Research on Hospital Human Resource Allocation and Scheduling Based on Multi-objective Optimization Algorithm

Nowadays, China’s social economy is realizing comprehensive development, the new medical system reform policy is orderly promoted, the social security system has also made great progress, the people’s health level and health consciousness have been greatly improved [1-2]. In China, the concept of development of public hospitals has also changed, the development mode began to change from pure scale expansion to focus on quality and efficiency, the hospital’s mode of operation from the rough management to the direction of fine management, at the same time, the allocation of resources from the emphasis on the material elements of the change to pay more attention to the human resources and technology elements [3-6]. Public hospitals are not only health institutions that provide high-quality and efficient medical and health services for the people, but also an important force for the country to prevent and resolve major epidemics and face unexpected public health risks, and a basic guarantee that provides strong support for the construction of a healthy China [7-8].

At present, China’s health care service system mainly has three types of institutions, the main institution of China’s health care service system is public hospitals, public hospitals in the entire public health service system, occupies a vital role, public hospitals to protect the people’s life safety and health, improve the fairness and accessibility of China’s basic health care services, at the same time, in the prevention and control of major epidemics and to solve the sudden public health risks and other aspects play a major role [9-12].

In recent years, with the deepening of China’s healthcare system reform and the promotion of high-quality development of public hospitals, China’s healthcare has made great progress, and at the same time, new requirements and challenges have been put forward for human resource allocation in public hospitals [13-15]. The level of human resource allocation will directly affect the quality and level of medical services in public hospitals, the standardization of medical behaviors, and the strategic development planning of hospitals, etc. In the new era and market environment, public hospitals should think about how to improve the comprehensive level and competitiveness of hospitals and achieve the healthy and sustainable development of hospitals by rationally optimizing the allocation of human resources [16-19].

Human resources is an important strategic asset of an organization, is the hospital in the competitive development of the primary resources, how to give full play to the advantages of human resources, better serve the public hospitals own image shaping and overall competitiveness, in health care services play an important role in the support of the force, human resource allocation is particularly critical [20-22]. Public hospitals should further optimize the basic content of human resource allocation from the human resources preparation and configuration, positions and configuration, departments and configuration, personnel and configuration, titles and configuration, personal promotion routes and configuration, etc., and gradually give full play to the role of human resource allocation through continuous enhancement of the core basic content, endogenous a force, and continue to enhance the level of medical services in public hospitals from the best to ensure the benign development of medical and health care [23-26].

In the study of hospital human resource scheduling, hospital human resource scheduling is mainly divided into traditional methods and modern information technology methods, the traditional methods are as follows, Apornak, A explained the importance of rational allocation of human resources for the emergency department services, and combined with the sample formula to obtain the nursing services of the department as well as the percentage of patients receiving services, the time period of the indexes confirm the optimal allocation of human resources to the emergency department [27]. Yang, Y et al. empirically analyzed the quantitative relationship between daily nursing work hours (DNW) and nursing human resources as affected by the case mix index (CMI) and used this as a basis to provide a reference for human resource allocation [28].

And the information technology methods that use information technology intelligent algorithms for modeling and analysis are as follows, Bodina, A et al. built a set of key research and teaching hospital assessment system to achieve the assessment of hospital resource allocation criteria, the assessment system considers a number of dimensions, such as strategic, organizational, managerial, economic, research and quality, which can be effective in providing the section of objective reference decision-making on the allocation of resources [29]. Yousefi, M et al. conceived a set of simulation optimization strategies for the emergency department with meta-model as the core logic and validated the feasibility through empirical analysis and evaluation, which effectively optimized the allocation of human resources in the hospital [30]. Hafezalkotob, A et al. envisioned a linear robust formula to observe the collaborative behavior between medical centers during post-disaster care, confirming the existence of a cooperative game theory of human resource allocation [31]. Jiao, H et al. proposed a human resource allocation model based on the learning rate adaptive algorithm, and in the model simulation and evaluation experiments, it was found that the model improved the efficiency of human resource allocation in hospitals to a certain extent, and reduced the losses caused by unscientific allocation of human resources [32]. Chen, P. S et al. designed a two-stage strategy containing hra1 (human resource allocation based on hospital size), HRA2 (human resource allocation based on average distribution) and HRA3 (human resource allocation based on the degree of punishment) and an improved particle swarm optimization algorithm to analyze the priority of human resource scheduling in hospitals under various scenarios, which effectively solves the problem of hierarchical allocation and scheduling in hospitals [33]. All of the above studies have promoted the optimization of hospital human resource scheduling and allocation, and the depth of research from the perspective of cost-effectiveness is still insufficient, so it is very necessary to pay attention to the advanced and suitable multi-objective optimization algorithms in the hospital human resource scheduling academic research.

