Single-machine scheduling with controllable processing times and learning effect

In this paper, we consider single-machine scheduling problem with controllable processing times and learning effect, i.e., processing times of jobs are controllable variables with linear costs and also are defined as functions of positions in a schedule. We concentrate on two goals separately, namely minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total compression cost and minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times, and total compression cost. The problem is modeled as an assignment problem and thus can be solved with the well-known algorithms.