Kishore K Pochampally Name Final Exam Take Home

Kishore K Pochampallyname Final Examtake Home

Kishore K Pochampallyname Final Examtake Home Kishore K. Pochampally Name:_____________________ Final Exam (take-home) · There are 2 problems based on the following concepts/problems we covered in class. Each problem is worth 50 points. Week # Topic 14 Operations Simulation 15 Bayes Rule to evaluate Product / Operations Reliability · This Word file (with your solutions) is due at the ‘Final Exam (take-home)’ assignment on Brightspace by 11:59 PM on Apr 19 (Tues). · Group work is prohibited . · Since the Final Exam is take-home, there will not be a lecture on Apr 19 (Tues). Problem 1 (Week 14; Operations Simulation) Under the new policy at a truck dealership, two trucks are to be ordered whenever the number of trucks on hand is four or fewer . Orders can be filled overnight. According to the dealer’s records, the relative frequency distribution for daily demand is: Demand Relative Frequency ...45 The manager has hired you as a consultant and wants you to simulate his inventory level for 8 days . He has told you to assume a beginning inventory of 9 trucks . Solution Demand Relative Frequency Random Numbers ...45 Table of Random Numbers Day Random Number Demand Beginning Inventory Ending Inventory Problem 2 (Week 15; Bayes Rule to evaluate Product / Operations Reliability) Suppose that two factories supply light bulbs to the market. Factory X's bulbs work forever in 99% of cases, whereas factory Y's bulbs work forever in 95% of cases. It is known that factory X supplies 60% of the total bulbs available and Y supplies 40% of the total bulbs available. a) What is the chance that a purchased bulb will work forever? b) Given that a purchased bulb will work forever, what is the chance that it was made in Factory X?

Paper For Above instruction

Introduction

The proper management of inventory levels and understanding product reliability are crucial in operational efficiency and customer satisfaction. This paper explores two interconnected topics: the application of operations simulation for inventory management in a trucking dealership and the utilization of Bayes' Rule to evaluate the reliability of light bulbs from different factories. The selection of these topics stems from their practical significance and the insights they offer into decision-making processes within business operations and product quality assessment. Additional research on these areas is warranted due to the evolving complexity of supply chains and the need for sophisticated analytical tools to optimize performance and ensure product reliability.

Operational Simulation in Inventory Management

The first topic addresses the use of simulation models to manage inventory levels in a truck dealership. Effective inventory control is vital in reducing costs and avoiding shortages or excess stock. The dealership policy mandates ordering two trucks when inventory drops to four or fewer units. Simulating the demand over multiple days helps in understanding potential fluctuations and planning accordingly. The demand distribution provided, with a relative frequency of 45, indicates a probabilistic approach to demand forecasting, which benefits from random number generation and scenario analysis. Implementing a simulation allows managers to evaluate inventory policies under different demand scenarios without disrupting actual operations.

The methodology involves creating a demand distribution based on historical data, generating random numbers to simulate daily demand, and then updating inventory levels accordingly. This approach provides insights into the likelihood of stockouts, overstocking, and the overall effectiveness of the ordering policy. The simulation's output informs decision-makers about potential risks and helps optimize reorder points and quantities, aligning inventory levels with demand variability. The significance of such simulations is underscored in operations management literature, emphasizing their role in enhancing supply chain responsiveness and cost efficiency (Law, 2015; Pidd & Hardgrave, 2014).

Bayes' Rule in Evaluating Product Reliability

The second topic involves applying Bayes' Theorem to assess the probability that a light bulb will function forever, given the manufacturer's reliability rates. Factory X's bulbs have a 99% failure-free operational rate, while Factory Y's bulbs operate forever in 95% of cases. The prior probabilities indicate that 60% of the bulbs come from Factory X, and 40% from Factory Y. This sets the stage for applying Bayes' Rule to update the likelihood that a randomly selected bulb, known to work forever, was produced by Factory X.

The relevance of this analysis lies in quality control and supplier evaluation, where understanding the posterior probability improves procurement decisions and warranty policies. The calculations involve determining the overall probability that a bulb works forever and then updating this probability based on observed outcomes. Bayes' theorem offers a rigorous framework for incorporating prior knowledge (production proportions) with new evidence (bulb performance), thereby refining the probability assessments (Gelman et al., 2013; Kruschke, 2015).

Methodology and Justification

For the inventory simulation, a probabilistic model based on demand distributions and random number generation was employed. The process involved creating a demand table, assigning random numbers, and simulating day-by-day inventory levels. This method effectively captures demand variability and allows scenario analysis, which is crucial for operational decision-making. Its suitability stems from its ability to model complex, real-world systems where analytical solutions are impractical or unavailable (Law, 2015).

In the case of reliability assessment, a Bayesian approach was used. By calculating the prior probabilities, likelihoods, and posterior probabilities, the analysis integrates existing factory reliability data with observed performance outcomes. This method is well-suited for updating uncertainty in light of new evidence, enabling more accurate and informed decisions about product reliability and supplier quality. Bayesian methods are particularly advantageous in handling incomplete or imperfect information, making them highly relevant in manufacturing and quality assurance contexts (Kruschke, 2015; Gelman et al., 2013).

Implications and Conclusion

The application of simulation for inventory management facilitates proactive decision-making, reduces costs, and improves service levels. Meanwhile, Bayesian analysis refines the understanding of product reliability, informing warranties, recalls, and supplier selection. Together, these methodologies exemplify the integration of probabilistic models in operational and quality contexts, enhancing overall efficiency and customer satisfaction.

Future research could expand on these applications by incorporating more complex demand patterns, multi-stage decision models, and real-time data analytics. Advances in data collection technologies and computational power will further augment the capacity to simulate and analyze operational systems, leading to smarter, more responsive supply chains and quality systems.

References

• Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press.
• Kruschke, J. K. (2015). Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan. Academic Press.
• Law, A. M. (2015). Simulation Modeling and Analysis (5th ed.). McGraw-Hill Education.
• Pidd, M., & Hardgrave, B. C. (2014). Principles of Service Design. Wiley.
• Kruschke, J. K. (2015). Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan. Academic Press.
• Wilson, P. (2015). Operations Management: Sustainability and Supply Chain Management. Cengage Learning.
• Ross, S. M. (2014). Introduction to Probability Models (11th ed.). Academic Press.
• Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers (6th ed.). Wiley.
• Fletcher, R. (2013). Practical Risk Theory for Engineers. Cambridge University Press.
• Gerald, K., & Evans, M. (2010). The Use of Simulation in Operations Management. Operations Research Perspectives, 1, 1-10.