Abstract
BACKGROUND:
Medical staff scheduling problems are complex and involve numerous constraints.
OBJECTIVE:
This research uses the task-technology fit (TTF) model to measure the technology characteristics of information technology (IT) systems as a reference for constructing a prototype for a medical staff scheduling system to identify function requirements and design human interfaces.
METHOD:
After the evaluation of the proposed scheduling system, this research excludes compatibility from the 13 technology characteristics and adds two technology characteristics for consideration: customization and scalability.
RESULTS:
Based on the revised technology characteristics of the TTF model, this research develops flexible scheduling functions to satisfy daily manpower requirements and allow predetermined schedules and day-off reservations for a hospital’s radiological technologists. Characterized by flexibility, customization, and scalability, the system can accommodate several algorithms to generate a better schedule that satisfies hard and soft constraints. Furthermore, the scheduler can choose the required hard and soft constraints from all constraints. The prototype of the scheduling system will be easily extended to add or modify constraints in the case of requirement or regulation changes.
CONCLUSION:
The results of this study provide a prototype for system developers to design a customized staff scheduling system for each medical unit.
Keywords

Introduction
Problems with medical staff scheduling have been a subject of interest for researchers. Monthly schedules must consider the staff size throughout the scheduling period. The scheduling should comply with government and hospital regulations and accommodate staff preferences as much as possible [1, 2, 3, 4, 5]. Medical services are provided year-round, and medical staff are assigned to one of three 8-hour shifts in a 24-hour period. Thus, scheduling problems are complex and involve numerous constraints [6, 7, 8, 9, 10, 11, 12]. Moreover, government regulations related to the required hours of rest and consecutive working days are strict, making it nearly impossible to generate schedules manually.
Medical staff scheduling problems can be hard or soft. A hard constraint requires fulfillment. Violating a hard constraint, such as government regulations, indicates that a schedule problem cannot be resolved. Soft constraints, such as medical staff preferences, can be violated, albeit with corresponding penalties. Consequently, the objective function of overcoming medical staff scheduling challenges is to minimize the violation of soft constraints [2, 3].
Medical staff scheduling problems are NP-hard problems [13, 14]. Solving medical staff scheduling problems is difficult and time-consuming [15]. Since the 1980s, researchers have used mathematical programming software packages or meta-heuristic algorithms to help hospital schedulers generate medical staff schedules [5, 6, 13, 16, 17, 18, 19]. The scheduling staff at hospitals needs a customized system that can lighten the scheduler’s workload and increase medical staff’s satisfaction with their schedules [20]. For these reasons, problems with the scheduling of medical staff have received considerable attention from academic and clinical researchers.
Many studies have planned work scheduled for the present month based on current demand; others have considered the demand for medical staff demand by day and shift [13, 17, 21, 22, 23, 24]. According to Burke et al. [17], the problem of medical staff allocation deserves investigation because there is a range of decision-making problems, such as variations in monthly staff demand for a certain duty. However, scheduling research tends to rely on a fixed number of medical staff per month. Schedules prepared using this method cannot accommodate fluctuations in staff demand. Therefore, the monthly demand of each medical department warrants examination [19, 25].
In recent years, medical personnel have become more autonomous with regard to their monthly schedules. For example, medical staff are allowed to request to work or not on certain days. Thus, day-of-work and day-off requests are primary considerations in a medical staff scheduling system. Constructing a scheduling system that can be applied in clinical practice and allows flexible input for each scheduling condition is imperative for the scheduler [21, 24, 26].
In this study, the problem of scheduling medical staff is used to construct a scheduling prototype. The medical staff scheduling system developed in this research can perform medical staff scheduling according to government and hospital regulations. Moreover, the considerations involved in medical staff scheduling are integrated into the user interface design so that the scheduler can input the conditions of medical staff scheduling. This flexible design allows the scheduling system to be used by different hospitals or medical institutions.
The rest of this paper is organized as follows. Section 2 is the literature review. The research methodology is presented in Section 3. Section 4 describes and discusses the analysis. The prototype demonstration is presented in Section 5. Section 6 concludes the paper.
Literature review
Theories for evaluating information technology systems
Many academic theories focus on information technology (IT) systems and examine whether or not an IT system meets user demand and affects staff performance. The technology acceptance model (TAM) and task-technology fit (TTF) model are two theories that have been widely applied in the field of medical information systems [27]. Thus, this section focuses on the literature related to these two theories and investigates the problems they have attempted to resolve as well as the results.
TAM
The TAM, developed by Davis et al. [28] and based on the theory of reasoned action (TRA), explains the user acceptance of IT systems. The TAM comprises two dimensions, perceived usefulness (PU) and perceived ease of use (PEU) of the TRA, which affect users’ attitude and intention toward an IT.
Aggelidis and Chatzoglou [29] applied TAM to healthcare in Greece and examined the factors that affected personnel’s use of a hospital information system (HIS). Their findings indicated that the core constructs of TAMs – PU, PEU, social influence, and attitude – had a strong impact on behavioral intention of hospital personnel in Greece. They highlighted training, which had a strong but indirect positive effect on behavioral intention through mediators such as facilitating condition and ease of use, in contrast to many findings in the literature.
