The cost of buying a new piece of machinery is $10,000. This price is not expected to change in the next decade. Our goal is to determine the optimal replacement policy. At the beginning of each year we must decide if we keep our current piece of machinery or if we sell it and buy a brand new piece of machinery. The operating costs and resale value of the machine are a function of its age, with operating costs increasing as the machine gets older and resale value decreasing as the machine gets older.

      Age              Resale Value                      Operating Costs for the Upcoming Year

      0                                        NA 300

      1                                         7000                                500

      2                                         6000                                800

      3                                         4000 1200

      4 3000                                       1600

      5 2000                                      2200

      6 1000                                         NA

Assume that it is the beginning of 2018 and that we have a brand new piece of machinery. Use dynamic programming to find the replacement policy that minimizes the cost of owning and operating the machinery for the next 6 years (2018, 2019, 2020, 2021, 2022, 2023). Include in your analysis the assumption our machine will be sold at the end of 2023.

To help read the above chart, suppose, for example, that we purchased a vehicle at the beginning of 2020. The costs for 2021 depend on whether i) we purchase a new vehicle at the beginning of 2021 or ii) we keep our current vehicle and use it in 2021. The cost for option i) is 10,000 – 7000 + 300 = 3300, and we would enter 2022 with a 1 year old machine. The cost for option ii) is 500, and we would enter 2022 with a 2 year old machine.