On the optimal input allocation of discrete-event systems with dynamic input sequence

We study in this paper an optimal input allocation problem for a class of discrete-event systems with dynamic input sequence (DESDIS). In this case, the input space is defined by a finite sequence whose members will be removed from the sequence in the next event if they are used for the current event control input. Correspondingly, the sequence can be replenished with new members at every discrete-event time. The allocation problem for such systems describes many scheduling and allocation problems in logistics and manufacturing systems and leads to a combinatorial optimization problem. We show that for a linear DESDIS given by a Markov chain and for a particular cost function given by the sum of its state trajectories, the allocation problem is solved by re-ordering the input sequence at any given event time based on the potential contribution of the members in the current sequence to the present state of the system. In particular, the control input can be obtained by the minimization/maximization of the present input sequence only.