Abstract
This paper deals with a single-machine resource allocation scheduling problem with learning effect and group technology. Under slack due-date assignment, our objective is to determine the optimal sequence of jobs and groups, optimal due-date assignment, and optimal resource allocation such that the weighted sum of earliness and tardiness penalties, common flow allowances, and resource consumption cost is minimized. For three special cases, it is proved that the problem can be solved in polynomial time. To solve the general case of problem, the heuristic, tabu search, and branch-and-bound algorithms are proposed.
Highlights
In the conventional scheduling models and problems, it is generally assumed that the job processing times are constants, but in practice, examples can be found to illustrate that the job processing times are not necessarily constants (Shabtay and Steiner [1], Biskup [2], and Azzouz et al [3])
For the linear and convex resource allocation models, they proved that problem of minimizing the weighted sum of makespan and total resource cost can be solved in polynomial time
We will consider the same model with Sun et al [6] and Lv et al [7], i.e., three popular features in the recent years: group technology, resource allocation, and learning effect. e contributions of this study are given as follows: (1) we study the SLK assignment single-machine group scheduling problem along with learning effect and convex resource allocation; (2) the optimal properties are provided for the total cost minimization; (3) we propose the heuristic, tabu search, and branch-and-bound algorithms to solve the problem
Summary
In the conventional scheduling models and problems, it is generally assumed that the job processing times are constants, but in practice, examples can be found to illustrate that the job processing times are not necessarily constants (Shabtay and Steiner [1], Biskup [2], and Azzouz et al [3]). Zhu et al [4] considered resource allocation single-machine scheduling problems with learning effects and group technology. We will consider the same model with Sun et al [6] and Lv et al [7], i.e., three popular features in the recent years: group technology, resource allocation, and learning effect. E contributions of this study are given as follows: (1) we study the SLK assignment single-machine group scheduling problem along with learning effect and convex resource allocation; (2) the optimal properties are provided for the total cost (including earliness, tardiness, common flow allowances, and resource consumption cost) minimization; (3) we propose the heuristic, tabu search, and branch-and-bound algorithms to solve the problem.
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