Considering the lack of the research on the relationship between HR flexibility and scheduling effect, a resourcecompetency matrixbased method was proposed in order to reveal the quantitative relationship between them. Meanwhile, a job shop scheduling model with HR flexibility was established and the improved genetic algorithm was used to solve the model. A case analysis demonstrated significant impact of HR flexibility on the scheduling effect, which provided valuable guidance for building flexible manufacturing systems.
In the traditional production scheduling problems, it is usually assumed that the workpiece processing time is a constant and the permanent workers are always available. However, in the actual production activities, the processing time of workpiece is not fixed, which changes with shifts of processing workers. For instance, in a standardized operating environment, the varying technical proficiencies of skilled and new workers will result in differences in processing time. For the problems concerning the optimal scheduling of product design projects, Yingzi et al. [
The above representative research findings on scheduling problem under the constraint of personnel flexibility, respectively, indicated the preliminary modeling and relationship between human resources and task matching in the product design; personnel assignment problem under different process routes; and workertask matching model for production shops. However, these studies were limited to specific cases merely, which lack indepth exploration on the relationship between personnel flexibility and scheduling effect, particularly the analysis and research into the quantitative relationship between them. As the most important resource in production activities, the study of scheduling problem with personnel flexibility is of great practical significance. Thus, this paper studies the job shop scheduling problem with personnel flexibility with the improved genetic algorithm by referring to the existing research on personnel flexible job scheduling and analyzes the rules and the interaction between personnel flexibility and scheduling effect, striving to provide a theoretical basis for the optimal designing and implementation of job shop scheduling.
Suppose the number of workpieces is
Personnel flexibility refers to the corporate personnel’s ability to quickly and efficiently handle different tasks with uncertain changes during the production process, which emphasizes the versatility of employees. To study the impact of personnel flexibility on corporate productivity, the personnel flexibility is characterized by the personnelmachine relationship diagram. Assume that there are
Ushaped production line.
Personnelmachine relationship diagram.
Based on the personnelmachine relationship diagram, a matrix structure can be mapped, which is known as personnelmachine (PM) matrix. PM matrix is a matrix of
PM matrix can be obtained.
For PM matrix of any size, the flexibility of production line workers can be measured with the flexibility equation. The relevant calculation equation is shown
FI value ranges between (
For (
When the number of rows was greater than the number of columns,
When the PM matrix was square, the number of rows was equal to the number of columns. Assuming that all the diagonal elements were 1, the calculation of FI satisfied the following inequality:
When the number of columns was greater than the number of rows,
Conventional production scheduling problems seldom consider the impact of personnel. But, in the actual production, a machine may be operated by different workers, where the processing time varies with the workers’ skills and experience levels. Therefore, production scheduling problems which take personnel flexibility into account are more complex ones. Firstly, arranging suitable machines for a certain procedure is required in the processing of workpiece. Secondly, appropriate personnel needs to be selected from a set of workers who were capable of operating the machine. Only in this way can the processing and sequencing of products actually be completed.
In addition, production scheduling problems considering personnel flexibility also needed to satisfy the following constraints:
One machine can only process one workpiece at a time.
A workpiece can only be processed with a single machine at a time.
No processing procedure can be interrupted once started.
Different workpiece owns the same priority level.
There are no precedence constraints between procedures of different workpiece, while precedence constraints exist between procedures of the same workpiece.
All workpieces are processable at time zero.
Workers are available at any time as long as there is no conflict.
Genetic algorithm (GA) has fast convergence speed. When an excellent chromosome has a far higher fitness value than the average population in the computation, its probability of being selected increases in case of proportional selection, thereby leading to the “prematurity” phenomenon. The simulated annealing algorithm (SA) has the ability to jump out of local optima, but the principal shortcoming of simulated annealing (SA) is that it takes too much computer time. To solve this premature convergence and timeconsuming problem, the paper proposes the improved simulated annealing genetic algorithm (ISAGA), so as to improve the optima searching performance.
Efficient encoding mechanism can help reduce the complexity of computation and avoid repair mechanisms. In this paper, threelayer encoding was adopted. The first layer was procedurebased procedure sequence encoding, where the processing order of various procedures was determined. The second layer was machinebased machine allocation encoding, where the processing machine for each procedure was identified. The third layer was the encoding of workers who operate the machines. Such an encoding approach directly reflected the feasible allocation schemes during scheduling process, where feasible solutions could always be produced. A threeencoding example is illustrated in Figure
Threelayer encoding.
The purpose of crossover operation is to retain the good information in the parent chromosomes through information exchange between them. In this paper, chromosomes consisted of three parts. The specific crossover process can be represented as follows.
Procedure chromosomes: multiple workpieces were operated in each chromosome using workpiecebased POX crossover, which can well inherit the fine characteristics of parents.
The workpiece set
Workpieces included in Jobset1/Jobset2 in the parent chromosome P1/P2 were copied to progeny chromosome C1/C2, while maintaining their locations and sequences.
Workpieces not included in Jobset1/Jobset2 in the parent chromosome P1/P2 were copied to progeny chromosome C1/C2 according to their original sequences.
Crossover of machinery and personnel chromosomes was done by the same method as used for the procedure chromosomes, while ensuring the correspondence between them was unchanged during the crossover process.
In mutation operation, minor disturbances were made on chromosomes by randomly altering certain genes in them to increase population diversity.
For procedure sequencing section, three mutation methods, that is, exchange, insertion, and reverse sequencing, were adopted. Each time, one of these mutation methods was randomly selected for operation.
For processing machinery selection part, a procedure was randomly selected, and then the processing machine currently in the chromosome was replaced with a different machine selected from the set of machines available for the procedure.
For personnel chromosome selection section, a machine was randomly selected from machine codes, and then the current staff in the chromosome was replaced with a different worker who was selected from the set of personnel capable of operating the machine.
For job scheduling problem in a personnel flexibility environment, the flow of ISAGA was as follows.
Initialize the algorithm parameters (number of population
Randomly generate initial population. Calculate the fitness value of each individual and assign
The algorithm terminates when the maximum number of iterations
Implement genetic operation on the population and calculate the fitness values of new individuals. If the fitness value is better than the optimal individual of the previous generation, replace the parent with the progeny while updating
Implement ISAGA operation on the current optimal individual in the population, calculate the fitness value of newly generated individual, and compare the variation of fitness
Output the optimal solution obtained in this calculation.
In this paper, simulation experiment was performed on a computer with Intel Core 2 CPU/2.00 GHz/2.00 GB RAM using Matlab R2009b programming language. Algorithm parameters were set as follows: number of iterations 100; population size 50; crossover probability 0.8; mutation probability 0.1; annealing rate 0.98; initial acceptance probability
To verify the impact of different personnel flexibilities on scheduling effect and to analyze the differences in scheduling effect between three situations of PM matrix (number of rows > number of columns; square matrix; number of rows < number of columns) and thereby identify the prominent impact of key personnel on scheduling effect, discussion was made for three situations.
When the number of rows is greater than the number of columns, the number of workers is greater than the number of machines. Relevant processing information is shown in Table
Flexible machine processing information.
Workpiece  Procedure 








