The space of solution alternatives in the optimal lotsizing problem for general assembly systems applying MRP theory

This current paper follows up the former paper by investigating the complexity defined as the number of possible feasible solutions (production plans) to compare. We therefore investigate how properties of external demand timing and properties of requirements (Bill-of-Materials) have consequences on the size of this solution space. Explicit expressions are developed for how the total number of feasible production plans depends on numbers of external demand events on different levels for, in particular, the two extreme cases of a serial system and a full system (the latter, in which items have requirements of all existing types of subordinate items). A formula is also suggested for general systems falling in between these two extremes. For the most complex full system, it is shown that the number of feasible plans will be the product of elements taken from Sylvester's sequence (an instance of doubly exponential sequences) raised to powers depending on numbers of external demand events.