Kitting process in a stochastic assembly system

Abstract. Nowadays, customers request more variation in a company's product assortment leading to an increased amount of parts moving around on the shop floor. To cope with this tendency, a kitting process can be implemented. As it gathers the necessary parts into a container prior to assembly, kitting enables a more cost-efficient and qualitative production. However, the performance of this preparation technique in an assembly process has merely been investigated. Therefore, we studied a kitting process with two parts as a continuous-time Markovian queueing model. Using sparse matrix techniques to solve our queueing model, we assessed the impact of kitting interruptions, bursty part arrivals and phase-type distributed kitting times on the behaviour of the part buffers. Consequently, this paper studies part buffer behaviour under realistic assumptions in order to evaluate the performance of kitting operations in a production environment.

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“…Explicitly accounting for finite buffer capacities, Som et. al [14] further refine the results of Hopp and Simon.…”

Section: Introductionmentioning

confidence: 48%

“…Kitting is a particular strategy for supplying materials to an assembly line. Instead of delivering parts in containers of equal parts, kitting collects the necessary parts for a given end product into a specific container, referred to as kit, prior to arriving at an assembly unit [1,14,2,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Performance Evaluation of a Kitting Process

Cuypere

Fiems

2011

Analytical and Stochastic Modeling Techniques and Applications

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“…They found accurate bounds for the buffer capacities of both parts. Explicitly accounting for finite buffer capacities, Som et al [28] further refined the results of Hopp and Simon. The exponential service times and Poisson arrival assumptions were later relaxed in [31] and [10].…”

Section: Introductionmentioning

confidence: 84%

A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times

Cuypere¹,

Turck²,

Wittevrongel³

et al. 2017

Proceedings of the 10th EAI International Conference on Performance Evaluation Methodologies and Tools

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We propose an efficient numerical scheme for the evaluation of large-scale Markov processes that have a generator matrix that reduces to a triangular matrix when a certain rate is sent to zero. The methodology at hand is motivated by coupled queueing systems. Such systems are a natural abstraction for kitting processes in assembly systems and consist of multiple parallel buffers. The buffers are coupled in the sense that departures from the different buffers are synchronised and that there is no service if any of the buffers is empty. As multiple customer buffers are involved, the Markovian description of the system obviously suffers from the state-space explosion problem. To cope with this problem, a numerical algorithm is presented which calculates the coefficients of the Maclaurin-series expansion of the steadystate probability vector. While the series expansion is a regular perturbation problem for the coupled queueing system with exponential service times, it is a singular perturbation problem if the service times are phase-type distributed. Some numerical examples show that the series expansion technique combined with a simple heuristic provides high numerical accuracy.

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“…Without a taxi cab, you have waiting customers; without customers, you have a line of waiting cabs. In other environments, such as telecommunication networks, computing (Parthasarathy et al, 1999), stock exchange, just-in-time assembly systems (Som et al, 1994), organ allocation (Zenios, 1999) etc., imbalances between demand and supply degrade the system performance through operational inefficiencies, rather than revenues lost.…”

Section: Introductionmentioning

confidence: 99%