O.R. ApplicationsA heuristic algorithm for the hospital health examination scheduling problem
Introduction
Preventive medicine based on health examinations has proven to be the most efficient type of medical treatment in modern health care [8], [23], [25]. Most hospitals provide all kinds of checkups for people of different genders, ages, and disease conditions. In a reciprocal relationship, examinees, or patients, are instructed in advance about lifestyle choices that will prevent chronic diseases or further deterioration of certain symptoms, and health examination centers obtain their profits from the health examination operations that they dispense [8], [23], [25]. At the National Taiwan University Hospital (NTUH), for example, more than 30 examinees check in every day for regular health examinations, and each one pays a fee of NT$20,000 (US$575). With a 30% gross profit rate, the hospital earns more than NT$180,000 (US$5,625) in profits every day, or NT$46,800,000 (US$1.5 million) each year [23], [25]. The number of health examination requirements continues to increase dramatically as the concept of preventive medicine becomes more and more popular. Health examination procedures have become a major source of income for many hospitals, who have responded by setting up new departments to coordinate the workforce required for this new service.
Three types of scheduling problems have been studied in the literature related to the hospital management: problems related to nurse scheduling, to lab capacity planning, and to special medical equipment planning. Most studies of the nurse scheduling problem are connected to hospital labor regulation policies, specially trained nurse scheduling, and emergency room nurse scheduling [7]. These studies generally have adopted Linear programming (LP), Integer programming (IP), or Binary integer programming (BIP) techniques to solve the scheduling problem. Some of them employed powerful software like LINGO [2] or CPLEX [15] to solve the IP or BIP models. Some developed heuristic approaches – including well-known heuristic algorithms such as the Tabu search [10], the Column generation approach [3], [4], [5], or GA-based methods [1] – when the IP or BIP models became too complicated for the computer to solve.
Most studies about lab capacity planning and special medical equipment planning problems have focused on the issues related to capacity planning [7], [12], [13], [14], [15]. They have adopted a variety of techniques in their solution processes: simulation [12], [15], rule-based AI [20], or knowledge-based agents [14]. Decision support systems (DSS), for which simple rules (e.g., FIFO, priority, and random) were adopted to solve emergency situations, are often used to facilitate planning and scheduling of hospital resources [18].
The health examination scheduling (HES) problem considered in this study is different from both the nurse scheduling problem and the lab capacity planning problem in that its objectives and constraints are very different and there is no uncertainty involved. Scheduling health examinations differs from other hospital operations, such as surgery, in that a complete health examination includes more than 20 different examination procedures and may require many different medical specialists and/or specialized equipment [9], [23], [25]. The examinees know beforehand that they need to check in at a certain time on a certain date and that most health examination procedures take a set amount of time. When special concerns arise during the examination process, further advanced tests or doctor appointments are scheduled apart from the regular health examination procedure. For these reasons, interruptions or emergencies seldom occur during the health examination process.
The health examination scheduling (HES) problem is, in fact, very similar to the sequence-dependent shop-floor scheduling problem in a manufacturing plant [6], [11]. Checking the feasibility of the health examination request for a patient can be compared to checking the availability of a work center for a customer demand [6], [11]. Like the HES problem, a general shop-floor scheduling problem can be formulated as a MIP, BIP, or IP model [17], [19]. Local search algorithms, such as simulated annealing and variable-depth search [6], [11], can be used to find the feasible solution when it is impossible for a computer to solve the MIP, BIP, or IP models [17], [19]. Nevertheless, it is true that such search algorithms become quite inefficient as the number of constraints and variables increase in both kinds of problems [17], [19].
Obviously, there are differences due to context. To provide efficient health examination services, hospitals must separate common procedures – such as body composition analysis and HMC-Med consultation – from special advanced procedures – such as MRIs or diagnostic thallium scans [9], [23], [25]. All the examinees are subjected to the common examination procedures, but only some undergo the optional advanced procedures, which incur extra charges. Different combinations of common examination procedures are grouped into “health examination packages” targeting the different genders and age groups. For example, a health examination package for male examinees includes a urology consultation, while the one for female examinees includes a gynecology consultation. Female examinees over the age of 40 need mammography, while those under 40 need only breast sonograph [9], [25].
Scheduling all the required examination procedure for all examinees within a limited period of time is an enormous challenge due to time (16 hours per day) and resource (doctors, nurses, and equipment) constraints. An added complication is the often contradictory goals of the two sides of the equation: the hospital wants to provide health examination services as efficiently as possible without increasing the available resources, while all the examinees want the earliest available time slots without incurring extra charges. Our objective in this study is to minimize the waiting time of both doctors and examinees, while respecting the time and resource limitations, thus solving the health examination scheduling problem efficiently.
The rest of the paper is organized as follows. Section 2 describes the problem. Section 3 develops our heuristic algorithm for scheduling health examinations. Section 4 demonstrates the heuristic algorithm using two simple cases, compares the results obtained with the heuristic algorithm to those obtained with the BIP method, and evaluates the algorithm’s efficiency and optimality. Finally, Section 5 offers our conclusions and our suggestions for future research.
Section snippets
Problem description
The purpose of health examinations is to prevent chronic diseases by identifying health problems through screening tests when examinees are still asymptomatic. A complete health examination package includes at least 20 different procedures, ranging from HMC-Med consultations to upper GI endoscopies [9], [21], [22], [23], [25]. Different packages have been designed for different types of examinees. Table 1, Table 2 show 6 of the 17 health examination packages offered by the National Taiwan
Health examination scheduling algorithm (HESA)
To solve the health examination scheduling problem described above, we propose a heuristic algorithm, called the health examination scheduling algorithm (HESA). HESA is by nature a greedy algorithm, adopting the “Round Robin” prioritizing rule in which the algorithm immediately assigns an examinee to any available doctor as soon as the examinee becomes available. The “Round Robin” prioritizing rule operates as that when an examinee is delayed or unavailable, he or she will be placed at the end
The HESA solution process and computational analysis
To demonstrate the HESA solution process, a simple health examination scheduling problem is described below. The information about the examination procedures and doctors for the first example are given in Table 3 for one examination package, A01. In the first example, there were a total of 4 examinees to be scheduled, with an assumption of two examinees per group. The total number of planning time buckets was 7 with α = 2 time buckets and β = 1 time bucket.
When applying HESA to solve the problem in
Conclusion
This study proposes a heuristic algorithm, called the Health Examination Scheduling Algorithm (HESA), to solve health examination scheduling problems for health examination centers. Though Binary integer programming (BIP) is often used to solve such problems, the BIP models are often unsolvable due to the complexity of the problem caused by large numbers of variables and constraints. Furthermore, solving BIP models always takes a lot of computing time and requires computers with enormous
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