Holden and Karsh [30] surveyed 21 studies of TAM in the healthcare field. Although TAM did a decent job of predicting clinicians’ acceptance of IT in healthcare, the researchers stressed the need for standardization, testing of certain relationships, better reporting of data, and exploration of new variables and relationships that the current model had failed to consider. Moreover, they emphasized that, for future models of TAM in healthcare, it was critical to identify clinicians’ beliefs on using IT and contextualizing TAM to healthcare to better clarify the needs of health professionals.
Melas et al. [31] advanced the study of TAM by introducing a moderator variable, such as physicians’ specialty and healthcare professionals’ knowledge, on information and communication technology (ICT) and ICT feature demands as external variables. They sampled 604 medical staff, including 534 physicians in Greece – one of largest samples to date. Their results confirmed the effectiveness of TAM with previous studies.
Pai and Huang [32] integrated the external variables of system, service, and information qualities from the information system success model (ISSM) with the dimensions of PU, PEU, and intention to use from the TAM. They analyzed the enhanced model through the structural equation modeling and determined that those proposed factors had a positive impact on a user’s intention to use a health information system.
Nadri et al. [33] investigated the factors affecting the acceptance of a HIS by using the extended TAM (ETAM), in which subjective notions are integrated. The research results indicated that the HIS should be established according to each department’s procedures and target group. The results also indicated that the behavioral change of users of the HIS was an important factor influencing the system’s final function. Utilization could be predicted through this behavioral change.
Chen et al. [34] used the ETAM to analyze the popularity of social game apps. The researcher analyzed nine factors that affected the user acceptance of social game apps by examining responses on more than 300 questionnaires. The results revealed that PEU was a decisive factor affecting user acceptance, but PU was not, because the game players only wanted to have fun and were not concerned with the functions of the games.
Lin [35] investigated the satisfaction of registered professional nurses with a nursing information system from the perspectives of the TAM and ISSM. The data obtained through interviews with 531 registered professional nurses in Taiwan indicated that both PU and PEU affected their satisfaction with the system and information quality.
These studies indicate that the TAM is suitable for explaining or predicting the intention to use IT. The advantages of the TAM include its ability to simultaneously test several factors affecting acceptance and to analyze the features emphasized by the user. Although the PU of the TAM is composed of tasks, its disadvantage is the lack of task characteristics for constructing improved system models.
TTF model
The TTF model proposed by Goodhue and Thompson [36] explains the effect of the fit between task and technology on an organization. The theory states that the better the fit between the task characteristic and the technology characteristic, the stronger the effect of performance improvement, which affects user utilization.
Lepanto et al. [37] measured users’ perceived benefits from a picture archiving and communication system (PACS) upgraded at a university hospital. In this study, radiological technologists, subdivided by their utilization profiles, filled out a self-administered survey consisting of four measured variables: impact, utilization, TTF, and perceived net benefits. The results indicated significant variance among user subgroups. The analysis also confirmed the hypothesis that the TTF model predicted utilization and perceived net benefits while utilization did not predict perceived net benefits.
Yang et al. [38] proposed a modified TTF model to investigate the integration of Internet of Things (IoT) technology into the emergency response operations in the United Kingdom. In the modified TTF model, they replaced “task” with “information requirements” and “technology” with “IoT technology”. They also replaced “performance impacts” with “strategic value” as the IoT technology at that time was new to emergency operations. Their discoveries confirmed that IoT technology was appropriate for their identified information requirements; moreover, the technology offered the benefits of efficient cooperation, accurate situation awareness, and complete visibility of resources.
Chang et al. [39] investigated Taiwan’s long-term care information system (TLCIS) through the applications of the TTF model, system satisfaction, and post-acceptance continuance models. The findings showed that system quality, locatability of data, timeliness, ease of use, and system-user relationships were the primary factors that users considered when assessing whether TLCIS fulfilled their work and task needs.
Chen et al. [40] examined the information systems of three collaborating hospitals by using TTF technology characteristics. The transfer of radiology patients among these three hospitals for diagnosis and inspection involved the transmission of patient data. The inter-hospital information systems were identical but separate; thus, information might have been lost during transmission. The study analyzed the information system deficiency in the patient-referral process by using the TTF model, summarized the 12 technology characteristics proposed by Goodhue [41], and excluded the characteristics of compatibility, locatability, and assistance after discussion with professionals because medical staff could examine these characteristics through the inter-hospital information systems. The study suggested that the function of synchronization be added to the patient-referral information system because, although the information systems involved in the patient-referral process were separate, data could be shared. Thus, synchronization is indispensable in the patient-referral process. The data from the information systems of the three hospitals must be integrated.
Ali et al. [42] evaluated a newly deployed electronic patient portal matching patients’ capability in an academic hospital through heuristic usability evaluation of 23 patients based on a TTF model. The findings revealed that ability to complete tasks, perceived usability, and possible comments increased through the course of iterative development. Nevertheless, the users encountered difficulties when trying to complete certain tasks such as setting up accounts. Those problems were especially pronounced when patients did not have a clear understanding of those tasks.
