Single machine scheduling considering time value of money

Under the background of Industry 4.0, this paper studies the single machine scheduling problem by taking into account the time value of money and tardiness penalty. We establish a mixed integer nonlinear programming model for the considered problem, and then convert the above model into a novel integer linear programming model. Regarding the factor of time value of money, we mainly aim to find an optimal or near optimal processing sequence of the jobs such that the total future value of profits is maximized. We employ CPLEX to output optimal solutions for small-size instances. For large-size instances, we propose the genetic algorithm to produce near optimal solutions.