Scheduling to Minimize Makespan on Identical Parallel Machines [ READ ]
Yousef German, Ibrahim Badi, Ahmed Bakir, Ali Shetwan
Reducing production time is an important factor for companies which their main objectives are to maximize profits and minimize costs. To achieve these objectives one must follow the scientific methods for scheduling production time. This paper studies the Makespan Minimization for Identical Parallel Machines. The problem involves an assignment number of jobs (N) to a set of identical parallel machines (m), when the objective is to minimize the makespan (maximum completion time of the last job on the last machine of the system). In the literature the problem is denoted by ( ). The objective of this study is to find the optimal schedule (solution) for identical parallel machines scheduling problems, by using hypothetical situation under defined assumptions and constraints. Algorithms are developed and used in this paper to represent and solve the problem. Integer Linear Programming model (ILP) is used to formulate the problem. Longest Processing Time algorithm (LPT) is used to find (generate) the initial solution, then the developed algorithm is used to improve the initial solution. The solution of the algorithms are coded in MATLAB. The results demonstrated that, the mathematical modeling and the algorithms are powerful tools and are more effective for these kinds of problems, compared with traditional methods.
Yousef German, Ibrahim Badi, Ahmed Bakir, Ali Shetwan
Reducing production time is an important factor for companies which their main objectives are to maximize profits and minimize costs. To achieve these objectives one must follow the scientific methods for scheduling production time. This paper studies the Makespan Minimization for Identical Parallel Machines. The problem involves an assignment number of jobs (N) to a set of identical parallel machines (m), when the objective is to minimize the makespan (maximum completion time of the last job on the last machine of the system). In the literature the problem is denoted by ( ). The objective of this study is to find the optimal schedule (solution) for identical parallel machines scheduling problems, by using hypothetical situation under defined assumptions and constraints. Algorithms are developed and used in this paper to represent and solve the problem. Integer Linear Programming model (ILP) is used to formulate the problem. Longest Processing Time algorithm (LPT) is used to find (generate) the initial solution, then the developed algorithm is used to improve the initial solution. The solution of the algorithms are coded in MATLAB. The results demonstrated that, the mathematical modeling and the algorithms are powerful tools and are more effective for these kinds of problems, compared with traditional methods.
