24-09-2012, 12:19 PM
Simulation Analysis
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INTRODUCTION
A simulation is the imitation of the operation of a real-world process or system. The behavior of a system is studied by generating an artificial history of the system through the use of random numbers. These numbers are used in the context of a simulation model, which is the mathematical, logical and symbolic representation of the relationships between the objects of interest of the system. After the model has been validated, the effects of changes in the environment on the system, or the effects of changes in the system on system performance can be predicted using the simulation model. 1
Gnumeric includes a facility for performing Monte Carlo Simulation. Monte Carlo simulation involves the sampling of random numbers to solve a problem where the passage of time plays no substantive role. 2 In other words, each sample is not effected by prior samples. This is in contrast to discrete event simulation or continuous simulation where the results from earlier in the simulation can effect successive samples within a simulation experiment. The Monte Carlo simulation will be enabled through the use of the Random Number functions as described in ? and the results presented along with statistics for use in analysis.
Setting up the simulation model
The remainder of this chapter will illustrate use of the simulation tool using an example from Banks et. al. 1 A classic inventory problem is the newsvendor problem. A newsvendor buys papers for 33 cents each and sells for 50 cents. Newspapers not sold are sold as scrap (recycled) for 5 cents. Newspapers are purchased by the paper seller in bundles of 10. Demand for newspapers can be categorized as “good,” “fair,” or “poor” with probability 0.35, 0.45 and 0.20 respectively, with each day's demand being independent of prior days. The problem for the newsvendor is to determine the optimal number of papers to purchase when the day's demand is not yet known.
The daily profit equation for the newsvendor is:
Profit = [(Sale revenue) - (Cost) - (Scrap value)]
To set up the model, this example will use two tabs in Gnumeric, a tab labeled 'Profit' to calculate profit, and a tab labeled 'Demand Tables' to store the various tables needed to calculate the demand for any given sampling.
For the Profit tab, set up the profit tab as in Figure 6-1.
At the top of the Profit' tab, the Profit table will be entered . There are three variables: Sale revenue, Cost and Scrap value, and they take the per unit coefficients of 0.5, 0.33 and 0.05 respectively. Enter the coefficients in cells B13 through D13. In cells B12 through D12, enter the equations for sale revenue, cost and Scrap value that are in the list below. In cell E12, enter the equation for Profit