Relations between process state probabilities describing functioning of an inventory system

Problems associated with construction of a mathematical model of a real-life inventory management system have been outlined. The model enables determination of the crucial factors allowing investigation of system efficiency. Relations between absolute probabilities of states, Qk, and jump probabilities qik are formulated for three different work conditions of the given system. These relations were derived assuming that production flow y(t) is Markov with limited number of states. Using an auxiliary process x(t) the momentary capacity of the inventory z(t) was determined. The limit and transition states of the inventory have also been investigated.