To what extent may the concept of optimality be used in dynamic programming?

Server Farm Inc. (SFI) needs to upgrade its servercomputers. Company management has identified thefollowing two options: (1) shift to a Windows‐basedplatform from its current Unix‐based platform, or(2) stick with a Unix‐based platform. It is standardpractice at SFI to use a triangular distribution to modeluncertain costs.Along these lines, the company estimates that if itmigrates to Windows, the new server hardware couldcost as little as $100,000 or as much as $200,000. Thetechnical group’s best estimate is that the hardwareMantel_c04.indd 138 9/6/2016 4:52:35 PMcosts will be $125,000 if the Window’s option is pursued. Likewise, the company’s best guess regarding thecost to upgrade and convert its software to Windows is$300,000 with a range of $275,000 to $500,000.Finally, if the company converts to Windows, employeetraining costs are estimated to range between $9,000and $15,000, with the best guess being $10,000. If thecompany sticks with Unix, the new server hardwarewill most likely…

Case Scenario  Douglas and Associates Construction Limited is a privately owned construction firm based in New Zealand, specializing in the development of affordable alternative housing options, including tiny homes, small residences, and mobile homes. The company utilizes materials such as freight containers and reclaimed or recycled resources. Established in 2000 as a family-run business, the firm has experienced a significant increase in demand for its services, particularly in response to the global rise in real estate prices and the ongoing effects of the pandemic, which have rendered homeownership increasingly unattainable for many individuals. This surge in interest has been further influenced by the "Tiny Home Movement," leading to notable growth in both demand for the company's offerings and expansion into international markets. Currently, Douglas and Associates Construction Limited employs 500 individuals and aims for further growth.    The company is led by co-founders and…

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative d₁ d₂ = EV(d₁) EV(d₂) The optimal decision is ? States of Nature $1 $2 230 80 $3 80 5 Suppose that the decision maker obtained the probabilities P(S₁) = 0.65, P(S₂) = 0.15, and P(S3) = 0.20. Use the expected value approach to determine the optimal decision. 80 55

How did you find the solutions in the table for the range of optimality for the profit coefficient?

Uncertainties and risks are always associated with large real world projects and may obstacle and threaten projects in some ways. Failure in accurately identifying the project risks increases the total cost and may cause social and environmental damages as well as casualties during project execution. The aim of this study is to develop a mathematical programming model for selecting risk response strategies for construction projects. All risk response strategies for the analysed project have been identified and a mathematical model is presented based on project iron triangle; time, cost and quality to obtain the optimal risk response strategy for the construction project.Uncertainties and risks are the inherent characteristics of the real world construction projects. The project risk management deals with identifying and controlling the risks before they occur. Various risks happen in project execution phase which may reduce the performance efficiency and even cause the project failure.…

A decision maker is faced with a choice between two projects, both of which have start-up costs in the first year of $150m and project closing costs of $20m in year 5. Project A is expected to generate net returns of $10m, $20m, $50m and $200m from year 2 to year 5 respectively. Project B is expected to generate net returns of $100m, $80m, $50m, and $20m for year 2 to year 5 respectively. a) Show whether these projects are viable at discount rates of 1% and 10%. b) Show which project is preferred at 1% and which at 10%. c) Offer an intuitive explanation for your preferences at different interest rates d) If these are public sector projects, state two other considerations that could affect the choice of the project.

Suppose you have a choice of three projects to choose from. Here the expected profits from these projects under the following economic scenarios: Project Poor/Fair Moderate/Stable Strong/Booming A -200 $400 $700 B -700 600 1200 C 100 500 900 Now suppose the probability of a Poor/Fair economy is 25%, a Moderate/Stableeconomy is 45% and there is a 30% chance for a Strong/Booming economy.A) Setup a decision tree.B) Determine the expected value (EV) for each project. What project shouldbe selected based on the expected value approach? Why?C) Determine the expected value with perfect information about the states ofnature?D) Determine the expected value without perfect information about the states ofnature?E) Determine the expected value of perfect information.