The concepts of deteriorating jobs and learning effects have been individually studied in many scheduling problems. However, most studies considering the deteriorating and learning effects ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as ‘group technology’ in the literature. In this paper, a new group scheduling model with deteriorating and learning effects is proposed, where learning effect depends not only on job position, but also on the position of the corresponding job group; deteriorating effect depends on its starting time of the job. This paper shows that the makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, a polynomial optimal solution is also presented to minimise the maximum lateness problem under certain agreeable restriction.

The emergence of the new retail model of community group buying (CGB) has brought a significant impact on the traditional retail of community nanostores while community nanostores, as the leaders of the community, have the natural advantage of becoming the pick-up points of the CGB platform. Therefore, as the two core formats in the new community retail ecosystem, the CGB platform and community nanostore exhibit both competitive and complementary characteristics. Aiming at the community retail market composed of the CGB platform and the community nanostore, this study constructed a Hotelling game model to portray the competition and cooperation between these two channels and explored the impacts of different operational strategies on the equilibrium decisions and optimal profits of community retail market participants through comparative analysis. The research revealed that when retailers adopt the non-cooperation strategy, the community nanostore will occupy a larger market share, and the spillover effect between channels brought by the cooperation strategy is the main factor influencing retailers’ operation strategy. In addition, the type of pick-up point operated by the community nanostore will also affect the cooperation willingness of the CGB platform.

This paper considers single-machine rescheduling problems with agreeable job parameters under deterioration and disruption. Deteriorating jobs mean that the processing time of a job is defined by an increasing function of its starting time. Rescheduling means that, after a set of original jobs has already been scheduled, a new set of jobs arrives and creates a disruption. We consider four cases of minimization of the total tardiness costs with agreeable job parameters under a limit of the disruptions from the original job sequence. We propose polynomial-time algorithms or some dynamic programming algorithms under sequence disruption and time disruption.