Switched Max-Plus Linear-Dual Inequalities: Application in Scheduling of Multi-Product Processing Networks

Zorzenon, Davide; Komenda, Jan; Raisch, Jörg

doi:10.1016/j.ifacol.2022.10.343

Cited by 3 publications

(1 citation statement)

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“…time when transition t i ∈ T fires for the k-th time, where i ∈ 1, n and k ∈ N. Since the (k +1)-st firing of any transition t i cannot occur before the k-th one, it is natural to assume that x i is nondecreasing in k, i.e., x i (k + 1) ≥ x i (k) for all i ∈ 1, n and k ∈ N. The dynamics of a P-TEG can be described by the following system of infinitely many linear inequalities in infinitely many variables x i (k): for all i, j ∈ 1, n , µ ∈ {0, 1}, k ∈ N, 10 To be precise, in this paper we focus on P-TEGs with loose initial conditions, as defined in Zorzenon et al (2023). This means that we will not consider the arrival time of the initial tokens as part of the dynamics.…”

Section: Dynamicsmentioning

confidence: 99%

Bounded Consistency of P-Time Event Graphs

Zorzenon

Komenda

Raisch

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not violate any temporal constraints. In this paper, we solve the long-standing problem of characterizing the decidability of consistency by showing that, assuming unary encoding of the initial marking, this property can be verified in strongly polynomial time. The proof is based on a reduction to the problem of detecting paths with infinite weight in infinite weighted digraphs called N-periodic graphs.

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Section: Dynamicsmentioning

confidence: 99%

Bounded Consistency of P-Time Event Graphs

Zorzenon

Komenda

Raisch

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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Switched max-plus linear-dual inequalities: cycle time analysis and applications

Zorzenon,

Komenda,

Raisch

2024

Discrete Event Dyn Syst

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P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches; ii. a complete trajectory of the robot including start-up and shut-down transients.

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