Behaviour perception-based disruption models for the parallel machine capacitated lot-sizing and scheduling problem

Capacitated lot-sizing and scheduling problem under disruption environment is a frequently encountered problem in manufacturing industry. This paper focuses on dealing with the case that the disruption is caused by machine breakdowns. Such case frequently arises during the process of the execution of a planned schedule. As a result, a reschedule needs to be applied, and then the decision-maker naturally may compare the reschedule results with the original one. Rather than from the conventional cost-saving perspective, this paper makes comparison from the attitude or the human behaviour perception of decision-makers towards the deviation from the original schedule. A non-linear mixed integer programming model is constructed with the objective of minimising the negative deviation based on the Prospect Theory, a psychologically more accurate description of decision-making. The non-linear term introduced by the Prospect Theory is approximately linearised by a series of piecewise linear segments. Then, an MIP-based fix-and-optimise algorithm is proposed to solve the approximated MIP problem. In numerical experiments, the impacts of several key factors of the proposed model and algorithm are explored. Two adjustment policies are compared, and the trade-off between cost saving and minimisation of the human behaviour perception deviation of decision-makers is discussed as well.