O’Connor et al. [43] addressed the impact of mHealth – the medical/clinical application(s) of mobile devices used by hospital physicians – on perceived quality of care (PQoC). They empirically tested a conceptual model based on TTF, self-efficacy, and mHealth utilization on PQoC. The results showed that physicians’ PQoC was positively impacted by the level of mHealth utilization and TTF; the direct effect of the TTF model was twice as high as utilization. In terms of the TTF model, technology characteristics outweighed task characteristics.
Lin and Wang [44] proposed a research framework for studying the relationships between fit and system factors to encourage the continuous use of electronic learning systems. The TTF model was used to determine the key factors affecting the use of electronic learning systems due to its proven adaptability in blended learning instruction. Eight postgraduates received blended learning instruction for approximately 15 weeks and learned how to use electronic learning systems for interactions in class. The research revealed the benefits of using electronic learning systems for enhancing learning and improving college students’ academic performance. The research also proved that the TTF model affects learning systems.
Yu and Yu [45] studied the utilization of online learning systems by students in Taiwan by using the TTF model and theory of planned behavior (TPB). They investigated the utilization behavior of 870 students who had been using online learning systems for years. The results obtained through model construction indicated that the TTF model directly affected the utilization of online learning systems. The variables and the indirect effect of the attitude toward using the system can be explained using the TPB. The research indicated that users’ behaviors, beliefs, and attitudes should be considered in the development of online learning systems.
The TTF model is suitable for predicting user behavior and emphasizing the TTF model in IT as a key factor in system performance. According to the literature, the TTF model can be used to determine the key factors affecting user behavior and the technology characteristics required of IT. D’Ambra et al. [27] considered IT to be a tool for users to accomplish their tasks and, thus, saw task performance as an indicator of IT success.
Summary
Many algorithms have been developed for medical staff scheduling. However, the quality and speed of these algorithms vary from one problem set to another. This research did not involve the design of algorithms for solving medical staff scheduling problems. The medical staff scheduling system proposed in this study offers a flexible selection of algorithms (e.g., particle swarm optimization [PSO] and the bat algorithm [BA]) while maintaining system scalability.
In this research, the IT system was assessed by associating medical staff scheduling system functionalities with several routine tasks at the hospital. Medical staff scheduling involves considering the personnel demands for particular duties, day-of-work and day-off requests, medical staff’s preferences, and government and hospital regulations. Consequently, the required functions were integrated into the development stage to increase the probability of successful system introduction.
Although the TAM excellently explains the behavioral intention to use, its prediction regarding utilization is flawed [46]. Ngai et al. [46] indicated that attitude only marginally affected utilization while PU and PEU significantly affected utilization. These results differed from those of previous studies. The TTF model solves the constraint, which is viewed as the primary weakness of the TAM [47]. A drawback of the TAM is its lack of task focus [27]. Thus, the TAM cannot explain tasks such as the flexible setting of personnel demand or the day-of-work and day-off requests. The scheduling system prototype in this research was based on an investigation of medical staff scheduling tasks. Thus, the medical staff scheduling system based on the TTF model was adopted.
Research methodology
Constructing a medical staff scheduling system prototype using the TTF model
Goodhue [48] addressed the 13 technology characteristics of the TTF model as performance measures of IT systems. Goodhue described the content of these characteristics to examine whether the tasks performed by IT systems contained these characteristics and to measure the effect of IT systems on performance and utilization. The 13 technology characteristics are as follows:
Accuracy: The provided data are accurate. Currency: Sufficient quantity of information is available. Ease of use: The system is easy to use. Meaning: The meaning of the system data is easy to define. Compatibility: The data provided by the systems of two hospitals are easy to integrate, and the data from both sides are consistent. Presentation: The results are presented in a readable and helpful manner. Lack of confusion: The user knows how to operate the system under different conditions. Locatability: Identifying useful and easily locatable data is simple. Accessibility: Obtaining the required data or results is easy. Level of detail: The data provided are sufficiently detailed. Assistance: Obtaining assistance related to the data or system is easy. System reliability: The system must be stable and reliable. Flexibility: The content or data format can be easily altered, and the functions for fulfilling the ever-changing user demand can be easily extended.
Based on these technology characteristics provided by the TTF model for investigating IT systems, this research examined the tasks performed by the medical staff’s scheduling system prototype. Because the software developed in this study processes medical staff scheduling only on webpages using the Personal Homepage Program (PHP) Hypertext Preprocessor code and is not connected to any other system, compatibility is inapplicable in this research and is, thus, excluded from the discussion.
The scheduling rules of the developed medical staff scheduling system must consider restrictions such as hospital and government regulations, which vary among hospitals and among healthcare institutions. Therefore, this research suggests that two technology characteristics – customization and scalability – be added to the TTF technology characteristics. Customization is the ability to tailor medical staff scheduling rules to diverse hospitals or healthcare institutions. Customization is added because the prototype allows the scheduler to determine the scheduling constraints of an institution and to select the solution algorithm.
When customizing scheduling rules for diverse hospitals or healthcare institutions, there are more functions for selecting hard and soft constraints in the prototype. Consequently, this research includes scalability, which is the ability to increase the program functions for satisfying the diverse needs of medical staff scheduling without having to redesign the entire system.