The objective of this paper is to study the problem of human resource allocation and scheduling in hospitals by introducing algorithms to find a more optimal solution for the problem. Firstly, the theory of human resource allocation for health is discussed to highlight its importance. Then, modeling and algorithm optimization are carried out based on the actual human resource problem in the hospital. Furthermore, based on particle swarm and 0-1 planning improvement algorithm, the advantages of the 0-1MOPSO algorithm model in multi-objective decision-making of staff deployment are established and analyzed. And take Hospital Y as an example to deeply analyze the situation and problems related to its human resource allocation. Through an experimental comparison between the traditional PSO algorithm and the non-dominated solution of the 0-1MOPSO algorithm, a lower-cost and more efficient decision-making solution has been found for the multi-project staff deployment in Y hospital.

2

Health human resources allocation theory

Human resources in health care usually refers to the general term for people who have been trained in health professional and technical knowledge and relevant practical skills, who are engaged in health care services and related work, and who have made certain contributions to the development of health care. Health human resources is also a kind of human resources, also covers both the quantity and quality of human resources. Only here is it a branch of human resources that belongs to the healthcare system or organization. Therefore, the basic framework of human resources is equally applicable to health human resources, except that the characteristics of the health profession are emphasized. The category of contributing to health care is all the staff of the hospital, all of which are an important part of the human resources of the hospital.

The allocation of public health human resources is under the control of the national health system, and its main duty is to serve the public interest, with public health public welfare, and the purpose is to improve the health of the whole nation and the quality of life of the people.

Configuration of human resources in hospitals refers to the rational arrangement of human resources in hospitals through scientific ways and means, so as to enable individual employees to explore their maximum potential and make the whole system operate efficiently. Health human resource allocation is manifested in the selection, hiring, and assessment of healthcare personnel in hospitals, practicing and arranging for induction. First of all, in the selection process to actively extract the human resources in line with the needs of hospital development, the personnel will be arranged in the right position, to play its maximum potential, so that its personal development and the entire hospital organization organic combination, maximize the productivity of human resources, show their talents, for the hospital and society to provide more benefits. As far as contemporary hospitals are concerned, in addition to public hospitals, hospitals of various organizational forms are constantly emerging and competing fiercely, but no matter how severe the competitive situation is, the ultimate hospital development is ultimately driven by human resources with professional and technical levels. The competition in the market is also the competition of talents in the end, the health industry is no exception.

Characteristics of health human resources: First, give full play to the subjective initiative of health human resources, you can produce other health resources mechanical plus and can not reach the effectiveness of the work; Second, it is not storage or temporary preparation can be obtained, the need to be in accordance with certain policy requirements, in advance, good planning, a clear direction of cultivation, the number, specifications.

Uneven matching or irrational use of health human resources can seriously impede the development of medical and health care.

3

Modeling and optimization of human resources issues

Health human resource allocation problems affect the management and operational efficiency of hospitals, this part describes the concepts related to health human resource allocation, models the existence of human resource problems, and provides new ideas for solving the multi-project staffing problems in hospitals based on the 0-1 MOPSO model algorithm.

3.1

Modeling of human resources issues

In order to model the previous human resource problem as a constraint satisfaction problem, all problem components are converted to the form <variable, domain, constraint>. Modeling can be done in several ways, and a variable-based model is proposed in the paper that defines the problem variable $X_{i}^{p}$ as the time slot p of individual i, e.g., $X_{i}^{p} = s_{j}$ denotes the assignment of individual i to a service that is s_j in period p. The main reason for defining this variable is that the solution for human resource allocation must be a complete assignment of all individuals over the entire period.

3.1.1

Integrity constraints

Needs to be satisfied for any individual in the set of human resources: (1) $\sum_{| P e r i o d s |}^{p = 1} a s s i g n (X_{i}^{p}) = | P e r i o d s |$

Let domain $D = {s_{1}, s_{2}, \dots, s_{n}}$ , the set of n allocation units in the human resource allocation unit (UH), be the domain where all constraints satisfy problem variable $X_{i}^{p}$ . $X_{i}^{p} = s_{j}$ denotes that individuals i are affected by time phases p during the service cycle s_j.

