Optimization of rewards in single machine scheduling in the rewards-driven systems

The single machine scheduling problem aims at obtaining the best sequence for a set of jobs in a manufacturing system with a single machine. In this paper, we optimize rewards in single machine scheduling in rewards-driven systems such that total reward is maximized while the constraints contains of limitation in total rewards for earliness and learning, independent of earliness and learning and etc. are satisfied. In mentioned systems as for earliness and learning the bonus is awarded to operators, we consider only rewards in mentioned systems and it will not be penalized under any circumstances. Our objective is to optimize total rewards in mentioned system by taking the rewards in the form of quadratic for both learning and earliness. The recently-developed sequential quadratic programming (SQP), is used by solve the problem. Results show that SQP had satisfactory performance in terms of optimum solutions, number of iterations, infeasibility and optimality error. Finally, a sensitivity analysis is performed on the change rate of the objective function obtained based on the change rate of the “amount of earliness for jobs (Ei parameter)”.