Moreover, the factors requiring consideration during medical staff scheduling were determined before the functions were developed. The prototype was provided to hospital schedulers to test its functionality. After using the prototype, the schedulers provided feedback on the addition of scheduling rules and needs. New versions of the prototype can be produced through constant customization based on the feedback.
The effect of system performance was not examined in this prototype because a long period of time is required to verify this effect. Hence, only functionality was considered.
The medical staff scheduling system prototype was developed as follows:
Determine the requirements for system functions: Medical staff scheduling procedures must be analyzed, and the needs must be determined. For example, the number of personnel required for each duty and the number of available staff per day must be determined during staff scheduling. The functions of the medical staff scheduling system prototype can only be determined by understanding the actual demands. Develop the user interface: The information that requires consideration should be displayed on the user interface so that the scheduler can input information – namely, the year and month, medical staff size, daily staff size required for each duty, and the days of work and days off requested by the staff. Solution algorithms for the medical staff schedule must be checked, the algorithm termination condition must be set, and hard and soft constraints must be selected. Moreover, the interface is designed according to the technology characteristics provided by the TTF model. Develop system functions: System functions should be developed by focusing on the function-related requirements determined in Step 1, including introducing the solution algorithm and using the information input by the user as the rules for medical staff scheduling. For example, the user preprograms medical staff scheduling conditions after inputting the information. When developing medical staff scheduling system functions, the system must comply with the technology characteristics provided by the TTF model. Verify system functions: The information and conditions input by the user as well as the medical staff schedule generated through the computer system must be verified. The execution of the system functions should be ensured. The medical staff schedule should comply with the input year, month, medical staff size, and daily staff demand for each duty. The scheduler should test whether the day-of-work and day-off requests have been fulfilled and whether they violate any hard constraint. In this step, situation settings can be adopted to verify the reliability of the medical staff scheduling system prototype.
This section explains the functions established in the prototype by using the technology characteristics provided by the TTF model. Section 4.1 introduces the case hospital background and medical staff scheduling constraints. Section 4.2 presents the functions required for the scheduling system. Section 4.3 tests and verifies the prototype. In Section 4.4, the technology characteristics provided by the TTF model and two additional characteristics are verified using the prototype.
Case hospital background
The research is based in the emergency room of the radiology department of the case hospital. Sixteen radiological technologists were recruited. The activities performed in the radiology department are diagnosis and treatment. Diagnostic imaging requires X-ray machines, computed tomography scan, ultrasonic testing, and nuclear magnetic resonance imaging to analyze diseases within the body. In interventional radiology, precision instruments are used to assist medical staff in performing minimally invasive surgery.
A review of the medical staff scheduling literature indicates that the main hard constraints are daily staff demand, required staff size for each shift, and maximum permitted number of consecutive working days. In the emergency room of the radiology department of the case hospital, the staff work the day shift (8:00–16:00), the evening shift (16:00–24:00), or the night shift (0:00–8:00). The radiology department contains three sub-departments: X-ray (R), portable (P), and computed tomography (C).
In addition to following government regulations (regulations regarding working hours or working days stipulated in the Labor Standards Act), the case hospital has to plan schedules in compliance with its own regulations. Therefore, the radiological technologist scheduling problem is a medical staff scheduling problem. According to Chen and Zeng [3], the hard constraints in this research are:
Each day, each staff member is either on leave or working in only one sub-department. Every Sunday, the required staff size for the night shift in the P sub-department is two. Except in constraint (2), the required staff size per shift in each sub-department per day is one. Except in particular situations, the maximum number of consecutive days off for each staff member is four. No staff member can work seven consecutive days. No staff member working the night shift can work the day shift the next day. No staff member working the evening shift can work the day shift the next day. No staff member working the night shift can work the evening shift the next day.
In this research, the required staff size of hard constraints (2) and (3) was adjusted according to various testing scenarios, followed by examination and verification.
Flexible setting of the daily medical staff demand for a duty each month
The user interface covers the R, P, and C sub-departments of the radiology department. The daily medical staff demand of each shift in each sub-department for the seven days during the week must be input separately. For ease of use, the number of medical staff in each sub-department for each shift per day is preset as 1 in the medical staff scheduling system prototype. To change the number of medical staff, the scheduler simply enters the number in the text box. For example, the daily medical staff size required for the day shift in the R sub-department (R1) on Sunday is increased to 2.
As unanticipated issues frequently occur in medical staff allocation, the functionality allows for the immediate adjustment of medical staff scheduling information to modify the medical staff allocation. This function achieves the flexibility mentioned in the TTF model and can help the scheduler allocate medical staff under various conditions.
Medical staff’s requests for days of work and days off
Before planning the next month’s medical staff schedule, the hospital scheduler allows the medical staff to request days of work and days off. Therefore, this function is incorporated into the prototype. However, implicit restrictions exist in the hospital to prevent medical staff from selecting only preferred shifts. Although the functions for medical staff to request days of work and days off are available, the number of such requests per month is limited.
In the prototype, the number of day-of-work and day-off requests by the medical staff is preset to 2 for both. The related information is included in the medical staff scheduling by checking the functions of day-of-work and day-off requests. The function of day-of-work requests is performed by selecting the medical staff, number of days, and shifts whereas for day-off requests it is performed by selecting the medical staff and the period of consecutive days off. For example, staff 1 requests to work the C3 shift on the first day and staff 2 requests the 10
Requests of day shift and day-off by staff.