3.1.2

Constraints

The problem has two types of constraints: the first type expresses constraints related to the individual for determining the relationship between the individual and its own cycle; the second describes the relationship between the individual and the service it is in.

In order to express the above constraints rationally, the paper considers the number of fixed obligatory services provided to all individuals in the list of mandatory services of the HR ensemble $m (m \in [1, | O S |])$ , which should satisfy the following equation for any HR individual: (2) $\sum_{| P e r i o d s |}^{p = 1} i \sin (X_{i}^{p}, O S) = m$

In addition, the model still needs to satisfy the basic constraints: each individual has the basic service s_i for a given time period p, and the assignment of individual p + 1 to service s_i in the next period. For any one of the basic services $F S = 〈 s_{1}, s_{2} 〉$ , any time gap $p \in [1, | P e r i o d s |]$ with any human resource individual needs to satisfy the following equation: (3) $X_{i}^{p} = s_{1} \Leftrightarrow X_{i}^{p + 1} = s_{2}$

For any individual in the final stage of resource allocation, the constraints shall satisfy the following equation: (4) $X_{i}^{l a s t_p e r i o d} \neq s_{1}$

In the global constraint, each service capacity cannot exceed the constraint because of the planning capacity limit. That is, for any s ∈ services as well as any $p \in [1, | P e r i o d s |]$ , the following constraints should be satisfied: (5) $\sum_{| s t u d e n t s |}^{i = 1} (X_{i}^{p} = s) \leq c a p a c i t y (s)$

3.1.3

Optimization Objective Modeling

Service occupancy is of great importance for the quality of the solution. Therefore for each service i, define O_i as the occupancy, C_i as its capacity, and E_i as the exceeded value: (6) $E_{i} = O_{i} - C_{i}$

The above equation needs to satisfy E_i ≤ 0, i.e., the capacity of i is to be maintained; otherwise, the service will be overloaded. Subsequent operations are intended to ensure that the service capacity is maintained or minimally destroyed as much as possible. Thus for any service i, within any cycle p, the global constraint will be replaced by the objective function $M i n i m i z e (E_{i}^{p})$ .

3.2

Multi-objective decision-making for staffing based on 0-1 MOPSO

3.2.1

Algorithm Improvement Based on Particle Swarm and 0-1 Planning

The main factors affecting particle motion are individual optimal pBest and global optimal gBest. In single-objective optimization, both individual optimal and global optimal are determined by a single objective function, therefore, when solving multi-objective functions, it can be similarly considered that multiple objective functions can be used to determine pBest and gBest together. From the perspective of space vectors, that is, the particles do not move along the direction of one function optimization, but along the direction of multiple function optimization vectors so that the multiple functions do not become larger, and reach the non-inferior optimal objective domain after many iterations. Therefore, the traditional PSO can be improved according to the above idea, so that it can be adapted to the solution of multi-objective decision-making problems. Before each iteration, the global optimum of each particle with respect to each objective function is calculated gBest[s]. The individual optimums of m particles with respect to R objective functions are also calculated $p B e s [t, r]$ and $s \in [1, R] \in s [1]$ . When updating the velocity of each particle, the average value of each gBest[s] is used as the global optimum gBest, and the individual optimum of a single particle is determined by calculating the distance between pBest[r, s] and gBest[s]. In this way, by adjusting the values of the global and individual optimums, the particles are avoided to gather towards the optimum value of one objective function only, and the conversion process from PSO to MOPSO is realized.

