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1) At the beginning of each week, a machine is either running or broken down. If the machine runs throughout the week, it earns a revenue of $100. If the machine breaks down during a week, it earns no revenue for that week. If the machine is running at the beginning of the week, it has a 75% chance of breaking down during that week. We may either do nothing or perform maintenance or replace the machine. If maintenance is performed the chances of a breakdown reduce to 25%. Maintenance costs is $20. Replacing the machine with a new one costs $80 but the new machine is guaranteed to run throughout the first week of its operation, If the machine breaks down during a week, it must be repaired or replaced at the beginning of the following week. Repairing a machine, costs $40 and the probability that a repaired machine will break down during the week is %25. Maintenance, repair, and replacement occur instantaneously, meaning that these actions take an instant and the machine starts working for the week immediately. Use dynamic programming to determine a repair, replacement, and maintenance policy that maximizes the expected net profit earned over a three-week period. Assume that the machine is running at the beginning of the first week. Write down how you define the stages, the states, and the decisions clearly. Express the optimal

1) At the beginning of each week, a machine is either running or broken down. If the machine runs throughout the week, it earns a revenue of $100. If the machine breaks down during a week, it earns no revenue for that week. If the machine is running at the beginning of the week, it has a 75% chance of breaking down during that week. We may either do nothing or perform maintenance or replace the machine. If maintenance is performed the chances of a breakdown reduce to 25%. Maintenance costs is $20. Replacing the machine with a new one costs $80 but the new machine is guaranteed to run throughout the first week of its operation, If the machine breaks down during a week, it must be repaired or replaced at the beginning of the following week. Repairing a machine, costs $40 and the probability that a repaired machine will break down during the week is %25. Maintenance, repair, and replacement occur instantaneously, meaning that these actions take an instant and the machine starts working for the week immediately. Use dynamic programming to determine a repair, replacement, and maintenance policy that maximizes the expected net profit earned over a three-week period. Assume that the machine is running at the beginning of the first week. Write down how you define the stages, the states, and the decisions clearly. Express the optimal

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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1) At the beginning of each week, a machine is either running or broken down. If the machine runs throughout the week, it earns a revenue of $100. If the machine breaks down during a week, it earns no revenue for that week. If the machine is running at the beginning of the week, it has a 75% chance of breaking down during that week. We may either do nothing or perform maintenance or replace the machine. If maintenance is performed the chances of a breakdown reduce to 25%. Maintenance costs is $20. Replacing the machine with a new one costs $80 but the new machine is guaranteed to run throughout the first week of its operation. If the machine breaks down during a week, it must be repaired or replaced at the beginning of the following week. Repairing a machine, costs $40 and the probability that a repaired machine will break down during the week is %25. Maintenance, repair, and replacement occur instantaneously, meaning that these actions take an instant and the machine starts working for the week immediately. Use dynamic programming to determine a repair, replacement, and maintenance policy that maximizes the expected net profit earned over a three-week period. Assume that the machine is running at the beginning of the first week. Write down how you define the stages, the states, and the decisions clearly. Express the optimal strategy explicitly.
Transcribed Image Text:1) At the beginning of each week, a machine is either running or broken down. If the machine runs throughout the week, it earns a revenue of $100. If the machine breaks down during a week, it earns no revenue for that week. If the machine is running at the beginning of the week, it has a 75% chance of breaking down during that week. We may either do nothing or perform maintenance or replace the machine. If maintenance is performed the chances of a breakdown reduce to 25%. Maintenance costs is $20. Replacing the machine with a new one costs $80 but the new machine is guaranteed to run throughout the first week of its operation. If the machine breaks down during a week, it must be repaired or replaced at the beginning of the following week. Repairing a machine, costs $40 and the probability that a repaired machine will break down during the week is %25. Maintenance, repair, and replacement occur instantaneously, meaning that these actions take an instant and the machine starts working for the week immediately. Use dynamic programming to determine a repair, replacement, and maintenance policy that maximizes the expected net profit earned over a three-week period. Assume that the machine is running at the beginning of the first week. Write down how you define the stages, the states, and the decisions clearly. Express the optimal strategy explicitly.
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