in the general case. Many methods have been proposed to solve the cyclic scheduling problem. Among them, we focus on the mathematical programming approach. We will propose here a mathematical model for cyclic scheduling with assembly tasks and Work-In-Process minimization, and we illustrate this approach with an example from literature.

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“…In everyday practice, these processes arise in different application domains (such as manufacturing, time sharing of processors in embedded systems, digital signal processing, and in compilers where scheduling loop operations for parallel or pipelined architectures takes place) as well as in service domains, covering such areas as workforce scheduling (e.g., shift scheduling, crew scheduling), timetabling (e.g., train timetabling, aircraft routing and scheduling), and reservations (e.g., reservations with or without slack, assigning classes to rooms) [7,10,11,14,15,19,21,23,24]. Such cyclic scheduling problems belong to the class of decision problems, i.e., problems aimed at finding whether or not there exists a solution satisfying certain assumed conditions [21]. Moreover, because of their integer domains, the considered problems belong to a class of Diophantine problems [9,18].…”

Section: Introductionmentioning

confidence: 99%

Declarative approach to cyclic steady state space refinement: periodic process scheduling

Bocewicz

Banaszak

2013

Int J Adv Manuf Technol

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Problems of cyclic scheduling are usually observed in flexible manufacturing systems which produce multitype parts where the automated guided vehicle system plays the role of a material handling system, as well as in various other multimodal transportation systems where goods and/or passenger itinerary planning plays a pivotal role. The schedulability analysis of the processes executed in the so-called systems of concurrent cyclic processes (SCCPs) can be executed within a declarative modeling framework. Consequently, the considered SCCP scheduling problem can be seen as a constraint satisfaction problem. Such a representation provides a unified way for evaluating the performance of local cyclic processes as well as of multimodal processes supported by them. Here, the crucial issue is that of a control procedure (e.g., a set of dispatching rules), which would guarantee the cyclic behavior of the SCCP. In this context, we discuss the sufficient conditions guaranteeing the schedulability of both local and multimodal cyclic processes, and we propose a recursive approach in designing them.

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Formal Approach of FMS Cyclic Scheduling

Cited by 19 publications

References 20 publications

A Min-Max Problem for the Computation of the Cycle Time Lower Bound in Interval-Based Time Petri Nets

A Min-Max Problem for the Computation of the Cycle Time Lower Bound in Interval-Based Time Petri Nets

A Mathematical Model for Cyclic Scheduling with Assembly Tasks and Work-In-Process Minimization

Declarative approach to cyclic steady state space refinement: periodic process scheduling

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