The above modification makes the particle swarm algorithm can be used to compute the multi-objective decision-making problem, but the staff deployment problem proposed in this paper is a 0-1 planning problem, each employee must and can only undertake one task. The above MOPSO algorithm uses two objective functions to jointly guide the movement of particles in the process of particle evolution, it may occur that the deployment value of a particle is greater than 1 or deployed to work on two projects at the same time, which is beyond the scope of the solution, so the above algorithm is still not suitable for solving the 0-1 planning problem. From the commonality of particle swarm iteration and 0-1 planning, if a particle’s vector of a certain dimension is the non-inferior optimal solution of two objective functions at the same time, then in the next iteration, in order to ensure that the value of the objective function does not change the difference, at least this dimension should be kept unchanged. In project management, if assigning an employee to work in a project department is simultaneously locally optimal with respect to both the cost function and the benefit function, then the employee should be temporarily saved to work in that project department until some function becomes worse and then adjusted. If the employee is not assigned a job, then a job is randomly assigned. Based on the above idea, the crossover operation of a particle relative to the optimal solution of two objective functions can be defined as: (7) $C r o s s (p, q) = p \times q$

That is, the result of the crossover operation is 1 only if p, q is 1 at the same time, otherwise it is 0. If p, q is a matrix, the above operation is performed with the same position of the matrix. Also, when an employee is idle, a job is randomly assigned to that employee. By using the above improvements in the MOPSO algorithm, the problem of crossing the boundaries during particle updating can be solved and the solution is guaranteed to be a number between 0 and 1.

3.2.2

Algorithm for the 0-1 MOPSO model to address multi-project staff redeployment

Based on the above algorithmic improvement ideas, this paper constructs a 0-1MOPSO model for solving the multi-objective decision-making of staff deployment, now the direction of the two objective functions are unified, and the two ends of the same time add the negative sign transformed into a minimum value: (8) $\min (- \sum_{i = 1}^{n} \sum_{j = 1}^{m} L (x_{i j}))$

Recompose the multi-objective decision-making problem for multi-project staffing, where each solution to the problem corresponds to a two-dimensional vector, i.e., $X_{t} = {x_{i j}}$ . Follow the following steps to solve the problem: 1)

Particle swarm initialization. Set the size of the swarm as N, and use a randomized method to generate the position X_t, velocity V_t, and t = 1, 2, …, N of each particle.

2)

Calculate the fitness of each particle separately using the two objective functions as fitness functions: (9) $F i t_{1} [t] = \sum_{i = 1}^{n} \sum_{j = 1}^{m} C (x_{i j}), x_{i j} \in X_{t}, t = 1, 2, \dots, N$ (10) $F i t_{2} [t] = - \sum_{i = 1}^{n} \sum_{j = 1}^{m} L (x_{i j}), x_{i j} \in X_{t}, t = 1, 2, \dots, N$

Where Fit₁[t] indicates that the tnd particle uses the cost function as the fitness function, similarly the benefit function fitness can be calculated for each particle. 3)

Solve the individual optimal value of each particle relative to the two objective functions respectively. In the first iteration, the initial position of each particle is its individual optimal, to be followed by subsequent iterations, according to the following rules to find the individual optimal value: (11) $\begin{matrix} i f (F i t_{1} [t] < p B e s t [1, t]) \\ p B e s t [1, t] \leftarrow F i_{1} [t] \end{matrix}$

where pBest[1, t] ← Fit₁[t] means that the optimal position of a particle with respect to the cost function is mapped to an individual optimum, and similarly the individual optimum of each particle with respect to the benefit function can be found pBest[2, t]. 4)

Calculate the mean gBest and distance dgBest of the two global optima according to the following equation. (12) $g B e s t = C r o s s (g B e s t [1], g B e s t [2])$ (13) $d g B e s t = {g b e s t [1], g B e s t [2] |$

Where Equation (12) represents the intersection of the globally optimal solutions of two objective functions. Equation (13) represents the distance between the global optimal solutions of the two objective functions. 5)

Calculate the current distance between each particle relative to the optimal values of the two objective functions dgBest[t]: (14) $d p B e s t [t] = 1 p B e s t [1, t], p b e s t [2, t] |, t = 1, 2 \dots, N$

Calculate the individual optimal value pBest[t] for each particle with respect to the whole multi-objective planning problem according to Eq. (14), if $(d p B e s t [t] < d g B e s t)$ , i.e. then: (15) $p B e s t [t] = r a n d (p B e s t [1, t], p B e s t [2, t])$

Otherwise the optimal position of the particle is taken as: (16) $p B e s t [t] = C r o s s (p B e s t [1, t], p B e s t [2, t])$

The significance of the above steps is to get the gBest and pbest[t] that affect the particle’s speed. firstly, the individual and global optimization of each particle with respect to a single objective function are found out respectively, and then the individual and global optimization of the particle swarm with respect to the whole multi-objective decision-making are obtained by vector sum and random selection. 6)

