Mat540 Homework Week 3: Simulation And Analysis Of Emergency

Mat540 Homework Week 3: Simulation and Analysis of Emergency Calls and Maintenance Data

The assignment involves simulating various operational scenarios such as emergency call arrivals, vehicle arrivals at a service station, machine breakdowns, weather-dependent sales decisions, and repair times at a manufacturing plant. The goal is to use probability distributions and random number simulations to analyze these processes and make informed decisions based on the results. For each scenario, the tasks include generating simulated data, calculating averages, comparing simulated outcomes with expected values derived from probability distributions, and providing interpretations of the findings.

Paper For Above instruction

Introduction

The use of simulation techniques in operational analysis provides invaluable insights into complex or stochastic systems. This paper explores several case studies involving emergency call arrivals, vehicle arrivals at a fueling station, machine breakdowns, sales decision-making under varying weather conditions, and machine repair times. By leveraging probability distributions and random number generation, we aim to estimate average behaviors, compare simulated results with theoretical expectations, and support decision-making processes.

Simulation of Emergency Call Arrivals

The first scenario examines the time between emergency calls received by the Hoylake Rescue Squad. The data is based on a probability distribution of the time between calls in hours with associated probabilities and cumulative probabilities. To simulate the calls, a random number table is used where random numbers map to specific time intervals based on their position relative to the cumulative probability ranges.

Using random numbers, three calls over a 3-day period are simulated. The random numbers selected yield intervals of 2, 6, and 3 hours between calls. The average simulated time between calls is thus (2 + 6 + 3)/3 = 3.667 hours. The expected value, calculated from the distribution, is a weighted sum: (1×0.05) + (2×0.10) + (3×0.30) + (4×0.30) + (5×0.20) + 6×0.05 = 3.65 hours. The close proximity of both results confirms the accuracy of the simulation but also demonstrates the variability inherent in small sample simulations compared to the expected theoretical mean.

Vehicle Arrivals at Petroco Service Station

The second scenario analyzes vehicle arrivals within a specified period. The probability distribution indicates the time between arrivals in minutes with associated probabilities. The total time for 20 arrivals is summed as 41 minutes, leading to an average interarrival time of 41/20 = 2.05 minutes. To enhance accuracy, a second simulation uses a different set of 20 random numbers summing to 46 minutes, resulting in an average of 2.391 minutes per interval. The discrepancy between the two outcomes reflects the randomness of arrivals and emphasizes that larger samples tend to stabilize estimations around the true mean.

Machine Breakdowns in a Manufacturing Setting

Next, the scenario involves the weekly number of machine breakdowns at Dynaco Manufacturing, modeled by a specific probability distribution. Over 20 weeks, the total number of breakdowns observed is 51, yielding an average of 2.55 breakdowns per week. Simulation with random numbers extends this analysis to estimate weekly breakdowns, which help in scheduling maintenance and planning inventory. The results under investigation highlight the practical application of probability models in predicting operational disruptions.

Decision-Making Based on Weather Conditions

The fourth case examines a managerial decision about selling sun visors or umbrellas during an outdoor football game, considering the weather forecast. Probabilities for rain, overcast, and sunshine are 30%, 15%, and 55% respectively. Each choice’s profit is contingent on weather conditions, with simulation applied to assign weather scenarios based on random numbers. The analysis shows higher average profits from selling sun visors (average $920) than umbrellas (average $54.50), favoring the sun visor decision. This illustrates how probabilistic models can guide operational decisions in uncertain environments.

Repair Time at Dynaco Manufacturing

The final scenario involves simulating the repair times for machine breakdowns, modeled with three possible durations: 1, 2, or 3 hours, with respective probabilities. Using random numbers, the total repair time over 20 weeks is estimated at 38 hours, averaging 1.9 hours per week. This estimate assists in capacity planning and resource allocation in maintenance scheduling.

Conclusion

The simulations demonstrate that stochastic modeling provides realistic insights into operational variability and aids in decision-making. Although small sample sizes may deviate from theoretical expectations, larger simulations tend to converge towards the expected values, reinforcing the importance of understanding probability distributions in managing operations. The integration of random number techniques with probability models stands as a powerful tool for operational analysis in various industries.

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