Capacity improvement of an unreliable production line – an analytical approach

This paper addresses the problem of capacity estimation and improvement of a multi-stage, multi-product production line where workstations are subject to random failure and repair. The production line can process a variety of products in a batch production environment. Products are processed according to a predefined sequence. A linear programming model is used and modified by taking into account the random behaviour of unreliable stations. Station's downtime is modelled as a fictive product added to the production sequence at appropriate positions. A general procedure for the insertion of fictive products is presented. The procedure considers the states up and down that a station may experience while processing the product mix. It consists of two main steps. Firstly, enumerate the station's states and insert fictive products where appropriate. Secondly, find the best buffer size that minimizes the cycle time. The proposed approach considers more parameters than the Markovian models and the approximation methods where multi-product production lines longer than 2-station 1-buffer can be studied. Numerical examples are presented to show all the steps involved to compute the expected cycle time. Buffer contribution to minimize the cycle time of the production line is also addressed. Simulation is used to validate the results obtained.