We study single-machine group green scheduling considering group setup time deterioration effects and job-processing time learning effects, where the setup time of a group is a general deterioration function on its starting setup time and the processing time of a job is a non-increasing function on its position. We focus on confirming the job schedule for each group and group schedule for minimizing the total weighted completion time. It is proved that this problem is NP-hard. According to the problem’s NP-hardness, we present some optimal properties (including lower and upper bounds) and then propose a branch-and-bound algorithm and two heuristic algorithms (including the modified Nawaz–Enscore–Ham algorithm and simulated annealing algorithm). Finally, numerical simulations are provided to indicate the effectiveness of these algorithms, which demonstrates that the branch-and-bound algorithm can solve random instances of 100 jobs and 14 groups within reasonable time and that simulated annealing is more accurate than the modified Nawaz–Enscore–Ham algorithm.

This work studies single-machine scheduling with general position-dependent deterioration, where job processing times are general non-decreasing functions dependent on their positions in a sequence. The goal is to find a job sequence such that makespan is minimized. The problem can be extended to deal with green scheduling environment where processing time increases due to additional carbon-reduction procedure. Under some optimal properties, we prove that the problem is solved by the largest processing time (denoted by LPT) first rule.

Green scheduling that aims to enhance efficiency by optimizing resource allocation and job sequencing concurrently has gained growing academic attention. To tackle such problems with the consideration of scheduling and resource allocation, this paper considers a single-machine group scheduling problem with common/slack due-date assignment and a controllable processing time. The objective is to decide the optimized schedule of the group/job sequence, resource allocation, and due-date assignment. To solve the generalized case, this paper proves several optimal properties and presents a branch-and-bound algorithm and heuristic algorithms. Numerical experiments show that the branch-and-bound algorithm is efficient and the heuristic algorithm developed based on the analytical properties outruns the tabu search.

In this paper, we study a single-machine green scheduling problem with learning effects and past-sequence-dependent delivery times. The problem can be properly applied to tackle green manufacturing where production and delivery time are variable and highly subject to process-reengineering. Our goal is to determine the optimal sequence such that total weighted completion time and maximum tardiness are minimized. For the general case, we provide the analysis procedure of lower bound, and also propose the heuristic and branch-and-bound algorithms. Furthermore, computational experiments are conducted to demonstrate the effectiveness of our algorithms.

In the pursuit of high-quality economic development, addressing the challenge of high pollution and carbon emissions has become a critical issue. The rapid advancement of digital technology offers novel opportunities and tools to effectively mitigate these challenges. This study examines how digital technology empowerment can enhance the effectiveness of low-carbon city pilot (LCCP) policies in mitigating high pollution and carbon emissions, thereby improving green economic efficiency (GEE), using data from 283 Chinese cities between 2006 and 2021. The method adopted is a DID framework tailored for settings with staggered treatment adoption. Our analysis focuses on the low-carbon city pilot initiative, examining its consequences and how it interacts with digital technology. The results indicate that (1) the LCCP policy significantly promotes green economic efficiency; (2) digital technology empowerment demonstrates a substantial positive moderating impact upon the policy outcome, thus considerably reinforcing low-emission pilot policies’ improvement effect on GEE; (3) there are regional variations in the policy effectiveness, with the eastern region showing the most pronounced improvement, followed by the central region, while the western region exhibits a relatively lower response. This study provides theoretical and empirical support for further integrating digital technology with low-carbon policies and advancing urban green and high-quality development.