Aggregate plan of surgical interventions in hospital services

SUMMARY

The following work is aimed at the development of a planning, programming and control procedure (PPC), of surgical interventions in hospital services based on the study of the process approach and the combined use of mathematical techniques and trial and error methods., of operations research and statistics in the process of surgical interventions in hospital services.

Among the main results obtained, the theoretical, methodological and practical importance of the CPP procedure for surgical interventions elaborated by the authors can be highlighted, being possible to improve the hospital indicators of the surgical sub-directorate, with which it can be deduced that it would cause the reduction of costs related to said activity.

KEY WORDS: Linear Programming - Planning - Production - Assignment

INTRODUCTION

Around the world, today the healthcare industry continues to be under pressure from tremendous costs and the need to provide increasingly exceptional services. Since then it had been observed that there was no correct correspondence between strategic planning and the operational problems of hospitals, which had yet to join the strategic problems.

Today there is a tendency to narrowly focus on the problems of hospital and health center operations as a consequence of costs, capacity or staff planning. However, there are other aspects that cover a much broader range of decisions than those currently found in the literature, emphasizing the importance of strategic planning and direction in these services, which is why it is proposed that through the analysis of the operations function and the combined use of mathematical techniques and trial and error methods, of operations and statistical research, innumerable reserves of productivity, efficiency and organization can be found, which would contribute to a better performance of this type of organizations,being necessary to design a procedure for the planning, programming and control of surgical services, which includes, in turn, its continuous improvement, contributing to the better use and use of the resources and means available to the organization.

SITUATION OF THE ADMINISTRATION OF HOSPITAL SERVICES IN THE WORLD AND IN CUBA

Health sector reform is a priority issue on the political agenda of the countries of the Americas region, while the main health cooperation agencies and organizations have incorporated the issue of sector reform into their strategic proposals and health programs. action. Health sector reform has been defined as «… a process aimed at introducing substantive changes in different instances and functions of the health sector, with the purpose of increasing the equity of its benefits, the efficiency of its management and the effectiveness of its benefits for the satisfaction of the health needs of the population. It is a dynamic, complex and intentional process, carried out during a certain period of time and based on circumstances that justify and make it viable.PAHO / WHO (Pan American and World Health Organization respectively).

An argument of current importance that supports the need for reform is that public resources for health are and will be scarce in many countries, which forces them to be used as efficiently as possible.

ADMINISTRATION OF SURGICAL PROCESSES.

According to Valdés Llanes, internationally it is considered that an efficient use of operating rooms, in hospitals with a surgical profile, has to be for the Major Elective Surgery (CME) the performance of 4.0 or more surgical interventions for each of them in One day. From the analysis of the 14 surgical specialties existing in the hospital under study, it was observed that in 10 of them performance similar to the one internationally recommended as an institutional average can be achieved. The administrative or managerial translation of this information can be defined as: if adequate planning of surgical shifts by specialty and of interventions according to complexity is achieved, as well as optimal use of the useful surgical time of each operating room,Cuban institutions can exceed that 4.0 which is considered efficient.

PROCEDURE FOR PLANNING, PROGRAMMING AND CONTROL OF SURGICAL INTERVENTIONS

The studies for the design and elaboration of the procedure began with an analysis of the flow of people in the guardhouse through a historical series of data corresponding to the total number of patients treated in this area, each month, in the last four years, as well as the influx of people in two different months and belonging to different seasons (winter and summer).

The multifactorial analysis carried out corroborated the authors' criterion that the demand is not completely random in relation to the different pathologies, but rather that there are causal phenomena that govern its behavior. Thus, during this period, it was observed that the historical behavior of the interventions of each specialty, in relation to the total of the year, occurred with the same frequency and, in addition, the demand for each of the months was estimated using forecasting techniques.

From the analysis derived from the previous studies, it was possible to construct the proposed procedure for the planning, programming and control of surgical interventions in a hospital that is shown in FIGURE 1.

AGGREGATED PLAN FOR SURGICAL INTERVENTIONS

To obtain the aggregate plan of surgical interventions, that is, the number of operations, according to specialty (families) to be carried out in each month of the year, it is proposed to use the linear programming technique, posing the problem in the following model:

Decision variables:

In the country there are 14 surgical specialties, but here only 8 surgical specialties will be analyzed, resulting in a total of 96 decision variables. For greater ease, they are expressed as follows:

X ij: Surgical interventions of specialty i in month j

(j = 1,2,3….., 12), (i = 1, 2,…., 8).

Objective Function (FO):

Restrictions:

Quantity:

∑

i = 1

(X ij)

1. Xij ≤

% (NRIEA) For i = 1,2,…, n and j = 1,2,…, 12

These restrictions are repeated for each of the eight specialties treated up to a total of 96 restrictions of this type.

Capacity:

There are also a total of 12 of these types of restrictions.

Non-negativity condition:

X ij ≥ 0 where:

NRIEA: Real needs for elective interventions per year. Those that can really be done according to the efficiency index.

%: percentage that represents the specialty of the total NRIEA, according to time series.

CRIEM: real capacity according to the time fund allocated for month j, taking the efficiency index per room as a reference.

n: number of specialties.

In this way, the problem statement is left with a total of 109 restrictions and an objective function.

The calculations made to perform certain mathematical devices are shown below, changing the coefficients of all the variables in the restrictions with a percentage value that will guarantee the frequency of occurrence detected in the forecasts made, with an example of each of the restrictions (see takes as a sample the specialty of Otorhinolaryngology, ENT).

X11 + X12 + X13 + X14 + X15 + X15 + X16 + X17 + X18 + X19 + X110 + X112

≤ 0.1591 * (NRIEA)

The number of operations in the Otorhinolaryngology (ENT) specialty represented 15.91%, on average, of the total elective interventions carried out during the study period, while in January it represented 6.83% of the total for the month or a close figure in the same month of each of the years recorded since 2003, but the most important thing was to keep the proportional increase or decrease in the future. The steps followed are shown below:

(forecast of interventions for 2007 of the ENT specialty in January)

This procedure is repeated for each of the specialties in each of the months, leaving the restriction in the input matrix as exemplified below, with one for quantity and another for capacity, repeating the procedure for all the others.

0.92X11 ≤ 4393

where 4393: the real needs for interventions for 2007, assuming there are no delays from 2006.

Capacity Restriction:

X11 + X21 + X31 + X41 + X51 + X61 + X71 + X81 ≤ 283.5; being 283.5, the real capacity for elective interventions in the month of January.

From the results obtained, the positive behavior of the following indicators can be verified:

Use of the Surgical Time Fund per month Use of the Surgical Capacity installed in elective surgery Reduction of the average length of stay per patient by reducing the waiting queue Balance in the use of the workforce and use of the working day.

These are some of the carriers of the improvements where you can see the result of the proposed procedure.

Conclusions

Currently, the hospital services sector is a subject that has not yet been explored in depth by Industrial Engineers and specialized literature, both nationally and internationally.The combination of mathematical techniques and trial and error methods, of operations research and Statistical analysis, without absolutizing any in particular, is a way to achieve high levels of efficiency in organizations that offer hospital services and in all those engaged in improving their competitiveness. The possibility of developing a procedure for planning, programming and control was demonstrated. of surgical interventions that improve hospital indicators and therefore should achieve the corresponding reduction in costs associated with them,regardless of the theoretical and methodological value of said procedure.

Bibliographic references

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