Two-stage Stochastic Programming for Parallel Machine Multitasking to Minimize the Weighted Sum of Tardiness and Earliness

Multitasking scheduling is essential for decision making in many academic disciplines, including operations management, computer science, and information systems. In multitasking settings, each waiting job interrupts the currently in-processing job, causing an interruption time and switching time. It is difficult to make production planning under the multitasking settings, especially when considering uncertainty. However, most existing works about the problem focus on the deterministic environment, which is unpractical in actual life. In this paper, we investigate a multitasking scheduling problem on parallel machines. Moreover, uncertain processing times, which may be caused by multi-skilled workers, different machines and so on, are taken into account. The objective is to minimize the weighted sum of the earliness and tardiness. A two-stage stochastic programming formulation based on scenarios is developed. The first stage is to determine the operating machine for each job, and the processing sequence of jobs is made in the second stage. Sample average approximation (SAA) is adopted to solve the model. Finally, computational experiments are conducted and we give the impacts by sensitivity analyses.