Calculate the movement speed and next position of each particle, and the whole particle swarm is iteratively evolved: (17) $\begin{array}{rcl} V_{t} & = & ω \times V_{t} + c_{1} \times rand () \times (p B e s t [t] - X_{t}) \\ + c_{2} \times R a n d) \times (g B e s t - X_{t}) \end{array}$ (18) $X_{t} = X_{t} + V_{t}$

When the particle learns from the individual optimum and the global optimum, there may be a situation where a dimension value is not an integer, and if the dimension value is less than 0, it will be categorized as 0. If the dimension value is greater than 1, it will be categorized as 1. 7)

Repeat steps 2)-6) until the termination condition is satisfied.

3.2.3

Model analysis

In hospitals, the problem of imbalanced staff deployment among multiple projects is more common, and the multi-objective decision-making for multi-project staff deployment described above is a multi-objective decision-making model that takes into account both the minimization of the cost of the staff deployment scheme and the optimization of the benefits. To address this type of problem, the multi-project staff deployment problem is modeled by the improved 0-1 MOPSO, and in the processing of the multi-objective function, the vector sum of the individual optimal position of the particle swarm with respect to a single objective function and the optimal position of the group, and the stochastic selection are used to process, so that the cost function and the benefit function jointly provide guidance to the iterative process of the particle swarm. Meanwhile, the crossover operation is used to solve the transgression problem that may occur when the two objective functions jointly guide the particle iteration. The established model has some generality and is of practical significance for solving the multi-project staffing problem in hospitals.

4

Practice and research on human resource allocation in hospitals based on 0-1MOPSO

In conjunction with the previous section, modeling the multi-project staffing problem through the improved 0-1 MOPSO helps to solve the multi-project staffing problem in hospitals. In this section, based on the 0-1 MOPSO algorithmic model, we study the multi-project staffing problem in a specific hospital and analyze the data of the experimental results.

4.1

Analysis of human resource allocation in hospitals

4.1.1

Basic information on hospitals

Hospital Y is a comprehensive Grade 3A hospital directly under the Provincial Health and Family Planning Commission, which integrates medical treatment, prevention, health care, rehabilitation, first aid, teaching and scientific research, and is a large-scale general hospital with high medical, teaching and scientific research levels.

Y Hospital currently covers an area of 68,000m² in the medical area, with a building area of more than 160,000m², complete functions, reasonable processes, and a beautiful environment. In 2015, the new ward building was put into use, and the number of open beds increased to 1,890. The hospital has 63 clinical medical and technical departments, including Endocrine Metabolic Disease Department and Emergency Department, which are national key clinical specialties; Chinese medicine ophthalmology, which is a provincial key specialty in Chinese medicine; 7 provincial key clinical specialties; 8 provincial key disciplines in medical specialties; and 5 provincial key development disciplines.

At present, there are 6 doctoral supervisors and 69 master’s supervisors in Y Hospital; 185 chief physicians, professors and other senior professionals and technicians, many of whom hold important academic positions in domestic and provincial professional and technical related fields. There are 15 experts enjoying special allowance from the State Council, 8 provincial outstanding experts, and 13 young and middle-aged science and technology management experts with outstanding contributions in Hebei Province. Y Hospital is the training base for doctoral students in endocrine, cardiovascular, neurological and internal surgery, and general surgery, etc.; in the past three years, it has trained more than two hundred postgraduates of doctoral and master’s degree; it has undertaken a number of subjects of the national and provincial natural funds, and has won more than 40 awards above provincial level, including five prizes for the most important subjects. It has undertaken many national and provincial natural resource projects and won more than 40 awards at the provincial level, including 5 first-prize awards.

In recent years, Y Hospital has won a number of national and provincial commendations and awards.

4.1.2

Hospital human resource allocation planning objectives

In 2020, Y Hospital formulated the “14th Five-Year Plan” (2021-2025) development plan, and put forward the development goals during the “14th Five-Year Plan” period, that is, to improve the quality level of medicine, teaching and research as the core, strengthen the scientific, standardized and standardized management of the hospital, fully realize and consolidate the goals and standards of the tertiary hospital, accelerate the reform of the hospital management system, operation mechanism and technological innovation system, and strive to greatly improve the comprehensive capacity of the hospital during the “14th Five-Year Plan” period, and make the functional facilities more completeThe technical force is stronger, the talent echelon is more reasonable, the discipline construction is more complete, the medical ethics and medical style are better, and the hospital develops better and faster.

