DYNAMIC PROGRAMMING

The decision maker uses a smart phone. The purchase cost of the smart phone is $4000. The maintenance cost of the phone depends on its age. We denote by m; as the maintenance cost of the phone at its ith year of utilization. The phone can be used up to 3 years. After its ith year, it can be replaced by a new one. It It can also be sold for an amount that is equal to its salvage value, denoted by Si. The values of m and sj are summarized below: Year i 2 3 240 320 480 m ($) Si ($) 3200 2400 2000 Page 2 of 1 You need to determine a replacement policy that minimizes the total cost over the next five years, assuming that at the end of the 5-year period, the analyzer will be sold for its salvage value. A replacement policy means that after the purchase of a new phone, you should know when to replace it with a new one. Suppose that you don't have a phone at the beginning of year one. 1-Define the stages. (5points) 2-Define the states. (5points) 3-what are the decisions that you can make at the beginning of each stage? (10points) 4-Define the recursive function. (10points) 5-Depict the stages and the states in the form of a network. 6-Calculate the minimal cost over the five years 6-a-Stage 5: (10points) 6-b-Stage 4: (10points) 6-c-Stage 3: (10points) 6-d-Stage 2: (10points) Page 4 of 1 6-e-Stage 1: (10points) 7-what is the optimal replacement policy? (when we should replace the phone during the five years horizon), Hint: there could be more than one optimal solution. (10points) The decision maker uses a smart phone. The purchase cost of the smart phone is $4000. The maintenance cost of the phone depends on its age. We denote by m; as the maintenance cost of the phone at its ith year of utilization. The phone can be used up to 3 years. After its ith year, it can be replaced by a new one. It It can also be sold for an amount that is equal to its salvage value, denoted by Si. The values of m and sj are summarized below: Year i 2 3 240 320 480 m ($) Si ($) 3200 2400 2000 Page 2 of 1 You need to determine a replacement policy that minimizes the total cost over the next five years, assuming that at the end of the 5-year period, the analyzer will be sold for its salvage value. A replacement policy means that after the purchase of a new phone, you should know when to replace it with a new one. Suppose that you don't have a phone at the beginning of year one. 1-Define the stages. (5points) 2-Define the states. (5points) 3-what are the decisions that you can make at the beginning of each stage? (10points) 4-Define the recursive function. (10points) 5-Depict the stages and the states in the form of a network. 6-Calculate the minimal cost over the five years 6-a-Stage 5: (10points) 6-b-Stage 4: (10points) 6-c-Stage 3: (10points) 6-d-Stage 2: (10points) Page 4 of 1 6-e-Stage 1: (10points) 7-what is the optimal replacement policy? (when we should replace the phone during the five years horizon), Hint: there could be more than one optimal solution. (10points)