Galaxy Co. distributes wireless routers to Internet service providers. Galaxy procures each router for $75 from its supplier and sells each router for $125. Monthly demand for the router is a normal random variable with a mean of 100 units and a standard deviation of 20 units. At the beginning of each month, Galaxy orders enough routers from its supplier to bring the inventory level up to 100 routers. If the monthly demand is less than 100, Galaxy pays $15 per router that remains in inventory at the end of the month. If the monthly demand exceeds 100, Galaxy sells only the 100 routers in stock. Galaxy assigns a shortage cost of $30 for each unit of demand that is unsatisfied to represent a loss-of-goodwill among its customers. Management would like to use a simulation model to analyze this situation.

a. What is the average monthly profit resulting from its policy of stocking 100 routers at the beginning of each month?
b. What percentage of total demand is satisfied?

Sales. Every unit sold adds (125-75)=$50 to the profit. We have to consider the condition that the maximum amount of units that can be sold is 100 units.
The remains cost. If the monthly demand is under 100 units, the profit is reduced by $15 per each remaining unit.
The shortage cost. For each unit demanded that exceeds the 100 units, the profit is reduced by $30.

The equation can be expressed as:

[tex]Profit=50*Max(Q;100)-15*Max(100-Q;0)-30*Max(Q-100;0)[/tex]

A simulation with 10,000 trials is done, and the average monthly profit calculated for this policy is $4237.

The demand was calculated with the Excel function INT(NORMINV(RAND(),100,20)), to mimic a normal distribution with mean 100 and standard deviation 20.

b) The satisified demand is calculated for each trial as the minimum value between Q (quantity demanded) and 100, as if Q is bigger than 100, only 100 units of the demand are satisfied.

The percentage of total demand satisfied is:

[tex]\%Satisfied=\dfrac{Q_{satisf}}{Q}=\dfrac{918759}{997005}=0.9215=92\%[/tex]