Minimizing the number of tardy jobs with controllable processing times

This research basically extends the boundaries of the minimization of the number of tardy jobs (N_T) problem to where processing times are controllable by allocating a common, continuous, and nonrenewable resource. Most of the research on scheduling with controllable resource-dependent processing times assumed either a linear resource consumption function, that does not obey the law of diminishing returns or a specific convex consumption function, that applies only to a limited number of problems. We, on the other hand, assume a general consumption function, which guarantees a very robust solution that can be applied for a very wide range of problems and is appropriate for real life situations. We established the computational complexity for the N_T problem with controllable resource dependent processing times, proving it to be NP-hard. We present a polynomial algorithm to solve a special case of that problem, where all jobs are identical. We also suggest and compare four different heuristic algorithms to solve this problem.