A simulation model is a computer model that imitates a real-life occurrence. The computer model explicitly incorporates uncertainty in at least one input variable, and thus facilitates effective tracking of any resulting output variables of interest. Therefore, with the use of these simulation models, once can easily see how outputs vary as a function of the varying input. Simulation models have acquired a variety of application in the healthcare sector. Today, simulation techniques, such as the Markov models, the discrete-event simulation, the system dynamic modelling, and SD+, among others are evident in the healthcare sector. Furthermore, tools such as the @RISK, which is an add-in the Microsoft Excel have become essential in addressing multiple simulation problems in hospital operations and management.
The Markov models can be used to describe a sequence of possible events where the probability of each event depends on the state that is attained in the previous occurrence. Various variations of the Markov model, include the Hidden Markov model, the Markov chain, the Markov chain Monte Carlo, and the Markov decision process, among others. The simulation model is overly employed in the defensible resource allocation decisions. The model can also be used in hospital planning and management. Short-term hospital operations improvement, particularly staffing costs, hospital bed management, and inpatient placement, can be achieved with the aid of the Markov model.
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The Discrete Event Simulation (DES), on the other hand, is employed in modeling operation of systems with discrete sequence of events of a given period. Previous application of the simulation technique in the healthcare sector include the containment of hospital acquired infections, planning for disease outbreak, analyzing hospital bed requirement, and the identification of appropriate ordering policies in the blood supply chain. Other application of this modelling technique include the planning, scheduling, reorganization and management of healthcare and hospital services, as well as economic evaluation.
The system dynamic modeling (SD) is efficient when analyzing the behavior of a complex system over a given duration. It addresses internal feedback loops and time delays that impact on the behavior of the entire system. The computer-based analytical modelling approach facilitates the observation of the previous, current, and the anticipated future changes. In other instances, hospitals may use the system dynamic modeling technique and the DES techniques simultaneously in the analyzing of hospital operation and management.
The @RISK Excel add-in is one of the commonly used tool in the simulation of various healthcare problems. The tools addresses various probability distribution problems including uniform, normal, discreet, and gamma distribution, among others. In the problem discussed below, the RiskNormal and the RiskGamma, along with the Risksimtable functions of the @RISK Excel add-in have been employed to solve Problem 40.
Problem 40
The worksheet used to solve the problem is as below:
The simulation was conducted six time with iteration of 1000. The simulation analyzes a one-year medical expenses, contribution and taxes. The salary retained is the amount left upon the payment of the medical expenses, the contribution, and the 30% tax. The graph representing the medical expenses is as show below:
With the salary retained cell (Cell C12) being the output cell, six simulations with 1,000 iterations produced the optimal FSA contribution as shown below:
The optimal FSA contribution according to the simulation is $1,800. With the contribution of $1,800, the salary retained will be at its maximum of $53,740 as shown below: 
In part b, the RiskGamma function was used instead of the RiskNormal function in cell B12.
Therefore, the distribution is slightly skewed. The medical expenses graph is as shown below:
The optimal FSA contribution is $1,000, which is relatively low compared to when a normal distribution is used as shown below:
