Algebraic solution of a problem of optimal project scheduling in project management

A problem of optimal scheduling is considered for a project that consists certain set works to be performed under given constraints on the times start and finish works. As optimality criterion scheduling, maximum deviation time taken minimized. Such problems arise in management when it required, according technological, organizational, economic or other reasons, provide, wherever possible, simultaneous all The consideration formulated as constrained minimax optimization then solved using methods tropical (idempotent) mathematics which deals with theory applications semirings idempotent addition. First, investigated defined terms general semifield (an semiring invertible multiplication), complete analytical solution derived. result obtained applied find direct compact vector form ready further analysis solutions straightforward computations. an illustration, numerical example solving four