Chaining set partitions with applications in manufacturing system configuration planning

Knowing the number of candidate configurations is the first and critical step in manufacturing system configuration planning because it determines the methods for subsequent optimisation tasks. However, counting the total number of candidate configurations is a challenging partitioning problem due to the multiple sets of work elements that are often chained by the overlapping elements between adjacent sets. Starting with simple partitioning scenarios, this paper presents a new mathematical treatment and derives the formulas for calculating the number of candidate system configurations, which can eventually lead to algorithms for system configuration selection, simulation and optimisation.