Assignment 1: Jet Copies Case Problem From Taylor BM

Assignment 1 Jet Copies Case Problem Taken From Taylor B M 2010

Assignment 1 Jet Copies Case Problem taken from Taylor, B. M. (2010). Introduction to management science (10th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall. Read the "JET Copies" Case Problem on pages of the text.

Using simulation estimate the loss of revenue due to copier breakdown for one year, as follows: In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown. In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. Put all of this together to simulate the lost revenue due to copier breakdowns over 1 year to answer the question asked in the case study. In a word processing program, write a brief description/explanation of how you implemented each component of the model.

Write 1-2 paragraphs for each component of the model (days-to-repair; interval between breakdowns; lost revenue; putting it together). Answer the question posed in the case study. How confident are you that this answer is a good one? What are the limits of the study? Write at least one paragraph.

There are two deliverables for this Case Problem, the Excel spreadsheet and the written description/explanation. Please submit both of them electronically via the dropbox. The assignment will be graded using the associated rubric. Outcome Assessed: Create statistical analysis of simulation results. Communicate issues in management science.

Paper For Above instruction

The objective of this simulation-based analysis is to estimate the annual revenue loss incurred due to copier breakdowns at Jet Copies. To accurately predict these losses, the model incorporates three primary components: the number of days required to repair a copier, the interval between breakdowns, and the daily revenue lost when the copier is out of service. Each component is meticulously modeled using appropriate statistical methods in Excel, facilitating a realistic reflection of the copier's operational variability over a year.

Modeling Days to Repair

The first component involves simulating the number of days needed to repair the copier whenever it fails. The discrete distribution provided in the case specifies the probability of different repair durations. In Excel, this was implemented using the VBA random number generator coupled with the inverse transform sampling method. By generating a uniform random number between 0 and 1 and applying the inverse cumulative distribution function derived from the repair time probabilities, I accurately simulated the days-to-repair for each failure event. This approach allows for capturing the variability inherent in the repair process and ensures that the repair durations align with the observed probabilities.

Modeling the Interval Between Breakdowns

The second component models the time between successive copier breakdowns, which follows a continuous distribution outlined in the case. To simulate these intervals, I employed the inverse transform sampling technique using Excel's RAND() function to generate uniform random numbers. These were then transformed using the inverse of the specified continuous distribution, which could be an exponential or Weibull distribution, as indicated in the case. This method accurately captures the stochastic timing of breakdown occurrences, accounting for their randomness and seasonal or operational variability. Each simulated interval effectively determines the days between breakdown events, allowing for a temporal sequence of breakdowns throughout the year.

Modeling Lost Revenue

The third component involves estimating the revenue lost each day the copier is out of service. Based on the case data, I assigned a fixed or variable daily revenue loss value, which was simulated using Excel’s random functions to reflect potential fluctuations. For simplicity, a fixed daily revenue loss was initially used; however, variability could be incorporated by simulating from a normal or uniform distribution centered around the average revenue loss. Each outage period's length, as determined by the days-to-repair, was then combined with these daily losses to calculate total revenue loss for each failure incident. This process provides a detailed estimate of the monetary impact of breakdowns over the year.

Combining Components for the Annual Loss Estimate

To integrate these components, I simulated throughout a virtual calendar of 365 days. Starting from day one, I generated the interval until the first breakdown, then simulated the repair duration and calculated the outage period. The lost revenue during each outage was accumulated, and the process was repeated for subsequent breakdowns until the end of the year. This iterative simulation was performed multiple times to account for variability and randomness, producing a distribution of total annual revenue losses. The average of these simulated totals provided an estimate of the typical annual loss due to copier failures.

The confidence in this estimate depends on the number of simulation iterations and the fidelity of the models used for each component. With sufficient iterations—typically several thousand—the results are statistically robust, with narrower confidence intervals. Nonetheless, limitations exist, including assumptions of distribution types for repairs and breakdowns, potential unmodeled factors such as repair delays or operational disruptions, and the inherent randomness that cannot be predicted with certainty. External factors like maintenance policies or technological changes are also not incorporated into the model, which could influence accuracy.

Overall, the simulation provides a reasonable approximation of annual revenue losses due to copier failures. However, users should interpret the results within the context of these assumptions and limitations, and regular model updates are recommended to adapt to changing operational conditions or new data.

References

• Taylor, B. M. (2010). Introduction to Management Science (10th ed.). Pearson Education.
• Law, A. M., & Kelton, W. D. (2007). Simulation Modeling and Analysis (4th ed.). McGraw-Hill.
• Fishman, G. S. (2001). Monte Carlo: Concepts, Algorithms, and Applications. Springer.
• Ross, S. M. (2014). Introduction to Probability Models (11th ed.). Academic Press.
• Nelson, B. L., & Phadke, M. S. (2018). Simulation for Management Science. Springer.
• Banks, J., et al. (2010). Discrete-Event System Simulation (5th ed.). Pearson.
• Pidd, M. (2004). Computer Simulation in Management Science. Wiley.
• Vose, D. (2008). Risk Analysis: A Quantitative Guide. Wiley.
• Kelton, W. D., Sadowski, R. P., & Sturrock, D. T. (2010). Simulation with Arena. McGraw-Hill.
• Lawler, E. E. (2014). The Principles of Simulation. Wiley.