Multi-machine scheduling with general position-based deterioration to minimize total load revisited

•We propose a more general job processing time model for multi-machine scheduling.•We propose polynomial algorithms to solve the considered scheduling problems.•An effective polynomial algorithm is proposed to solve a special case.

In this paper, we investigate multi-machine scheduling problems with general position-dependent effects where the actual processing time functions of jobs are not only associated with the job's position in the sequence but also associated with the machine number and the job number. All the processing time functions of jobs are not restricted to any specific form. The objective is to minimize the total load on machines. Analytical results show that all the considered multi-machine scheduling problems can be optimally solved in polynomial time.