YASAI (Yet Another Simulation Add-In)

YASAI Functions for Generating Random Variables
These functions return random numbers with specified distributions. They will generally return a different value each time they are called, depending on their arguments. Here are the functions that are currently implemented:

GENUNIFORM(a, b): Both arguments are numbers. Normally, it is expected that a < b. If so, a random number uniformly distributed over the interval [a, b)  -- that is, x such that a < x < b -- is returned. If a = b, then the value a (or equivalently b) is returned. If a > b, an error value is returned.

GENNORMAL(m, s): Both arguments are numbers. If s < 0, an error value is returned. If s is zero, the return value is m. Otherwise, a random value with a normal distribution with mean m and standard deviation s is returned.

GENBINOMIAL(n, p): The first argument n must be a nonnegative integer, and the second argument p must be a number in the range [0, 1]. Otherwise, an error value is returned. If these conditions are met, then the return value is an integer drawn randomly from a binomial distribution with n trials and probability p of success at each trial. Note that if n = 0, then the return value is 0. The implementation is efficient even when n is large.

GENPOISSON(m): The argument m is a nonnegative number. A negative argument causes an error value to be returned. A zero argument causes zero to be returned. Otherwise, the return value is randomly chosen from a Poisson distribution with mean value m. The implementation is efficient even when m is large.

GENTABLE(V, P): The argument V and P are blocks of cells or lists (for example, "{1,3,7}") having the same number of cells.  Essentially, the function returns each value in V with the probability specified by the corresponding element in P.  If the two arguments have the same number of cells but differing numbers of rows and columns, the correspondence is determined by scanning first across the first row, then across the second row, and so forth.  Non-numeric entries in P are treated as if they were zero.  If the two arguments do not have the same number of cells, or if P contains any negative numbers, or if P contains only zeroes, an error value is returned.  If the values in P do not sum to 1, they are rescaled proportionally so that they do.  For example, GENTABLE({1,2,3},{.2,.5,.3}) returns 1 with probability 0.2, 2 with probability 0.5, and 3 with probability 0.3.

GENEXPON(a): The argument must be a positive number, or an error value is returned. If so, the return value is randomly chosen from an exponential distribution with mean value 1/a.

GENTRIANGULAR(a, b, c):  Returns a value from a triangular distribution with minimum a, mode b, and maximum c.  The arguments must be numbers with the property a < b < c, or an error value is returned.

Specifying Scenarios
To specify different trial values for decision variables, YASAI provides the function PARAMETER(L, k, name). The first argument, L, is a block of cells or a list specifying the possible return values. The name argument is a character string describing the parameter, and is used only in the output reports. The k argument specifies the number of scenarios between changes in the parameter. For example, a cell containing =PARAMETER({1,2,3},1, "woof") specifies a parameter called "woof" that will change every scenario, first taking the value 1, then 2, and then 3. A cell containing =PARAMETER({1,8,2.3,-2},2, "snort") defines a parameter called "snort" that takes the value 1 for the first two scenarios, then 8 for the next two, 2.3 for the next two, and -2 for the last two. The argument k makes it possible to try combinations of values of various parameters without having to write every combination out in a list.

Specifying Output
To specify an output of the simulation, use the formula SIMOUTPUT(x, name): This function returns the value x. During simulation runs, the values of x encountered are saved for later analysis, as described below. The argument name is a character string to describe the output in the simulation reports. For example a cell containing =SIMOUTPUT(A4+B7,"profit") defines an output called "profit" whose value is A4+B7.

Running the Simulation
Once you have built your model, specified scenarios (if any), and specified outputs, you can run your simulation. To do so, select "YASAI Simulation" from the Tools menu. This will cause a dialog box to appear.

YASAI analyzes your spreadsheet to determine how many scenarios appear to be needed.  It places this number in the default number of scenarios box.  If this number is satisfactory, click on the "Default" button.  If you would like a different number of scenarios, click on the "set to" button and enter the number of scenarios you want.

The "Sample Size" box is the number of times YASAI will recalculate your model for each scenario.  It defaults to 1000, but you can enter any positive whole number.

 Optionally, you may indicate a fixed random number seed to use, and whether the seed should be reset for each scenario (resetting is good practice, and is the default). Press "Simulate" to start the simulation, or "Cancel" to return to Excel.

The simulation involves only the current sheet of the current workbook. If the number of scenarios" is N, and the "Sample Size" is S, then YASAI will recalculate the current sheet NS times. These recalculations are divided into N blocks of S recalculations, each block constituting a scenario. Output data are collected separately for each scenario, and the values returned by any PARAMETER functions in the sheet will vary from scenario to scenario, as described above.

A "progress" display indicates how quickly the simulation is progressing.  When the simulation is over, there will be a short delay while the outputs are processed. The output report is automatically placed in a new sheet named "Simulation Output n", which YASAI inserts into the current workbook. YASAI makes this report the current sheet and then returns control to Excel. For each output-scenario combination, the report contains the mean, standard deviation, minimum, maximum, and percentiles in 5% intervals. Currently there are no graphics or other output data, although improvements are planned for later versions.

Aborting a Simulation
You can abort a YASAI simulation while it is running by clicking on the "Abort" button, or simply by pressing the escape key on your keyboard. It may take up to 5 seconds for the simulation to abort.

Testing a Model Interactively
To test a model interactively, simply press the F9 key. Excel will perform a single recalculation, drawing new values for all the random variable generation functions. New values will also be generated for each PARAMETER function call.