Risk Management - Company Machine Case

[Example 1] A company has a machine which is 3 years old. The company needs to determine the optimal replacement policy for the machine over the next four years (n years, in general). Per the guidelines of the manufacturer, a 6 years-old machine must be replaced. The cost of a new machine is Rs. 100,000. The revenue usually decreases with the age of the machine, the annual operating cost of the machine increases with its age, and the salvage value of the machine decreases with the age of the machine. The Table below gives the relevant data for decision making:

Age of

machine

(t, in years) Annual

Revenue

(r(t), in Rs.) Annual

Operating cost

(c(t), in Rs.) Salvage

value

(s(t), in Rs.)

0 20,000 200 N.A.

1 19,000 600 80,000

2 18,500 1,200 60,000

3 17,200 1,500 50,000

4 15,500 1,700 30,000

5 14,000 1,800 10,000

6 12,200 2,200 5,000

That is, at the beginning of year 1 we have a decision problem whether to keep the machine for replace the machine. Suppose, we denote keeping by K and replacing by R.

If we keep the machine, we are using a 3-year old machine for the 1st year and at the end of year 1 that is, beginning of year 2 we will have a 4-year old machine; the effective profit r(t)+s(t+1)-c(t) over year 1 would be Rs. (17,200+30,000-1,500)=Rs. 45,700.

In contrast, if we had replaced the machine at the beginning of year 1, we would have used using a new or 0-year old machine for the 1st year and at the end of year 1 that is, beginning of year 2 we would have had a 1-year old machine; the effective profit over year 1 would have been Rs. (20,000+50,000+80,000-200-100,000)=Rs. 49,800. Similar decision making questions would arise at the beginning of every year!

Question: What should be the replacement plan of the machine over the next four years (that is, at the beginning of each year from the beginning of year 1 to year 4)?

Solution: What? RKRK? KKRR? RKKR? RRKK? ... How much would be the profit over 4 years?

Modeling: How?

Machine

Age

in

years

6 K(4,6)