Analytical Solution of the serial Bernoulli production line steady-state performance and its application in the shipbuilding process

The modern shipbuilding industry is faced with numerous challenges urging abiding improvement of the shipbuilding process and its management. Such a demanding problem is usually approached using complex production management models involving large data basis handling. The same problem can be solved using simpler, intuitive and mathematically transparent models developed within production system engineering. For these purposes, the analytical solution of the serial Bernoulli production line steady-state performance involving an arbitrary number of machines and buffers of arbitrary occupancy is developed based on Markov chain approach and eigenvalue problem including formulation of the generalised transition matrix as a key novelty. Performance measures in case of general serial Bernoulli production line are developed and the theory is validated using serial Bernoulli lines composed of two, three, four and five machines. The obtained results are compared to those determined using a semi-analytical approach. In order to further demonstrate the applicability of the developed theory, performance measure analysis is performed in cases of longer lines composed of 6, 7, 8, 9 and 10 machines with non-equal buffer capacities. Application of the developed procedure in the analysis of the shipbuilding process is illustrated in a case of the plate prefabrication line usually placed in each shipyard.