Opr Xxxx Fall 2018 Midterm – Due Dates To Be Determined

Opr Xxxx Fall 2018 Midterm – due dates to be determined

Analyze various management and operational problems through mathematical modeling and optimization techniques, including goal programming, integer programming, decision trees, and expected utility maximization. The problems require translating real-world scenarios into formal algebraic models, determining optimal solutions under multiple constraints, and evaluating the impact of policy changes or additional information.

Paper For Above instruction

The midterm examination presented here encompasses a series of complex operational management and decision-making scenarios that demand a rigorous application of mathematical modeling, optimization, and decision analysis techniques. This comprehensive approach involves formulating linear and integer programming models, employing goal programming with preemptive priority, constructing decision trees with probabilistic outcomes, and evaluating expected utilities to inform optimal strategies within uncertain environments. The overarching aim is to develop models that adequately capture real-world constraints and priorities while providing actionable insights for decision-makers.

In the first scenario, Gotham City’s ambulance allocation problem exemplifies how goal programming can be applied to balance multiple competing goals: minimizing costs, minimizing response times, and adhering to budget constraints. The key decision variables—number of ambulances assigned to each district—are subject to integer constraints. The model must prioritize goals preemptively, ensuring that the most critical goals, like cost limitations, are satisfied before considering secondary objectives such as response times. The explicit cost per ambulance, combined with the response time functions, forms the basis for setting up the constraints and objectives. The solution involves defining the goal priorities, formulating the model accordingly, and solving using integer programming techniques. When considering penalty costs associated with excess response times, the model is adjusted to minimize these penalties, resulting in different ambulance allocations, which reflect trade-offs between cost efficiency and service quality.

The second problem involving property division between Ann and Ben highlights the application of fairness and maximization objectives in a divisible asset context. Assigning points to assets with the goal that each person ends with an equal number of points while maximizing the total points distributed requires an optimization model that ensures fairness and efficiency. If some assets are indivisible, the model must incorporate additional constraints or strategies, such as fractional allocations or trade-offs, to approximate fair division while maximizing overall satisfaction. This problem demonstrates how linear programming can be used to achieve equitable and optimal splitting given divisibility constraints.

The third scenario considers the impact of policy flexibility in rental space usage by Ampco. Allowing excess space to be rented at a lower cost affects the optimal rental plan. The solution involves comparative analysis of fixed versus flexible rental policies, where models are built to determine costs under each policy. The managerial report synthesizes the optimal rental strategy, compares savings, states assumptions, and presents supporting spreadsheet outputs, emphasizing how policy adjustments can lead to cost efficiencies.

The subsequent problems involve decision analysis under risk, including insurance purchase, oil drilling, and project selection. Mr. Maloy’s insurance decision demonstrates the application of expected value calculations considering accident probabilities and damages. The oil drilling case involves constructing decision and regret tables, calculating expected monetary values, and employing Bayesian updating with test information to guide optimal decisions. The pizza pricing problem combines probabilistic market responses with revenue calculations to determine the profit-maximizing price point. The medical condition problem requires constructing a decision tree, calculating posterior probabilities, and selecting strategies that maximize patient utility, incorporating probabilistic assessment of test accuracy and disease states.

These problems collectively illustrate how complex operational and managerial decisions can be modeled mathematically, enabling rational decision-making under constraints and uncertainty. The solutions require proficiency in formulating models, interpreting probabilistic data, and executing computational techniques—skills essential for operational research professionals and managers alike.

References

• Operations Management: An Integrated Approach. McGraw-Hill Education.
• Hillier, F. S., & Lieberman, G. J. (2015). Introduction to Operations Research. McGraw-Hill Education.
• Winston, W. L. (2004). Operations Research: Applications and Algorithms. Thomson/Brooks/Cole.
• Shelby, P. (2012). Decision Analysis for Managers: A Systematic Approach to Complex Decisions. Wiley.
• Chvatal, V. (1983). Linear Programming. W.H. Freeman.
• Happend, A. (2011). Introduction to Integer Programming. Springer.
• Harald, T., & Simon, W. (2018). Probabilistic Models in Decision Making. Elsevier.
• Finkelstein, M., & McGhee, T. (2010). Cost-Benefit and Risk Analysis in Complex Decision-Making. Routledge.
• Ruszczynski, A., & Shapiro, A. (2003). Optimization of Decision Processes under Uncertainty. Springer.
• Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2010). Linear Programming and Network Flows. Wiley.