50  37  40  —  — 

—  30  —  20  20  

115  14  15  —  —  




31  —  35  —  32 

40  30  —  —  60  

—  —  40  —  57  




50  60  —  —  — 

—  40  —  30  50  

—  —  13  —  12  




29  —  27  29  — 

—  26  —  24  —  

10  —  13  —  —  


Worker  (1)  (2)  (3)  (4)  (5) 
Scheduling effects.
As can be seen from (
Figure
To accurately reflect the correlation between scheduling effect and personnel flexibility for the case of number of rows greater than the number of columns, this paper begins the study where each of six employees is only able to operate one machine till all employees could operate any machine. First rule of increasing personnel flexibility is to increase the number of operators in descending order of processing time. For instance, processing times of
Relationship curve between personnel flexibility and scheduling effect.
As can be seen from Figure
The number of rows equaled the number of columns. If only the first five workers are considered, a processing environment comprising five machines and five workers would be formed. For initial production environment, it is assumed that the diagonal element in PM matrix is 1, while the rest is zero. Principle of adding worker flexibility is the same as above. Increasing step size is 5, which meant that five operators are added at a time for one machine. Relationship curve obtained is shown in Figure
Relationship curve between personnel flexibility and scheduling effect.
As can be seen from Figure
When the number of rows is less than the number of columns, the number of personnel is less than the number of machines. Assuming that only the first four workers are considered of whom
Relationship curve between personnel flexibility and scheduling effect.
As can be seen from Figure
To comparatively analyze the performance of the proposed improved algorithm, three situations (
Comparison of computational structure between algorithms.
Situation  Algorithm  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9 

(1)  ISAGA  100  100  100  100  100  97  96  97 
GA  100  100  100  100  99  93  91  90  
SA  100  100  95  92  91  90  90  


(2)  ISAGA  100  100  100  100  100  
GA  100  100  100  95  95  
SA  100  100  100  94  95  


(3)  Algorithm  0.25  0.5  0.75  1  
ISAGA  100  100  100  100  
GA  100  100  100  100  
SA  100  100  100  100 
After the above analyses, the following conclusions can be drawn.
At a fixed number of equipment pieces, minimized maximum completion time decreases gradually with increasing personnel flexibility, which eventually stabilizes and no longer changes with changing personnel flexibility. This indicates that the unlimited increases in personnel do not necessarily bring high efficiency.
Comparative analysis of the three situations found that the minimized maximum completion time is superior for the situation when the number of personnel is greater than the number of devices to the other two situations at flexibility of 1. Moreover, the results are worst for the situation when the number of personnel is less than the number of devices. As shown in Figure
Simulation analysis demonstrates that the ISAGA has certain advantages in solving optimization problems of similar scale, with number of times converging to the optimal solution significantly superior to the other two algorithms. The improved algorithm can be used to solve largescale optimization problems.
The above findings have important implications for guiding the design and optimization of flexible production lines.
In this paper, personnel flexibility scheduling problem aimed at minimizing maximum completion time is studied; ISAGA for solving the problem is proposed to make a classified study based on different personnel flexibilities. The results demonstrate certain interaction between the personnel flexibility and the scheduling effect. These conclusions have important guiding value for the improvement of corporate productivity. In the next step, our team will study the quantitative proof method, hoping to get more general, regular knowledge to better guide the design and optimization of production system flexibility.
The authors declared no competing interests.
The authors are supported by Key Program of Hunan City University Grants (2015XJ02), China Postdoctoral Science Foundation Funded Project (2016M590929), and MOE (Ministry of Education in China) Project of Humanities and Social Sciences (13XJC630011).