Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arriva...Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arrivals, may compromise the observance of on-time supplies for some orders. The purpose of this paper is to evaluate the conditions of post-optimality for stochastic order rate governed production systems in order to observe OTD. Instead of a heuristic or a simulative exploration, a Cartesian-based approach is applied to developing the necessary and sufficient mathematical condition to solve the problem statement. The research result demonstrates that increasing </span><span style="font-family:Verdana;">speed of throughput reveals a latent capacity, which allows arrival orders </span><span style="font-family:Verdana;">above capacity limits to be backlog-buffered and rescheduled for OTD, exploiting the virtual manufacturing elasticity inherent to all production systems to increase OTD reliability of non JIT-based production systems.展开更多
Respecting the on-time<span><span><span> </span></span></span><span><span><span>delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch &a...Respecting the on-time<span><span><span> </span></span></span><span><span><span>delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed.</span></span></span><span><span><span> 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 </span></span></span><span><span><span>by</span></span></span><span><span><span> 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 develo</span></span></span><span><span><span>ping</span></span></span><span><span><span> 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 defin</span></span></span><span><span><span>ing</span></span></span><span><span><span> 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 </span></span></span><span><span><span><span><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><img src="Edit_e545052a-10c6-459e-aa8a-2bccefd4a1a7.png" alt="" /></span></span></span><i><span>T</span></i><span> is large enough</span></span></span></span><span><span><span>, </span></span></span><span><span><span>hence the importance of having fast and flexible production lines.</span></span></span>展开更多
The recently experienced hype concerning the so-called “4<sup>th</sup> Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production S...The recently experienced hype concerning the so-called “4<sup>th</sup> Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.展开更多
文摘Respecting the on-time-delivery (OTD) for manufacturing orders is mandatory. This depends, however, on the probability distribution of incoming order rate. The case of non-equal distribution, such as aggregated arrivals, may compromise the observance of on-time supplies for some orders. The purpose of this paper is to evaluate the conditions of post-optimality for stochastic order rate governed production systems in order to observe OTD. Instead of a heuristic or a simulative exploration, a Cartesian-based approach is applied to developing the necessary and sufficient mathematical condition to solve the problem statement. The research result demonstrates that increasing </span><span style="font-family:Verdana;">speed of throughput reveals a latent capacity, which allows arrival orders </span><span style="font-family:Verdana;">above capacity limits to be backlog-buffered and rescheduled for OTD, exploiting the virtual manufacturing elasticity inherent to all production systems to increase OTD reliability of non JIT-based production systems.
文摘Respecting the on-time<span><span><span> </span></span></span><span><span><span>delivery (OTD) for manufacturing orders is mandatory. However, for non-JIT Batch & Queue Push-manufacturing systems, the compliance of OTD is not intrinsically guaranteed.</span></span></span><span><span><span> 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 </span></span></span><span><span><span>by</span></span></span><span><span><span> 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 develo</span></span></span><span><span><span>ping</span></span></span><span><span><span> 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 defin</span></span></span><span><span><span>ing</span></span></span><span><span><span> 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 </span></span></span><span><span><span><span><span style="font-size:10.0pt;font-family:;" "=""><span style="font-size:10.0pt;font-family:;" "=""><img src="Edit_e545052a-10c6-459e-aa8a-2bccefd4a1a7.png" alt="" /></span></span></span><i><span>T</span></i><span> is large enough</span></span></span></span><span><span><span>, </span></span></span><span><span><span>hence the importance of having fast and flexible production lines.</span></span></span>
文摘The recently experienced hype concerning the so-called “4<sup>th</sup> Industrial Revolution” of production systems has prompted several papers of various subtopics regarding Cyber-Phdysical Production Systems (CPPS). However, important aspects such as the modelling of CPPS to understand the theory regarding the performance of highly non-ergodic and non-deterministic flexible manufacturing systems in terms of Exit Rate (ER), Manufacturing Lead Time (MLT), and On-Time Delivery (OTD) have not yet been examined systematically and even less modeled analytically. To develop the topic, in this paper, the prerequisites for modelling such systems are defined in order to be able to derive an explicit and dedicated production mathematics-based understanding of CPPS and its dynamics: switching from explorative simulation to rational modelling of the manufacturing “physics” led to an own and specific manufacturing theory. The findings have led to enouncing, among others, the Theorem of Non-Ergodicity as well as the Batch Cycle Time Deviation Function giving important insights to model digital twin-based CPPS for complying with the mandatory OTD.