RENO Solution:

Define a Random Variable to describe the demand for newspapers.

Define a Constant that represents the number of papers that the newspaper boy buys. This will be varied during the simulation to determine the optimum quantity.

Define an Equation Variable to calculate the newspaper boy’s supply costs, which is the quantity of papers purchased (represented by the “Quantity” Constant) multiplied by 15 cents.

Construct the flowchart as follows:

Step 1: Use a Block to determine the demand for the newspapers based on the Random Variable called “Demand.”

Step 2: Use a Conditional Block to check whether the amount of papers on hand (represented by the Constant called “Quantity”) is equal to or greater than the demand determined in the previous step. If true, then the quantity of papers sold is equal to the Demand and this number is passed to the TRUE path. If false, then the quantity of papers sold is equal to the Constant called “Quantity” and this number is passed to the FALSE path.

Steps 3a and 3b: Use two Blocks called “Revenue 1” and “Revenue 2” to calculate the amount of revenue from the TRUE and FALSE paths. When supply meets or exceeds demand, this is the demand quantity passed from the Conditional (represented in the equation by the reserved keyword IN) multiplied by the price (25 cents) less the supply cost (represented by the Equation Variable called “Cost”), as shown next. A similar equation is defined for the FALSE path, where the number of papers sold is equal to the Constant called “Quantity.”

Step 4: Use a Result Storage construct to calculate and store the average revenue from all simulations.

For this example, it is important to note that a single simulation run provides a single answer; thus multiple runs will be needed to arrive at an optimum solution. This can be done using the Sensitivity Analysis page in the Simulation Console.

To first explore the area from 50 to 150, specify 500 simulations (with a seed of 1 for repeatability) on the General page of the Simulation Console then set the Sensitivity Analysis page as shown next.

RENO will perform 500 simulations per run, with the Quantity set to 50 for the first run, 60 for the second run, and so on up to 150. After the simulation completes, the plot indicates that the optimum value lies somewhere between 80 and 100.

The next plot shows the results from repeating the simulation with the Quantity varied from 80 to 100 and incremented by 1.

Given the small number of simulations (500), noise is present. The next step is to increase the number of simulations to 50,000 and focus on the region between 90 and 96, incrementing by 1, as shown next.

In addition to the manual technique described above, RENO can automatically perform multiple analyses designed to determine the quantity that will maximize revenue. To do this, specify 2,000 simulations on the General page, specify 60 to 120 with an increment of 12 on the Sensitivity Analysis page and configure the Multiple Analyses page as shown next.

The resulting plot of Average Revenue vs. Quantity will include a marker and a line to identify the optimum value, as shown next.

A RENO project with the solution for this example (called "Newspaper Boy.rnp") is shipped with the software and stored in the Examples\Reliability folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\Optimization\Newspaper Boy.rnp).