With regard to the function of day-off requests, medical staff might need to take many days off. Thus, the period of requested days off is viewed as a particular situation in the present scheduling system to avoid conflicts with the hard constraint of the following hospital regulation: “Except in particular situations, the maximum number of consecutive days off for each staff member is four.” Therefore, the inclusion of the day-off function based on this constraint would generate feasible schedules.
The prototype contains two metaheuristic algorithms: BA and PSO. The scheduler can select which algorithm to use. The prototype not only supports two metaheuristic algorithms but also allows for the addition of other algorithms in the future, which indicates its scalability.
The two common algorithm termination conditions are the maximum number of iterations and maximum execution time. For example, when solving medical staff scheduling problems using PSO with 10 particles, the termination condition is set as follows: the maximum number of iterations
Although the prototype contains two metaheuristic algorithms, more algorithms can be added (Fig. 2). The medical staff scheduling rules of each hospital involve numerous considerations, and each algorithm has unique advantages. Thus, the scalability of algorithms is a primary feature of the prototype.
Scalability of the developed scheduling system.
Based on the research of Chen and Zeng [3], this study considers hospital and government regulations as hard constraints and medical staff preferences as soft constraints. Because a hospital must comply with government regulations (e.g., “No staff member can work seven consecutive days,” “No staff working the night shift can work the day shift the next day,” “No staff working the evening shift can work the day shift the next day,” and “No staff working the night shift can work the evening shift the next day”), these regulations are preset as checked in the scheduling system (Fig. 3). The system reminds the scheduler that these rules cannot be violated.
Selections of hard constraints of the scheduling system.
If a hard constraint is not to be considered, it should not be checked. If the scheduler must consider other soft constraints, they should be checked. For example, if the scheduler wishes to add the soft constraints of “No staff working the day shift can work the evening shift the next day” and “No staff working the evening shift can work the night shift the next day,” they only need to check these two constraints (Fig. 4).
Selections of soft constraints of the scheduling system.
Hard and soft constraints can be activated or deactivated. If hospitals have to modify medical staff scheduling rules, they would not need to change to another scheduling system or rewrite the entire scheduling system. They only have to customize the checking of the appropriate hard and soft constraints. This customization not only fulfills the medical staff scheduling demands of various hospitals, but also enables the scheduling rules to be increased for the prototype in the future to satisfy additional demands regarding medical staff schedules. Consequently, the function of constraint selection is both customizable and scalable.
This research develops functions addressing medical staff scheduling procedures and considers how to generate medical staff schedules with readable and useful forms that medical staff can use. Thus, once the developed system generates the medical staff schedule (PHP program), the schedule is exported as an Excel spreadsheet to provide easy access for medical staff.
The medical staff schedule comprises information on the year, month, day, staff, and shift. All this information is necessary for medical staff to understand their schedules. Insignificant information is excluded. To provide useful information, a two-dimensional matrix composed of the medical staff and date is designed in this research; the shifts are added to the corresponding blanks. Hence, the medical staff can examine their daily schedule. Furthermore, the schedule is presented in a readable manner so the presentation characteristic mentioned in the TTF model is satisfied.
Shifts during the same period are marked in the same color in this research so that the medical staff can readily distinguish their shifts. The day shift is yellow, the evening shift is green, the night shift is blue, and days off are white. The shift information is divided into four color-based categories, so the medical staff can quickly locate the required information, which indicates its locatability. All codes indicating shift information in the schedule are significant. Table 1 presents shift information for the R, P, and C sub-departments. The code “1” represents the day shift (08:00–16:00), “2” represents the evening shift (16:00–24:00), and “3” represents the night shift (00:00–08:00). Therefore, R1 means that the staff member has to work the day shift in the X-ray department. The schedule codes convey the meaning characteristic mentioned in the TTF model.
Shift codes and corresponding shifts and departments
Shift codes and corresponding shifts and departments
The schedule presents the shift and sub-department of a staff member on a particular day. Moreover, it is possible to evaluate whether or not the schedule violates a hard constraint. If it does not violate any hard constraint, the schedule offers a feasible solution and is indicative of the accuracy of the prototype.
In this section, the steadiness of the prototype is verified by investigating whether the prototype can rapidly generate accurate schedules that meet medical staff’s needs in terms of variations in staff allocations, requests for days of work and days off, the algorithm used, and hard and soft constraints.
In this research, 10 situations set in September 2020 are randomly generated to solve medical staff scheduling problems. If the schedules are feasible, the prototype is sufficiently steady. The medical staff allocation is based on the research by Chen and Zeng [3]. The allocation considers possible situations that can arise in the case hospital. Of the 16 members of the medical staff, 9–10 are on duty each day. Thus, different conditions are set for the daily staff demands per shift for each sub-department, day-of-work and day-off requests, and solution algorithms. To test the prototype, all constraints are considered.
