A Requirement on Quantitative Methods in Management

AdDu – DDC MBA Program

“Maximizing the Revenue Based on Capacity”

EFFICIENT CAPACITY MANAGEMENT at CHDC HOSPITAL

Submitted To:

John Stephen G. Curada, PhD

Submitted By:

Chenelly D. Alcasid

Dr. Jeanie E. Himagan

September 28, 2013

Background and Literature Review

Healthcare institution executives and administrators are always looking for ways to

increase profit, improve operational efficiency and the consequent value of care to patients. Treatment capacity in a health care facility, such as hospitals, does not have a clear, universal definition. The term "capacity" is generally used to refer to the sustainable maximum output that is produced in an organization, depending on factors such as labor and technology availability (Kuntz, Scholtes, & Vera, 2007). In the case of hospitals, the term “capacity” usually refers to number of beds --- capacity to admit patients.

The health and social care systems have become more streamlined and have been operating and planning healthcare services more often on their bed capacity. Bed occupancy and the ratio of beds per population remain as the predominant metrics in hospital capacity planning (Green, 2002-2003). Thus, planning includes coping effectively with given and unexpected pressures which pose an increasingly difficult challenge. Pressures (e.g. number of rooms, number of doctors, length of stay per patient, etc.) which place the acute availability of beds to rise which may result in the refusal of emergency admissions, the premature discharge of existing patients, the cancellation of elective admissions and operations and hence potential rises in hospital waiting lists and times. Therefore, these pressures would affect the ability to generate maximum income or revenue for this kind of institutions. A review of international practice found that bed capacity continues to be the preferred unit for planning hospital care in Finland, Germany, Italy, New Zealand and most Canadian provinces. Of the countries included in the review, only England and France were moving towards planning based on service volume and activity (Ettelt et al., 2008).

Because of this reason, it is more challenging to plan for capacity in services than in manufacturing. Healthcare executives and administrators are always searching for better ways to improve production capacity for medical treatment and thereby, improving operational efficiency and generation of profit. Many times, capacity in health care organizations is a vague, hard-to-measure concept which varies over time and with local economic conditions. In any hospital, resources are limited and they are mostly dissimilar in nature. This dissimilarity of resources in a hospital or healthcare facility makes the maximizing of revenue based on capacity very important in order to determine the exact capacity of the system taken as a whole. Inappropriate capacity identification would lead to inaccurate system capability, resulting in inefficiencies in the system – observed in excessive waiting, poor capacity utilization across different resources and poor bottleneck management. On the other hand, when the right maximum capacity is determined properly, it could lead to efficient service models in a hospital by minimizing all the wastage and inefficiencies mentioned above leading to cost efficiency and revenue maximization.

This paper addresses this issue of capacity management at CHDC Hospital and offers a method to analyze bed occupancy setup in this institution considering given constraints in a health care service provision environment. This would help determine the maximum revenue that CHDC Hospital can achieve through making a decision whether to expand by increasing bed

capacity or not. Therefore, resulting to improved system efficiencies and added value of care provided to their prospect customers or clients. Managing Capacity

The healthcare industry has been looking into different strategies to manage capacity with a view to enhance efficiency and productivity, which can add value of the service they provide. Some of the common methods that generic service companies apply can also be applied by the healthcare industry (Fitzsimmons and Fitzsimmons 2006). These methods include daily work shift scheduling (for doctors and nurses), increasing customer participation (patients’ share of responsibilities), creating adjustable capacity (adjustable physical resources such as rooms and beds), sharing capacity (with other services), cross-training employees (nurses and staff), part time employees (floating staff), etc.

Some of these methods have found varied degrees of success. These capacity management strategies can be reasonably successful when handled one resource at a time. But when a facility is operating with multiple bottleneck or near-bottleneck resources, the capacity management becomes increasingly complex. This paper addresses this complex issue of capacity management with multiple critical resources in a hospital. Managing Demand

While it is common to attempt to manage capacity, which is internal to a service provider (supply side) with the thinking that demand is external and therefore not controllable by the provider, increasing number of service firms today are also addressing the demand side of the equation. These demand management strategies attempt to influence the consumer behavior in a way so as to suit the desired operations of the service firm. Some of the demand management strategies include: demand partitioning (walk-in vs. appointments), offering price incentives (two for the price of one), promoting off-peak demand (off-season surgery discounts), developing complementary services (keeping customer flow going), overbooking and “no-show management”.

