Title: Model of production system with time delay using stochastic bilinear equation

Authors: Kenji Shirai; Yoshinori Amano

Addresses: Department of Information System, Niigata University of International and Information Studies, Mizukino 3-1-1, Nishi-ku, Niigata City, Niigata Pri., 950-2292, Japan ' Kyonan Elecs Co. Ltd., Nishiuracho 8-48-2, Fushimi-ku, Kyoto City, 612-0029, Japan

Abstract: This study proposes a stochastic bilinear differential equation to model the production process by including a time delay. The time delay is caused by factors such as variations in workers' skill levels, the delay in delivering materials, and logistical issues. We verify the existence of a unique solution to the proposed mathematical model. To obtain a unique solution, we introduce a stochastic bilinear partial differential equation. We consider that a manufacturer with external companies produces some of the ordered equipment. For the model evaluation, we compare the model results with actual data, which were obtained from the production of control equipment.

Keywords: stochastic bilinear PDEs; partial differential equations; time delay; distributed parameter systems; average regression models; production system modelling; skills levels; materials delivery; logistics; mathematical modelling; control equipment.

DOI: 10.1504/AJMSA.2015.071897

Asian Journal of Management Science and Applications, 2015 Vol.2 No.1, pp.81 - 103

Received: 11 Feb 2015
Accepted: 28 May 2015
Published online: 22 Sep 2015 *

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