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

Application of Semi-Analytical Methods in Production Systems Engineering

“…Some authors claimed that it is not possible or even necessary to solve these issues [9]. However, this problem was finally solved in 2018 [6].…”

“…The multi-machine and -buffer problem was solved recently [6]. The first step is the creation of the transient matrix which is built up form constitutive matrices Pi(pi) (6). There can be three different types of constitutive matrices.…”

“…The first matrix, the last matrix and the matrices between the first and the last matrix. For each type, there is a set of four different boundary conditions, which defines the elements of these matrices [6]. The number of constitutive matrices is equal to the number of machines in the line.…”

“…These elements can be used to calculate the following parameters: PR -Production Rate, WIP -Work in Process, BL -Blockages and ST -Starvations. Formulas are listed in the paper [6].…”

“…For a long time, the problem could not be solved for an arbitrary number of machines and for the buffers with arbitrary capacity because of the complexity to define the transition matrix. The generalized transition matrix was formulated recently [6]. Methods for the evaluation, analysis, and control of the system's continuous random variables were developed by using the analytical approach [7].…”