With the development vision of “creating a first-class provincial hospital in China”, Y Hospital puts forward the development strategy of “building the hospital on virtue, developing the hospital by science and education, and strengthening the hospital by talents”, and puts the management of human resources in a strategic position. During the “14th Five-Year Plan” period, the scale of the hospital was expanded, and in order to make the allocation of human resources meet the needs of the hospital’s development, the hospital put forward specific requirements for the allocation of human resources in the “14th Five-Year Plan”. 1)

Gradually increase the number of human resources allocation in the hospital to meet the needs of the hospital’s development; adjust the structure of the number of various types of positions in the hospital, and gradually meet the requirements for the construction of a tertiary hospital;

2)

Build a scientific age echelon, so that the hospital gradually formed a good atmosphere and pattern of old, middle-aged and young “passing on”;

3)

Stabilize the number and structure of hospital personnel, especially strengthen the management of non-staff personnel and reduce the departure rate.

4.1.3

Distribution of academic qualifications and titles

Table 1 demonstrates the proportion of academic degrees of personnel in Y hospital. Regarding the academic structure, as of the end of 2023, Y Public Hospital had 215 employees with doctoral degrees, with the higher number of physicians, followed by medical technology and support staff, which were 177 and 35 employees, respectively, and a small number of administrative and other technical staff, which were 2 and 1 employees, respectively. The hospital has 1,100 employees with master’s degrees, with the highest number of physicians, followed by medical technology and support staff, nursing staff, which are 958, 75, and 29, respectively, in addition to a certain percentage of administrative and technical staff, which are 20 and 18, respectively. In the whole team, there are 2,369 employees with bachelor’s degree, and there are also 530 people with low education. Among all the doctors in the hospital, 85.66% of some of them have a master’s degree or higher; among the medical technical and auxiliary staff, 26.89% have a master’s degree or higher; and in terms of other technical staff, 14.19% of the total number have a master’s degree or higher. Among administrative staff, 16.26% of the total number of staff have a master’s degree or higher.

Table 1.

Education ratio of Y hospital personnel

Category	Doctoral candidate	Postgraduate	Undergraduate course	Junior college and below
Medic	177	958	188	2
Medical technology and paramedical personnel	35	75	247	52
Nurse	0	29	1712	375
Other technical personnel	1	20	107	20
Administrative management	2	18	85	18
Work skills personnel	0	0	30	63
Total	215	1100	2369	530

From the statistical results in Table 1, physicians are a population with high academic qualifications, with 85.66% of the section having a master’s degree and higher, and 13.34% of the section having a PhD. In general, the staff of the hospital meets the requirements of the Ministry of Health in terms of educational structure, but there are shortcomings, and there is still a lack of highly educated administrators and nursing professionals.

Table 2 shows the title structure of the staff of Hospital Y. With regard to the structure of titles, according to the acquisition of national technical qualifications, public hospital Y has 1,072 senior titles (640 physicians, 292 nurses, 95 medical technicians and paramedical staff, 20 other technicians, and 25 administrators); 1,332 intermediate-level positions (441 physicians, 699 nursing, 118 medical technology and medical support staff, 36 other technicians, and 38 administrative staff); 1,810 junior titles (289 physicians, 1,129 nurses, 212 medical technicians and paramedical staff, 96 other technicians, and 84 administrators). In addition, among the hospital’s skilled workers, there is a relatively large number of level 2, level 3 and level 5 workers, 32, 28 and 24 respectively, while there are 4 and 5 level 1 and level 4 workers respectively.

Table 2.

Title structure of staff in Y hospital

Category	Senior title	Intermediate professional title	Junior title
Medic	620	424	281
Medical technology and paramedical personnel	85	114	210
Nurse	312	735	1069
Other technical personnel	20	32	96
Administrative management	21	28	74
Total	1058	1333	1730

From the enumerated data in Table 2, the title level of physicians is high, with intermediate title and above as high as 78.79%, among which the senior title is as high as 46.79% and the intermediate title is as high as 32%; the proportion of titles needs to be further improved, with the ratio of senior, intermediate and junior titles being 1:1.51:2.21, and according to the Principles of the Structural Ratio of the Positions of Professional and Technical Personnel in Medical Institutions, the ratio of the three-tier hospitals’ The ratio of senior, intermediate and junior staff should be 1:3:6. The ratio of junior and intermediate technicians is obviously low, and the introduction of young backbone forces needs to be further strengthened.