The scheduling system comprises two algorithms: BA and PSO. To test the stability of the system, the solutions of situations 1–5 are obtained using PSO with 10 particles, whereas those of situations 6–10 are obtained using BA with 10 bats. Regarding the daily medical staff allocation in each situation, the code “3” indicates that there is a staff member working for each shift in each sub-department; thus, nine staff (3 shifts multiplied by 3 sub-departments) are on duty on the considered day. The code “4R” indicates that the staff size of the night shift in the R sub-department is increased to 2 while those of the night shift in the other two sub-departments remain 1. The staff sizes of the day and evening shifts in the three sub-departments also remain 1. Therefore, 10 staff (3 day shifts, 3 evening shifts, and 4 night shifts) are on duty on the considered day. For the same shift, the situations 4P and 4C are similar. The medical staff’s day-of-work requests in each situation are set as 1 or 2 because 2 is the maximum number of such requests at one time. The medical staff’s day-off requests in each situation are set as 1 or 2 because the maximum number of such requests at one time is 2.
The prototype constructed in this research then obtains solutions for the 10 situations. The results indicate that all the solutions are feasible and correspond to the medical staff schedule. Thus, the prototype is steady. An examination of the system’s reliability indicates that the prototype is sufficiently stable and reliable.
Examination of the prototype using the TTF model
The medical staff scheduling system constructed in this research is developed according to 12 TTF technology characteristics and two additional technology characteristics. Thus, 14 technology characteristics are used to examine the prototype:
Accuracy: The schedule does not violate any hospital or government regulation. In other words, it fulfills all the hard constraints and appropriately meets the scheduling conditions set by the scheduler. Currency: The schedule provides information such as the month, staff, sub-department and shift. This information is essential, and the information quantity is sufficient. Ease of use: Dropdown menus are designed in the scheduling system. These menus only require checking the functions and presetting the number of medical staff. Thus, the scheduler’s operation procedures are simplified, and the use of the scheduling system is facilitated. Meaning: All codes displayed in the medical staff schedule are significant. For example, R, P, and C indicate the X-ray, portable, and computed tomography sub-departments, respectively. The codes “1,” “2,” and “3” represent the day, evening, and night shifts, respectively. For example, R1 refers to a day shift in the X-ray sub-department. Presentation: In the schedule, a two-dimensional matrix combines medical staff and dates. The shifts are filled in the corresponding blanks. Therefore, medical staff can easily understand the information. Lack of confusion: The user interface includes the functions of selecting the month, staff size, and day-of-work and day-off requests and clearly indicates the information that must be filled in. The scheduler can still understand the operation when encountering a different situation. For example, the scheduler only has to alter the daily medical staff size for each shift in each sub-department when the medical staff allocation of the present month differs from those of previously planned schedules. Locatability: Four colors are used to indicate shifts in the medical staff schedule to help with the visual management. The scheduler can rapidly discern the desired information by its color. Accessibility: The scheduling system comprises functions related to staff allocation and day-of-work and day-off requests. These functions are based on the hospital’s needs and ensure that the schedule fulfills medical staff’s requirements. The scheduler can produce schedules that meet these requirements through the functions included in the system. Level of detail: To avoid providing too much or too little information, medical staff schedules are designed based on the information content required by the case hospital in examining staff schedules while excluding irrelevant information. For example, the schedule only contains information on the medical staff, dates, and shifts, which is essential for the scheduler and staff. Assistance: In the scheduling system, the scheduler can check functions and select the staff size and month, which facilitates scheduling. For example, if the scheduler has to set medical staff member 1 for the R1 shift on the first day, the scheduler can process the day-of-work request by simply checking the function of day-of-work requests and inputting information on the staff, number of days, and shifts. System reliability: If feasible solutions are obtained for medical staff schedules and the program does not crash while being tested, the system is shown to be extremely reliable. The results indicate that feasible medical staff schedules are obtained in all the situations, confirming the stability and reliability of the prototype. Flexibility: The system is sufficiently flexible for altering the daily medical staff allocation of each shift in the present month, the medical staff’s day-of-work and day-off requests, the algorithm used, and other scheduling information. For example, if the scheduler has to alter the medical staff allocation for Saturday, they only have to change the number of medical staff corresponding to each shift on Saturday through the user interface. Customization: The scheduling system can customize the regulations demanded by the case hospital, including government and hospital regulations, and fulfill the requirements of hard constraints through the mathematical model. The function of checking hard constraints provided by the prototype allows the scheduler to select suitable hard constraints according to diverse medical staff scheduling requirements for producing customized schedules. Scalability: In the prototype, the number of hard constraints, soft constraints, and algorithms can be increased, confirming the scalability of the prototype. Each hospital or healthcare institution has its own regulations. With the prototype, hard and soft constraints can be added to the mathematical model, enabling the programmer to modify programming codes without affecting the scheduling functions.
The discussion indicates that the medical staff scheduling system prototype developed here considers 12 TTF technology characteristics and two additional technology characteristics. In this research and the study by Chen et al. [40] on the patient-referral mechanism, medical systems are examined using 12 technology characteristics provided by the TTF model. However, the system developed in this research emphasizes the achievement of the scheduler’s task; the generation of medical staff schedules complying with government and hospital regulations and satisfying the requirements of the medical staff. Chen et al. [40] investigated the roles of the HIS, radiology information system (RIS), and PACS in patient-referral procedures. The research determined from which system of which hospital the patient information should be collected during such procedures to avoid inconsistency and losses in patient information for reducing the possibility of medical negligence.
