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# Mt. Sinai Hospital’s Expansion Problem Report (Assessment)

Mt. Sinai Hospital in New Orleans has a serious hospital expansion problem. Although it already has 600 beds, the administration has decided to increase the number of beds to 690. Increasing the number of beds has been in line with increasing the hospital’s revenue. Since the hospital’s laboratories, x-ray equipment, and operating rooms are underutilized, the hospital’s management does not see the need for expanding these areas (Haksever and Render 34).

The problem at Mt. Sinai hospital is that, out of the 90 beds, it is difficult for the management to determine the number of beds to be allocated to surgical staff for surgical patients and the number of beds assigned to medical personnel for medical patients while maintaining maximum profits. The principal objective is to find the optimal solution for the current hospital expansion problem by highlighting critical issues that should be addressed.

## The number of medical beds and how many surgical beds should be added to maximize the total revenue

Assuming that the hospital operates 365 days,

Let: X1 = number of medical patients

X2 = number of surgical patients

Maximize revenue = USD2,280.00 X1 + USD1,515.00 X2

subject to:

8X1 + 5X2 =< 32,850 (patient days available)

365 days’ x 90 new beds

3.1 X1 + 2.6 X2 =< 15,000 (lab tests)

1 X1 + 2 X2 =< 7,000 (x-rays)

X2 =< 2,800 (operations and surgeries) X1, X2 => 0

X1 = 2,791 medical patients

X2 = 2,105 surgical patients

Revenue = 9,551,659.00 USD per year

To translate X1 and X2 into the number of medical beds against surgical beds, there is need to establish the total number of hospital days for each type of patient: medical = (2,791 patients) (8 days) = 22,328 days, while surgical = (2,105 patients) (5 days) = 10,525 days (Haksever and Render 33). Therefore, 68 percent is a representation of the total number of medical days and 32percent surgical days, which yields 61 medical beds and 29 surgical beds.

## The respective number of medical patients and surgical patients per year

Since the number of medical beds is 61 and 29 surgical beds, this section determines the number of medical patients and surgical patients the hospital should admit per year (Kumar, Nagalakshmi, and Kumaraguru 27). The optimal number of medical patients at Mt. Sinai Hospital every year is 32850. On the other hand, the optimal number of surgical patients at the same hospital each year is 2800. After increasing the number of beds from the initial 600 to 690, the hospital’s maximum profit on a yearly basis is 2790.

## Are there any empty beds with this optimal solution? If so, how many empty beds are there?

Yes, the hospital has empty beds. At the optimal, rounding off to the nearest integer, the hospital has four empty beds. As established in the linear programming solution, x-rays of the unused capacity have one empty bed. The lab tests of the unused capacity have three empty beds, whereas the available unused operation rooms have two empty beds.

## Effect of acquiring more beds if needed

The design of a facility alongside its transferable and fixed equipment have a substantial effect on human performance. The efforts of improving staff and patient outcomes concealed adverse situations for clinicians used evidence-based designs are important. These efforts lessen disruptions, systematize the locations of the supplies as well as equipment and supplies, and ensuring there is sufficient space for the working and documenting areas. As described by Haksever and Render (33) the significance associated with the practices are based on codes that are designed to recompense the human cognitive weaknesses.

Principles of evidence-based practices apply to this situation in the sense that the acquisition of more beds at Mt. Sinai Hospital will affect hospital performance adversely. Although increasing the number of beds will increase productivity, nurses will not work efficiently because of the reduced working space. Another effect of increasing the number of beds is that the surgery room will be underutilized.

## Are the laboratories being used to their full capacity?

Laboratories have been used to their full capacity. With the increased number of beds, an assumption that can be made is that the overall number of patients will increase. Initially, the laboratory was not adequately used because of low numbers of patients. However, with the increased number of beds from the initial 600 to 690, laboratories will be utilized to their full capacity.

## The likelihood of carrying out more lab tests per year. If so, how many more?

As far as the increased number of beds is concerned, there is also no possibility of performing more lab tests on a yearly basis. Maximizing the profits will require that the hospital does not carry out more lab tests per year (Marques, Captivo, and Vaz Pato 417). As evident in the linear programming solution, profits made before more beds were acquired increased from the initial figure 14,123 USD a year to 15000. This is to mean that, since the lab test were underutilized, increasing the number of beds in the hospital helped the management to utilize its already available Laboratories.

## The effect of more lab space if needed

More lab space will improve the convenience of the lab technicians. As argued by Marques, Captivo, and Vaz Pato (411), since laboratories involve delicate health related issues, they should be spacious for convenience. Creating more space for the lab technicians will help to maximize profits.

## Is the x-ray facility being used to its maximum?

The hospital did not use its X-ray facility maximally. Underutilization of the X-ray facility is evident in the sense that, even after increasing the number of beds the profits made remained the same. This is to mean that the profits made remained at the initial mark of 7000USD.

## The possibility of performing more x-rays per year. If so, how many more?

There is no possibility of performing more X-rays at Mt. Sinai hospital. The increased number of beds at the hospital did not have an effect on the hospital’s performance. As indicated in the linear programming solution, the number of patients in need of X-ray services remained the same even after more additional beds were acquired.

## Analysis of the impact of acquiring more x-ray facilities if required

The additional 90 beds at the hospital present a challenge of space. X-ray facilities need more space of operation. Acquiring more X-ray facilities will be a waste of resources since, even after the number of beds was increased, the number of patients who needed X-ray services remained the same.

## Is the operating room being used to its full capacity?

The hospital management utilized the operating room to its full capacity. The increased number of beds at the hospital means that there is also an increased number of patient operations (Marques, Captivo, and Vaz Pato 407). As indicated in the linear programming solution, the profits made out of utilizing the operating room increased from the initial figures of 2104 USD to 2800USD. The increased profits show that the hospital management used the operating room to its full capacity.

## The possibility of performing more operations per year. If so, how many more?

There is an increased probability of performing more operations on a yearly basis. Since the number of beds will increase, there is an assumption that the operation rooms will have more work (Marques, Captivo, and Vaz Pato 407). With respect to the linear programming solution, the probability of performing more operations on a yearly basis is 1. Since the number of operations patients increased from the initial figure of 2104 to 2800. The hospital, therefore, operated 696 more operations after beds were increased.

## Analysis of the impact of acquiring more operating room facilities if needed.

As far as the case at Mt. Sinai Hospital is concerned, there are adverse effects of acquiring more operating room facilities. The additional 90 beds present a space challenge. Nurses at the hospital already have inadequate space for documenting their work and carrying out treatment procedures. Obtaining more operating room facilities will result in more inconvenience to the nurses.

## Works Cited

Haksever, Cengiz, and Barry Render. Service Management. Upper Saddle River, NJ: Pearson, 2013. Print.

Kumar, Mr. B.Satheesh, Ms. G Nagalakshmi, and Dr. S Kumaraguru. ‘A Shift Sequence for Nurse Scheduling Using Linear Programming Problem’. IOSRJNHS 3.6 (2014): 24-28. Print.

Marques, Inês, M. Eugenia Captivo, and Margarida Vaz Pato. ‘An Integer Programming Approach to Elective Surgery Scheduling’. OR Spectrum 34.2 (2011): 407-427. Print.

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