Table 3 demonstrates the results of the comparison between the staffing situation of Y hospital and the position setting situation filed by the Department of Human Resources and Social Affairs of Y province. In terms of staffing, the staffing structure of public hospital Y had a total of 4,214 active employees as of the end of 2023. Among them, there are 1,325 physicians, 2,116 nursing, 409 medical technology and medical auxiliary personnel (health technology, pharmacists, laboratory technicians, imaging technicians), 148 other technical personnel (engineers, archivists, statisticians, auditors, accountants), 93 service technicians, and 123 administrative personnel, excluding “double-shouldered” management personnel. Table 3 shows the hospital’s health technician staffing and the results of the filed comparisons. At present, the ratio of various types of positions in the hospital and the proportion of various types of positions approved by the Department of Human Resources and Social Security of Y Province, compared with 123 managers, accounting for only 2.9% of the total number of personnel, professional and technical posts 3998 people, accounting for 94.87%, 93 people in the workplace skills posts, accounting for only 2.26%, it can be seen that professional and technical posts as the main positions in the human resources ratios are also in the focus of the tendency of the Part of the current hospital open recruitment and talent introduction program also favors the recruitment of professional and technical personnel, work skills post due to the source of special and the national contraction of the workers’ establishment, the ratio of personnel will not grow with the overall total is also a general trend. And for the management post talent echelon of the degree of attention and recruitment and attraction of talent is far less than, only to stay in the maintenance of the hospital’s basic administrative affairs operation level, not with the expansion of the overall scale of the hospital and the steady growth of the hospital, which is also a reflection of the hospital’s leadership of human resources allocation concept is obsolete.

Table 3.

The staffing situation of Y hospital and the results of record comparison

	Total number of positions per unit	Category	Managerial position	Professional and technical post	Labor skills positions
Y province post allocation record	7680	Scale	5.1%	89.8%	5.1%
Y province post allocation record	7680	Quantity	388	6896	396
	Total number of positions per unit	Category	Managerial position	Professional and technical post	Labor skills positions
Actual post allocation in X hospital	4214	Scale	2.9%	94.87%	2.26%
Actual post allocation in X hospital	4214	Quantity	123	3998	93

4.2

Analysis of Hospital Multi-Program Staffing Practices and Outcomes

Combined with the analysis of hospital human resource allocation in 4.1, it is found that there are problems such as focusing on the allocation of professional and technical talents and neglecting the allocation of management positions in the actual position allocation of Hospital Y. The total number of positions is much less than the number of positions allocated by the Department of Human Resources and Social Affairs of the province. From the point of view of the actual situation of Hospital Y, it is particularly important to utilize the 0-1MOPSO algorithmic model for multi-objective decision-making of personnel allocation. At the same time, also in order to verify the effectiveness of the 0-1MOPSO algorithm model, the following is based on the human resource allocation of Hospital Y to carry out a multi-project staff deployment comparison experiment. The experimental example is described as follows: The problem is set up as assigning ten employees to a specific set of four jobs, and their expected efficiency and expected cost are given in Table 4 and Table 5. Analyzing the data in Table 4 and Table 5, it can be found that with the increase of employees, the expected efficiency and expected cost will also increase accordingly, in line with the general multi-project staff deployment law.

Table 4.

Expected costs c_ij

Number of jobs	Number of employees
Number of jobs	0	1	2	3	4	5	6	7	8	9	10
1	42	39	47	33	79	78	73	85	81	93	97
2	46	55	37	56	88	83	91	133	98	122	135
3	37	42	69	57	73	60	33	68	87	89	101
4	47	79	89	65	91	81	121	105	97	87	121

Table 5.

Expected efficiency e_ij

Number of jobs	Number of employees
Number of jobs	0	1	2	3	4	5	6	7	8	9	10
1	1	38	43	51	55	57	59	66	73	81	96
2	1	50	56	58	63	68	74	81	88	96	103
3	1	46	48	55	63	78	87	93	101	106	111
4	1	61	68	73	78	81	88	96	103	112	121

In order to reduce the total cost of multi-project staffing in Hospital Y and to improve the total efficiency of multi-project staffing, this paper continues to use the traditional PSO algorithm and the 0-1MOPSO algorithm to compute the experimental problem on the basis of the expected efficiency and the expected cost that have been obtained. In order to compare with the traditional PSO algorithm, 0-1MOPSO is calculated using the same number of cumulative iterations as its approximation, 1000 times.

