A neural network algorithm for servicing jobs with sequential and parallel machines

We consider the $FJ||C_\mathrm{max}$ problem of optimal servicing with respect to performance for a given set of jobs by sequential and parallel machines. The problem $FJ||C_\mathrm{max}$ is a generalization of the classical $J||C_\mathrm{max}$ problem for the case when the servicing system has not only sequential but also parallel (identical) machines. We propose a two-stage algorithm for a heuristic solution of problem $FJ||C_\mathrm{max}$. On the first stage, we solve the problem $J||C_\mathrm{max}$, i.e., we assume that the servicing system does not have parallel machines. On the second stage, operations are distributed over parallel machines. On both stages of the algorithm, we use neural network decision making models. The efficiency of a neural network algorithm for the problem $J||C_\mathrm{max}$ and problem $FJ||C_\mathrm{max}$ was evaluated on 20 test examples obtained from 20 known $J||C_\mathrm{max}$ problems by including into the servicing system a random number of copies of sequential machines.