A production facility utilizes a piece of machinery that has a usable lifespan o

ID: 347574 • Letter: A

Question

A production facility utilizes a piece of machinery that has a usable lifespan of six years. A new piece of machinery can be purchased for $10,000, and 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.

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 that 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.

Age Resale Value Operating Costs for the Upcoming Year NA 7000 6000 4000 3000 2000 1000 300 500 800 1200 1600 2200 NA

Explanation / Answer

Initial purchase cost = $ 10,000

Operating cost for year 1 = $ 300

2018 is Age 0

Therefore “end 2013” means Age 5

Age

Resale Value, $ / Cost,$

Operating cost,$

Cost of owning, $

Cost of owning and Operating at end of the year, $

10,000

300

10000 -7000 = 3000

3000 + 300 = 3300

7000

500

7000 – 6000 = 1000

1000 + 500= 1500

6000

800

6000 – 4000 = 2000

2000 + 800 = 2800

4000

1200

4000 – 3000 = 1000

1000 + 1200 = 2200

3000

1600

3000 – 2000 = 1000

1000 + 1600 = 2600

2000

2200

2000 – 1000 = 1000

1000 + 2200 = 3200

1000

THE REPLACEMENT POLICY THAT MINIMIZES COST OF OWNING AND OPERATING IS TO SELL THE MACHINE AT THE END OF YEAR 1 i.e AT THE END OF YEAR 2019 ( WHEN TOTAL COST OF OWNING AND OPERATING AT THE END OF THE YEAR IS $1500)

Age