Tables 6 and 7 show the non-dominated solutions obtained by solving the multi-program staffing problem of Hospital Y with the traditional PSO algorithm and 0-1MOPSO, respectively. Comparing the nondominated solutions of Table 6 and Table 7 through the scatter plot in Fig. 1, it is clear that 0-1MOPSO dominates most of the nondominated solutions of the traditional PSO algorithm and that the traditional PSO algorithm does not dominate any of the nondominated solutions of 0-1MOPSO. Accordingly, it is concluded that the 0-1MOPSO algorithm model is superior to the traditional PSO algorithm in solving the multi-project staffing problem, and it can provide a better configuration solution for the multi-project staffing problem in Hospital Y, reduce the total cost and improve the total efficiency.

Table 6.

Pareto solution of traditional PSO

Solution k	JX_1j	JX_2j	JX_3j	JX_4j	Total cost	Overall efficiency
1	4	3	2	3	211	224
2	1	0	7	3	194	201
3	2	3	4	0	178	180
4	4	2	5	1	165	170
5	2	2	7	1	215	237
6	2	1	7	0	194	205

Table 7.

Pareto solutions of 0-1MOPSO

Solution k	JX_1j	JX_2j	JX_3j	JX_4j	Total cost	Overall efficiency
1	2	3	7	2	183	242
2	4	3	3	4	201	228
3	3	3	4	0	160	187
4	2	0	5	2	186	198

5

Conclusion

Based on particle swarm and 0-1 planning improvement algorithm, this paper establishes 0-1MOPSO algorithm model, and finds a better multi-project staff deployment scheme for Hospital Y through specific experiments, which verifies that the 0-1MOPSO algorithm model is able to effectively reduce the cost of multi-project staff deployment in hospitals and improve its deployment efficiency. In the specific experiments, the total efficiency of the 0-1MOPSO algorithm model is between 187-242, which can dominate most of the traditional PSO algorithm, proving that the 0-1MOPSO algorithm is significantly better than the traditional PSO algorithm, and the optimization in this paper is effective.

In view of the advantages of the 0-1MOPSO algorithm model, this paper recommends the use of this algorithm model for decision-making assistance in human resource allocation and scheduling in hospitals, so that individual employees can explore their maximum potential and the whole system can operate efficiently.

Sprache:: Englisch

Zeitrahmen der Veröffentlichung:: 1 Hefte pro Jahr
Fachgebiete der Zeitschrift:: Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere

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Solution k	JX_1j	JX_2j	JX_3j	JX_4j	Total cost	Overall efficiency
1	4	3	2	3	211	224
2	1	0	7	3	194	201
3	2	3	4	0	178	180
4	4	2	5	1	165	170
5	2	2	7	1	215	237
6	2	1	7	0	194	205

Solution k	JX_1j	JX_2j	JX_3j	JX_4j	Total cost	Overall efficiency
1	4	3	2	3	211	224
2	1	0	7	3	194	201
3	2	3	4	0	178	180
4	4	2	5	1	165	170
5	2	2	7	1	215	237
6	2	1	7	0	194	205

Research on Hospital Human Resource Allocation and Scheduling Based on Multi-objective Optimization Algorithm

Zhuo Liu

Online veröffentlicht: 24. März 2025

Eingereicht: 01. Nov. 2024

Akzeptiert: 07. Feb. 2025

DOI: https://doi.org/10.2478/amns-2025-0783

SchlüsselwörterHuman resource allocation, Multi-objective optimization, 0-1MOPSO algorithm, Traditional PSO algorithm, Non-dominated solution

© 2025 Zhuo Liu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
Human resource allocation, Multi-objective optimization, 0-1MOPSO algorithm, Traditional PSO algorithm, Non-dominated solution

Solution k	JX_1j	JX_2j	JX_3j	JX_4j	Total cost	Overall efficiency
1	4	3	2	3	211	224
2	1	0	7	3	194	201
3	2	3	4	0	178	180
4	4	2	5	1	165	170
5	2	2	7	1	215	237
6	2	1	7	0	194	205