The Revenue Loss Estimation Problem at JET Copiers - Essay Example

II. The Simulation Tool
Such a business case demonstrates yet again how statistics can be used to reduce uncertainty. In particular, simulation modeling enables the quantification of events and outcomes with varying probabilities. Previewing all possible outcomes with unknown probabilities of occurrence helps to assess potential costs and benefits. Monte Carlo simulation is one such procedure that applies (Doane & Seward, 2007; Stout, 2007).

III. The Solution Parameters
The case requires accommodating the varying probabilities of three random variables that impact gross revenues (otherwise known as the stochastic input variables):
1. Demand of between 2,000 and 8,000 copies per day at $0.10 per copy.
2. Frequency of equipment breakdowns between 9 and 6 weeks.
3. Repair lead time of between 1 to 4 days.
These parameters require the use of a uniform model, where RV values vary within a given range with no central tendency or standard deviation assumed. For the first step of estimating randomly varying demand, the result of 52 iterations of revenue simulations (see Table 1 below) yields a somewhat skewed distribution with a mean of $540 daily, a median of $542, and a standard deviation of $184. Gross annual revenue before simulating the effect of mechanical breakdown would be $28,109. This is the baseline.

Table 1: Results of 52 Iterations of Revenue Simulation for Range Between $2,000 and $8,000
Class Interval %
$200-299 15.4
300-399 9.6
400-499 19.2
500-599 9.6
600-699 17.3
700-800 28.8

100.0

Next, we factor in the incidence of breakdowns and the lead time for repair. We employ the RAND function to estimate the probability that the copier will be trouble-free all days of the week (instead of defining it as “6 times the square root of r”). For the first week in the all-year iterations, therefore, the RAND value of 0.487 translates to a probability that the main copier will break down after just three days of operation. That same week, repair lead time is calculated using the VLOOKUP function based on the same column of RAND values. Since RAND=0.487 is lower than the 0.65 cumulative probability associated with two days’ repair lead time, the VLOOKUP function returns 1 day. Hence, revenue loss for the week comes to gross revenue times the proportion of 7 days that the main copier can reliably be predicted to work.

IV. Conclusion
As shown by the 52-week iteration in Table 2 overleaf, potential revenue losses do not reach the $12,000 criterion. The three partners need not avail themselves of a second loan for a backup copier. Read More