This paper would address primarily the supply side of the capacity management issues directly and address the demand side only indirectly, while acknowledging the importance of both. Dissimilar Resources in Hospitals

In any hospital, resources are generally limited. Considering the limited resources, it is essential to find the optimal way to admit patients in order to maximize efficiency and productivity, and thereby, patient output. This could directly affect the bottom line – maximizing revenue or profit.

Typically the resources in any hospital are: doctors, nurses, operating rooms, waiting

rooms, number of beds, laboratory, etc. Some of the variables that are also critical in defining the capacity of these resources are the following:

1. Number of surgeries per doctor per day that can be performed 2. Hours of operations in a day 3. Average stay of a patient 4. Days of the week for operations

Most of these resources are expensive for a hospital to maintain and one of the major

problems is to be able to maximize the utilization of each of these resources. One of the problems commonly faced while trying to maximize utilization and output is the difficulty in arriving with the ideal capacity with different types of resources and identifying the bottleneck. When any single resource’s capacity is increased, the bottleneck seems to shift to another resource. Similarly, if we increase the capacity of this bottleneck resource now, a brand new bottleneck may appear elsewhere. It is very difficult to find a balance in the resources where each one of them is performing to maximum capacity and thus the resources as a whole generate the maximum output for the entire system. Problem Statement in CHDC Hospital Situation The situation of CHDC Hospital discussed in this paper has been created after considering internal factors in the hospital operations environment. The base case is described as:

Community Health and Development Cooperative (CHDC) Hospital in Magallanes, Davao City is a private, tertiary, 70-bed facility, operating with laboratories, operating rooms, and x-ray equipment. In seeking to increase revenue, CHDC’s administration is contemplating whether to invest for expansion by adding 30 beds to their current 70 bed capacity available for occupancy or operate with their current capacity. The administrators however, feel that the overall major facilities and equipment of the hospital is not being fully utilized at present and adding 30 beds to their capacity may not be needed to handle additional patients. The expansion, on the other hand, involves deciding how many beds should be added to accommodate particularly the medical patients as well as the surgical patients. The hospital's medical records department has provided the following pertinent information:

The average hospital stay for a medical patient is 3 days, and generates an average of Php10,000 in revenues.

The average surgical patient is in the hospital 5 days and receives a Php50,000 bill.

The laboratory is capable of handling 2,550 tests per year.

The average medical patient requires 3 lab tests and the average surgical patient takes 5 lab tests. Moreover, the average medical patient uses one x-ray, whereas the average surgical patient requires two x-rays.

The x-ray department could handle up to 1,500 x-rays without significant additional cost.

Finally, the administration estimates that up to 500 operations could be performed in

existing operating room facilities. Medical patients do not require surgery, whereas each surgical patient generally has one surgery performed. CHDC Hospital is open for service 365 days a year. The administration and/or management aims to come up with a decision on how many medical beds and how many surgical beds should be added to maximize the hospital’s revenues or the option to operate still with their current 70-bed capacity together with utilizing their other major service facilities at a maximum. SOURCE OF DATA

Data, values and pertinent information used in this paper were based on CHDC

Hospital’s current situation and were duly provided by their medical records department for the purpose limited to the objective of this paper. Confidentiality is maintained in this paper by citing only relevant information and data (e.g. PHP round-off on revenue) exclusive of the details to be used by CHDC management for strategic decisions.

CHDC Hospital’s medical records department provided the data as incited in the

problem statement above and particularly was based on the Community Health and Development Cooperative (CHDC) Hospital’s Annual Medical Records of 2012.

DATA ANALYSIS

The data from this paper will be statistically processed using the QM for Windows

software particularly the Linear Programming method. We will correspondingly aim to effectively interpret the results from the mentioned software to aide us in providing the best recommendation and optimal solution to CHDC Hospital’s identified problem.

Output or results from the QM for Windows software will be generated in several forms.

The output from each section is presented in the following order: (1) Graph result shows the constraints, the feasible region which is the colored area, and the table which lists the corner points, (2) Results section gives the solution to the problem, (3) Range result which provides more sensitivity analysis information, (4) Solution List result presents the “basic” status for variables which are nonzero in value and “nonbasic” status for slack variables, and (5) Iterations result which lists the steps of analysis in the Simplex Method.

