Recursive decomposition/aggregation algorithms for performance metrics calculation in multi-level assembly/disassembly production systems with exponential reliability machines

Developing accurate and computationally efficient algorithms for system performance metrics calculation is critical to implementing effective control and optimization in manufacturing system operations. In this paper, we propose a recursive decomposition/aggregation-based method for calculating the performance metrics of assembly/disassembly systems with multiple merge/split operations and sub-assemblies. It is assumed that the machines follow the exponential reliability model and the buffers are of finite capacity. To achieve this, we first consider assembly systems with multiple component lines merging at a single assembly operation. By decomposing the system into a set of virtual serial lines, we derive an analytical procedure to approximate the starvation and blockage probabilities of the merge operation, which are used to recursively update the parameters of the virtual serial lines. Then, the performance metrics of the original assembly system are approximated based on the corresponding machines and buffers in these virtual serial lines. Next, we extend the algorithm to assembly/disassembly systems with multiple merge/split operations and sub-assemblies. This is accomplished by identifying the so-called assembly/disassembly units formed based on the virtual serial lines and applying the calculations derived earlier recursively. Simulation experiments are carried out to justify the convergence, computational efficiency, and approximation accuracy of the proposed algorithms. An industrial case study is presented to demonstrate the theoretical methods in practical applications.