Exploiting Virtual Elasticity of Production Systems for Respecting OTD-Part 1: Post-Optimality Conditions for Ergodic Order Arrivals in Fixed Capacity Regimes

Rüttimann, Bruno G.; Stöckli, Martin T.

doi:10.4236/ajor.2020.106018

Cited by 10 publications

(24 citation statements)

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“…With a series of papers, we intend to bridge this gap. This paper is a generalization of a previous paper [1], which examined the post-optimality conditions to comply with the OTD requirement for time-bound order rate (OR) above production capacity with deterministic or mainly ergodic order-arrival characteristic for a single mono-product manufacturing. A manufacturing theory textbook evoking the topic of OTD is [2].…”

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

“…In [1] were expanded the necessary and sufficient conditions for OTD, basic conditions defined with the OTD theorem in [2], with post-optimality conditions enouncing two additional corollaries. It reveals that a temporary (during ∆t) higher OR than the exit rate (ER) of a production system in a fix capacity regime can be backlog-buffered and rescheduled according to the difference ∆T of expected delivery time (EDT) and the process lead time (PLT).…”

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

“…Due to this, the process is OTD compliant. The ∆T is the virtual manufacturing elasticity leading to increased capacity, which has been defined in [1]. The increased capacity is only virtually increased and not physically.…”

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

“…x t represents a deterministic, but time-bound variable OR and ( ) , x t τ represents a stochastic OR with variable inter-arrival time τ, the λ represents the constant ER which should be in line with the average OR. The findings of the paper also have led to enounce the Second Corollary to the Theorem of General Production Requirement (Corollary of Strong and Weak OTD Solutions) formulating the necessary and sufficient condition for a strong OTD solution for Equations ( 1) and ( 2) [1]:…”

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

“…This intermediate step of analysis allows understanding the requirements to pay attention for the omnipotent CPPS, Industry 4.0 manufacturing system characterized by non-ergodic order processes with stochastically variable product-mix. In the following, we will apply the same approach, which has already been used in the paper [1]. That paper mainly dealt with the elasticity topic of production systems, i.e.…”

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

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Exploiting Virtual Elasticity of Manufacturing Systems to Respect OTD—Part 2: Post-Optimality Conditions for the Cases of Ergodic and Non-Ergodic Order Rate with Deterministic Product-Mix

Rüttimann¹,

Stöckli²

2021

AJOR

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Respecting the on-time delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed. As an OTD related manufacturing theory is largely missing it is crucial to understand and formalize the necessary conditions of OTD compliance for complex production environments for maximum exploitation of the production capacity. This paper evaluates the conditions of post-optimality while being OTD compliant for production systems, which are characterized by stochastic order rate and a deterministic product-mix. Instead of applying discrete event simulation to explore the real case-by-case order scheduling optimization for OTD compliance, a Cartesian approach is followed. This enables to define theoretically the solution space of order backlog for OTD, which contributes to developing further manufacturing theory. At the base stands the recently defined new concept of virtual manufacturing elasticity by reducing lead-time to increase virtually production capacity. The result has led to defining additional two corollaries to the OTD theorem, which sets up basic OTD theory. Apart from defining the post-optimal requirements to guarantee for orders at least a weak solution for OTD compliance, this paper reveals that for a deterministic product-mix a non-ergodic order arrival rate can be rescheduled into an ergodic order input rate to the shopfloor if the virtual elasticity ∆T is large enough, hence the importance of having fast and flexible production lines. How to cite this paper: Rüttimann, B.G. and Stöckli, M.T. (2021) Exploiting Virtual Elasticity of Manufacturing Systems to Respect OTD-Part 2: Post-Optimality Conditions for the Cases of Ergodic and Non-Ergodic Order Rate with Deterministic Product-Mix.

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Section: Introduction and Approach To The Problemmentioning

confidence: 99%

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

Section: Introduction and Approach To The Problemmentioning

confidence: 99%

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