An approach for modeling a new single machine scheduling problem with deteriorating and learning effects

• Presenting a non-linear mathematical model adapting the ability of operators for a single scheduling problem.
• Applying a continuous approach to calculate the deteriorating and learning effects.
• Using a multi-stage linearization procedure to convert non-linear into linear terms in the presented model.
• Utilizing an ACO-based hybrid ICA–GA to cope with complexity of the developed model.

This paper presents a new approach to model a mixed-integer mathematical programming for a single machine scheduling problem with deteriorating and learning effects. Neglecting the effect of performing a job on its own processing time is mentioned as a deficiency in the literature of industrial scheduling. At first, self-influential factors are defined and then equations are presented to utilize these new factors. GAMS IDE/CPLEX software is used to validate the represented model by solving small to medium-sized sample problems, in which the associate results are compared with a hybrid meta-heuristic algorithm based on Ant Colony Optimization (ACO), Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). The vitality of considering and modeling the effect of learning and deteriorating made by a job, on its own processing time is tested for several sample problems. Then a significant improvement is observed by comparing the results acquired by neglecting the self-influential factors with the results based on considering them. Finally, the computational results are analyzed and the conclusion is given.

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