# Replacement Theory in Operations Research

Replacement Theory in Operations Research

It is used in the decision-making process of replacing existing equipment with us by a new one. It is like replacing our old refrigerator, moped, car or any machinery in garage, workshop and so on. Some real life examples of this situation are decisions to buy a new TV, Car, Truck, Lathe Machine, even our House or Apartment.

What data is required to apply this technique?

One needs to two kinds of data in these situations. The first one being the maintenance cost of the equipment, that is, how much you are spending every period (every month, every year depending on the life of the item). This also keeps our spending in check and otherwise also it’s a good habit to maintain our expenses. Secondly, you need to have approximate resale value corresponding to the respective period that is weekly, monthly, yearly and so on. This resale values can be obtained by consulting experts in respective fields or even elders home.

What is the theory?

The costs mentioned above have typical characteristics. The maintenance cost of items usually goes up while its resale value goes down. This maintenance cost after a while can be huge while at the same time, the resale value of that item can drastically go down. This result into a total loss and most of the times, in such cases, we throw away that item or scrap it. Replacement theory gives a optimum trade-off between rising maintenance cost and declining resale value. This optimum period, when the replacement can be actually made, is the sum of maintenance and depreciation in the original cost of equipment.

Illustration

Consider the example of a Truck; the pattern of failure here is progressive in nature, that is, as the life of vehicle increases; its efficiency decreases. This results in additional expenditure in running or maintaining this vehicle and at the same time its resale value (also called as scrap value) keeps on decreasing. The above case makes this situation a typical case for applying ‘Replacement Theory’.

Lets see a text-book problem. A transport company purchased a truck for \$100000. The resale value of the truck keeps on decreasing from \$75000/- in the first year to \$20000/- in the eighth year while, the running cost in maintaining the truck keeps on increasing with \$3000/- in the first year till it goes to \$25000/- in the eighth year. Determine the optimum replacement policy?

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