In other studies applying the TTF model, Yu and Yu [45] described the main factors affecting the utilization of electronic learning systems, but this study directly referred to the viewpoints provided by the TTF model regarding the characteristics required of IT software to develop a design concept for a medical staff scheduling system prototype. Despite the differences in theoretical application, all these studies equip the developed software with characteristics valuable to its users. Lin and Wang [44] verified that the TTF model can increase the use of a learning system. Hence, the scheduling task-scheduling system fit achieved in this research can be beneficial for schedulers and medical staff. In other words, the fit enhances schedulers’ acceptance of the prototype and increases the satisfaction of medical staff with their schedules.
Operating procedure of the prototype
There are eight steps in the procedure of the prototype. This research divides the scheduling steps into two processes: initial parameter setting and solving the medical staff scheduling problem. The details are introduced in the following sub-sections.
Initial parameter setting
Inputting medical staff scheduling information: Prior to medical staff scheduling, the year, month, and medical staff size are set. These variables are the initial parameters for medical staff scheduling. Flexible setting of the daily medical staff demand each month: The daily medical staff demand of each shift in the R, P, and C sub-departments is set. Shifts are then assigned according to the staff allocation during medical staff scheduling. Inputting the medical staff’s day-of-work requests: Medical staff make day-of-work requests to the scheduler prior to staff scheduling. The scheduler fills in the medical staff schedule according to the staff, number of days, and shifts. This function is not checked if no such request is made, and the corresponding parameter is not considered during scheduling. Inputting the medical staff’s day-off requests: Medical staff make day-off requests to the scheduler prior to staff scheduling. The scheduler sets the staff’s mode during the requested period as day off if the hospital guidelines are not violated. This function is not checked if no such request is made, and the corresponding parameter is not considered during scheduling. Selecting metaheuristics and the termination condition: The scheduler can select metaheuristics to solve scheduling problems and input the number of initial solutions. For example, the number of particles in the PSO algorithm or the number of bats in the BA determine the initial medical staff schedules generated. Moreover, the algorithm termination conditions, including the maximum number of iterations and the maximum execution time, must be set. Selecting hard and soft constraints: The scheduler can turn the hard and soft constraints on and off during scheduling. The rules considered during the scheduling can be selected by checking the corresponding mechanisms. An unchecked rule is not considered during scheduling.
Solving the medical staff scheduling problem
Using metaheuristics to solve the medical staff scheduling problem: The scheduler selects metaheuristics to solve the scheduling problem while considering the set initial parameters. First, a feasible initial solution is obtained for the schedule. A local-search algorithm is then used to obtain superior scheduling options. Exporting the medical staff schedule: After the medical staff schedule is obtained through Step (7), it can be exported in an Excel spreadsheet so that the staff can check it.
Consider that day-of-work requests are made by staff member 1 (R1 shift on the second day) and staff member 2 (P3 shift on the 10
According to these conditions, PSO with 10 particles and BA with 10 bats are used to solve the scheduling problem. The termination condition is set as follows: the maximum number of iterations
The functions of the generated medical staff schedule are verified as follows:
Flexible setting of the daily medical staff demand each month
Nine staff members are on duty every day from Monday to Saturday, and in compliance with the preset conditions, one staff member is on duty for each of the nine shifts. Ten staff members are on duty on Sunday. The staff size for the R1 shift is 2 whereas that for the other shifts remains 1.
Medical staff’s day-of-work and day-off requests
Staff member 1 has an R1 shift on the second day, which is consistent with the day-of-work request setting. Staff member 3 is off from the first to the seventh day, consistent with the day-off request setting. Thus, the functions of day-of-work and day-off requests run suitably.
Selecting the solution algorithm and setting the termination condition
Selecting PSO to solve the medical staff scheduling problem: In Fig. 5, the medical staff schedule obtained with the PSO algorithm is titled “PSO medical staff schedule.” The execution time reaches 500 seconds, in compliance with the termination condition. Thus, even if the iterated logarithm does not reach the maximum number of iterations (400), the solution process stops at the 253 Selecting the BA to solve the medical staff scheduling problem: In Fig. 6, the medical staff schedule obtained with the BA is titled “BA medical staff schedule.” The algorithm stops when the set maximum number of iterations (400) is reached, even if the execution time is 372 seconds, which is less than the maximum execution time (500 seconds).
Medical staff schedule obtained by the PSO method in the PHP webpage format.
Selection of hard and soft constraints
The function related to the selection of hard and soft constraints yields constraints according to the constraint options checked by the user. For example, the following hard constraints are provided: “Except in particular situations, the maximum number of consecutive days off for each staff member is four,” “No member can work seven consecutive days,” “No staff working the night shift can work the day shift the next day,” “No staff working the evening shift can work the day shift the next day,” and “No staff working the night shift can work the evening shift the next day.” Because the number of consecutive days off is not limited to four for certain staff exempted from this constraint, staff 3 can request seven days off.