RESULTS AND DISCUSSION

Based on the problem statement presented for the case of CHDC Hospital, problem state formulation may be defined as: Given: Medical Patient = Php10,000 Surgical Patient = Php50,000

Medical Patient requires: 3 lab tests, 1 x-ray, average of 3 days stay, and no need to perform any operation

Surgical Patient requires: 5 lab tests, 2 x-ray, average of 5 days stay, and need to

perform generally 1 operation Constraints: (1) Maximum of 2,550 lab tests per year (2) Maximum of 1,500 x-ray operation in a year (3) 365 days operations (4) Maximum of 500 operations can be performed in a year Let X1 = Medical Patients X2 = Surgical Patients Max(Revenue) = Php10,000X1 + Php50,000X2 Subject to: (1) 3X1 + 5X2 <= 2,550 (lab test constraint) (2) 1X1 + 2X2 <= 1,500 (x-ray operations constraint) (3) 3X1 + 5X2 <= 10,950 (patient days available = 365days x 30 beds) (4) 0X1 + 1X2 <= 500 (operations performed/year constraint) (5) X1,X2 >= 0 (non-negativity constraint) Abovementioned variables were processed using Linear Programming Method of QM for Windows and has presented the following results with corresponding interpretation:

Graph Result

Z in this table means the total revenue for each row combination of medical patients

and surgical patients admitted. In this case the interior corner, or the place where the constraints cross, is the optimal solution which is equal to 17 (16.7) medical patients and 500 surgical patients respectively. Since there are four constraints identified, the following are the corner points’ generated:

Point 1: (X1=0, X2=0) Revenue = Php10,000(0) + Php50,000(0) = Php 0 meaning at this point there is no revenue that can be generated by the hospital.

Point 2: (X1=850, X2=0) Revenue = Php10,000(850) + Php50,000(0) = Php8.5M meaning at this point where CHDC hospital will admit 850 medical patients and none of the surgical patients they will be able to earn profit of Php8,500,000.

Point 3: (X1=0, X2=500) Revenue = Php10,000(0) + Php50,000(500) = Php25M meaning at this point where CHDC hospital will admit 500 surgical patients and none of the medical patients they will be able to earn profit of Php25,000,000.

Point 4: (X1=17, X2=500) Revenue = Php10,000(17) + Php50,000(500) = Php25.17M meaning at this point where CHDC hospital will admit 17 medical patients and 500 surgical patients they will be able to have a revenue of Php25,166,670. Therefore this point is considered as the optimal solution or mix where CHDC hospital may base their decision making for their expansion of additional 30 beds because this point returns the highest profit.

Linear Programming Results

It has been noted that the optimal solution for CHDC Hospital is to admit 17 medical patients and 500 surgical patients to be able to generate revenue of Php25,166,670. But in the “Results Section” table above, a new piece of information is presented under the column Dual. This part of information is desired in conducting a sensitivity analysis to the problem case presented in this paper.

In the “lab test” row the dual value is equal to 3,333.33. Remember also that lab test procedures of 2,550 in a year were already used up in this scenario. Therefore 3,333.33 means that if the hospital had one more or additional one procedure of lab test in a given year they could add 3,333.33 to the value of the objective function. So they could add Php3,333.33 to the revenue. The 3,333.33 is called a shadow price. The shadow price for the operating procedure is also 3,333.33. Meaning adding another one operation procedure would increase CHDC Hospital’s profit by Php3,333.33.

If a dual value, or shadow price, is zero that would indicate the constraint is not binding - meaning not all have been used in that constraint. So it would not add anything to the objective if it is added to the constraint.

Range Result

Notice the solution again for the medical patients and surgical patients. The lower and upper bounds for the medical patients and surgical patients are the range of values the original profit contributions can change and still not change the solution to the problem. Examining these values one at a time, the profit of medical patients can range between almost 0 and 30,000 and not change the optimal solution of 17 medical patients and 500 surgical patients (the profit value will respectively change).

In the constraint row the dual or shadow price column is again presented. Again, this is the profit contribution of adding one unit to the resource constraints. The upper and lower bound indicates the range of values for the resource constraints such that the shadow price would still hold. Thus, outside the upper and lower bound the shadow price shown is no longer valid.

Solution List Result

Going back to the solution arrived; CHDC hospital must make admission both for medical

patients and surgical patients to achieve optimum revenue. So medical patients and surgical

patients have nonzero solution values. In this case medical patients and surgical patients are

said to be "basic" variables because their values are nonzero. Moreover, in this case the slack

variable 1 and slack variable 2 are "non-basic” because they are zero in value.

Iterations Result

In the CHDC hospital situation it took 3 iterations to find the optimal solution. The first

iteration starts with slack variables as "basic" solutions. This corresponds to starting at the

origin in the graph. The second iteration brings in tables, but the solution is not yet optimal

because the cj - zj row has a positive value in it (10,000). The third, and final iteration shows

the solution again under the quantity column. Note under the slack columns, in the zj row the

shadow prices can be seen again (3,333.33).

