Abstract
This paper deals with teamwork scheduling problem in available time windows. This problem has been posed by combining the three constraints are the jobs can split into some sub-jobs which should not be less than a threshold called splitmin, the jobs are only assigned into available time windows and the jobs can be assigned into many people in the organization. Since then the four properties of this problem considered are everyone handles any jobs; a job can be handled by some person at the same time; jobs can be broken down into some sub-jobs; the size of the job/sub-job should not be less than splitmin. The goal aims to determine a feasible schedule that minimizes makespan. And a numerical example is presented to demonstrate the essential constraint with given input data to well define this scheduling problem. Besides the authors proposed a mathematical model to determine the optimal solution by using solvers to solve it and some simple heuristics with computing time less than one second to find the good solutions such as Assignment approach, SPT/LPT rules. All experiments were evaluated on two criteria are the maximum completion time for all jobs and runtime in seconds to determine the solution. These experiments were conducted by the comparison of the lower bound, the exact method based on using CPLEX solver to solve the MILP model, and proposed heuristics. The experimental results show it is very time consuming to determine the optimal solution by CPLEX solver, while the solution found by heuristic algorithms is only good enough.
Highlights
ContextPeople nowadays face a lot of pressure from life such as family, work, affection, etc., a lot of problems have to be solved in a proper and reasonable way
The teamwork scheduling problem in available time windows has been posed by combining the three constraints are the jobs can split into some sub-jobs which should not be less than splitmin, the jobs are only assigned into available time windows and the jobs can be assigned into many person in the organization
In this paper we considered the teamwork scheduling problem with availability time windows, splittable jobs and min-split constraint so as to minimize the makespan
Summary
ContextPeople nowadays face a lot of pressure from life such as family, work, affection, etc., a lot of problems have to be solved in a proper and reasonable way. As a pioneering result among [1,2,3], Min and Cheng 2 considered a cheduling resumable simple linear deteriorating jobs on a single machine with an availability constraint to minimize makespan The authors showed this problem is equivalent to a binary integer programming problem and proved it is NP-hard in the ordinary sense, and show there exists an FPTAS for it by applied the technique of Woeginger. The authors proposed new heuristics based on a multiplicative piecewise metric as an approximation of the slope of job value deterioration Combining both of these constraints together creates an interesting NP-Hard problem that was published at Nguyen et al 15.
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