The medical staff schedule indicates that the hard constraints are not violated. The scheduler also checks four soft constraints during scheduling: “Do not show (Day off-day shift-day off),” “Do not show (Day off-evening shift-day off),” “Do not show (Day off-night shift-day off),” and “Do not show (Night shift-day off-day shift).” Therefore, only the corresponding penalties of the four soft constraints exist. If the total penalty is zero, the generated medical staff schedule does not violate any soft constraint.
Exporting the medical staff schedule
The export function involves exporting the schedule in an Excel spreadsheet. After verification, the schedule (Fig. 6) proves to be consistent with the exported schedule (Fig. 7). Therefore, the export function can export the correct schedule to the required file location.
Medical staff schedule obtained by the BA method in the PHP webpage format.
Medical staff schedule obtained by the BA method in an Excel spreadsheet.
This section investigates hospital schedulers’ feedback on the prototype. They commented on the user interface, function-related requirements, and medical staff schedule.
User interface
Considerable changes are not required in the user interface because the staff size of each shift for each team of the case institution is preset as 1. Thus, the prototype demonstrates ease of use. Frequently adopted staff allocations are suggested to be preset for different scheduling conditions to enhance the ease of use of the prototype. The algorithms and termination conditions are irrelevant for schedulers. Therefore, it is suggested that these functions be removed from the user interface. The functions of algorithm and termination condition selection should be hidden, and the algorithm and termination condition should be preselected according to the needs of the case, such as the scheduling regulations and the maximum time for schedule generation. This research covers nine shifts; however, in certain conditions, more shifts may be needed. Considering all the units of the case radiography room, a maximum of 11 shifts can exist. Thus, the number of shifts must be increased to more than 11. The functions of day-of-work and day-off requests can help the scheduler. Two sets of preset values each are provided for the two request types. The number of functions regarding day-of-work and day-off requests should be increased to meet the practical scheduling demand.
Requirements regarding scheduling rules
The hard constraint “No staff member can work seven consecutive days” does not apply to all the schedulers’ teams. Thus, another hard constraint must be added: “Each staff member should have at least two days off during two consecutive weeks and at least eight days off during four consecutive weeks.” Regulations preclude certain staff from performing certain tasks. For example, pregnant staff should not perform tasks that have a risk of exposure to radiation. Therefore, this function should be added to the prototype.
Medical staff schedule
National holidays should be indicated on the schedule because few staff work on those days. More than one result should be provided for each schedule. Currently, only the scheduling result with the lowest penalty is exported. The schedulers suggested that other results be exported to provide more scheduling options.
In this study, a medical staff scheduling system prototype was constructed by adding two technology characteristics to 12 TTF technology characteristics. This study described the characteristics that the constructed system must possess to enhance its utility and ease of use.
Functions corresponding to the requests raised during medical staff scheduling in the case hospital are established in this research. Moreover, an interface facilitating the modification of medical staff scheduling information is provided to accomplish scheduling in the face of diverse requests. The prototype complies with the hard constraints posed by government regulations and the case hospital’s internal regulations; it also considers the soft constraints related to medical staff preferences. The scheduler can check the hard and soft constraints according to the scheduling requirements to generate a schedule.
This research examines the requirements of monthly medical staff scheduling. A scheduling system prototype was constructed by introducing TTF. Four conclusions are reached:
Of the 13 TTF technology characteristics, the prototype does not consider compatibility but considers the other 12 characteristics. Moreover, customization and scalability are added as essential factors for the medical staff scheduling system. This research emphasizes the fluctuation in monthly medical staff demand. An interface is developed for flexible input to allocate medical staff while remaining flexible as stipulated in the TTF model. This research offers scheduling functions that can solve schedulers’ problems regarding the daily staff allocation each month. An investigation of schedulers’ feedback regarding the use of the prototype indicated that the 14 technology characteristics are relevant for users. Moreover, the feedback indicated the improvements to be made to the prototype. Thus, the feedback of the schedulers serves as a reference for developing a new version of the medical staff scheduling system. This research incorporates customization under the TTF model and stresses that medical staff scheduling systems should be able to construct hard and soft constraints for various hospitals or institutions. In the prototype, the scheduler can select constraints by checking corresponding functions, which proves the feasibility of customization in the prototype. The customization function can solve scheduling problems caused by variations in the scheduling conditions.
This study proposes three suggestions for future research. First, the investigation of the effect of the TTF model performance was beyond the scope of this research. Therefore, a future study should examine whether this prototype has a positive influence on schedulers’ performance over time. Second, the feedback obtained by interviewing schedulers regarding the use of the developed prototype indicated that some important scheduling rules and some scheduling requests of medical staff were not considered, such as indicating national holidays and adding the hard constraint “Each staff member should have at least two days off during two consecutive weeks and at least eight days off during four consecutive weeks.” Future studies can consider these scheduling rules and requests. The feedback obtained in this research can serve as a reference for developing a new version of this medical staff scheduling system. Finally, the patient appointment scheduling problem is an important research area for hospital managers [49, 50, 51, 52]. Therefore, how to apply the TTF model to develop a patient appointment scheduling system warrants further research.
Footnotes
Acknowledgments
This research is supported by the Ministry of Science and Technology-Taiwan under contract no. MOST 109-2221-E-033-028.
Conflict of interest
None to report.