IMPLICATIONS AND RECOMMENDATION

In line with the results or optimal solution arrived to for the case of CHDC Hospital, the optimal mix of medical patients (X1) and surgical patients (X2) will be converted to the optimal mix of medical beds and surgical beds. In doing so, the hospital administrators or management will particularly identify how many beds will be for medical section versus beds for surgical section as correspondingly allocated for their plan of adding 30 beds to their current capacity.

To compute for the number of beds per variable given, there is a need first to compute the total number of hospital days for each type of patient based on the optimal solution arrived at:

Medical Patients (X1) = (17 patients)(3 days/patient) = 51 days

Surgical Patients (X2) = (500 patients)(5 days/patient) = 2,500 days

TOTAL = 2,551 days

This represents 2% medical days and 98% surgical days, which yields 1 medical beds and 29 surgical beds computed as follows:

Medical days = 51 days/ 2,551 days = 0.019 or 2% 30 beds(2%) = 1 medical bed

Surgical days = 2,500 days/ 1,551 days = 0.98 or 98% 30 beds(98%) = 29 surgical beds

The computations recently shown present that there are approximately 17 medical patients and 500 surgical patients per year in the optimal solution, which translates to 1 medical bed and 29 surgical beds in the 30-bed addition as part planned by the CHDC Hospital administrators. Furthermore, there are no empty beds with this optimal solution. Each additional patient day (over the current 2,551 days) will permit CHDC Hospital to increase revenue by Php9,815. That is, by acquiring another bed (or 365 patient days), the revenue can be increased by Php3,582,475.47 in a year. Moreover, looking into the various facilities of the hospital, laboratories need to increase capacity to accommodate additional 1* laboratory procedure. However, acquiring more laboratory space may not be that worthwhile for CHDC Hospital considering the expansion will be for only 1 additional laboratory procedure. X-ray facility has unused capacity of 483**, so still expansion in this area is not needed as of the moment. Lastly, the operating room is being used at maximum***. Each additional operation/ surgical procedure that can be handled will increase CHDC Hospital’s revenue by Php50,333.34***. Thus, expansion in this area is also not necessary.

It can be recommended that given the optimal solution CHDC Hospital administration and/or management should consider proceeding with their additional 30-bed expansion since two of their major facilities are already being fully utilized – their laboratories and operating rooms. With their decision of investing on a 30-bed expansion they will be able to generate as much as $25.17 million in revenues (if fully utilized per year) which can be seen as quite substantial to cover any expansion cost that they may incur.

Note: *Laboratories: 3X1 + 5X2 <= 2,550 3(17) + 5(500) = 2,551 2,550 – 2,551 = -1 **X-ray: 1X1 + 2X2 <= 1,500 1(17) + 2(500) = 1,017 1,500 – 1,017 = 483 ***Operating Room: 0X1 + 1X2 <= 500 0(17) + 1(500) = 500 500 – 500 = 0

In conclusion, the contributions of this paper are several: • It provided a general model that can be applied to multiple resource capacity management

situations • It identifies the constraint resources that are not very obvious, going by traditional methods • It offers managerial insights to this common situation in many hospitals that always scramble

to find more capacity • It offers a randomly determined scenario to capture variability in some of the process

parameters • It provides a platform for developing metrics for performance evaluation of different types of

resources in a healthcare institution

The model developed in this paper was kept at the basic level with the objective being a generic application for an hospital facing similar situation. When applied to specific situations, the basic model will be extended to more complex models to suit a hospital’s specific policies and needs. Overall, the techniques presented in this paper would help hospitals primarily to achieve their target bottomline (profit/ revenue), increase efficiency of healthcare delivery (increase output) and reduce waste (underutilization of resources), while not compromising with quality of care, safety and access.

The academic aspect of this paper covers the contributions of capacity analysis in the following three broad categories: (1) Improved operational efficiency – in minimizing excess capacity and in achieving a smoother utilization of capacities across a service enterprise like hospitals; (2) enhanced service operations strategy – in leveraging capacity utilization in obtaining a higher level of patient admission for a given set of resources; and (3) better capacity and demand management – in aligning capacity allocation with demand pattern of patient needs

REFERENCES

Ettelt S., Nolte E., Thomson S., & Mays N. (2008). International Healthcare Comparisons Network. Capacity planning in health care: a review of the international experience. Copenhagen: European Observatory on Health Systems and Policies. Fitzsimmons J., & Fitzsimmons M. (2006). Service Management: Operations, Strategy, and Information Technology. Green L.V. (2003-2003). How many hospital beds? Inquiry Kuntz L., Scholtes S., & Vera A. (2007). Incorporating efficiency in hospital-capacity planning in Germany, 8, 213-23.