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## Replacement Theory in Operations Research

**Replacement theory in operations research **

It is used in the decision-making process of replacing existing equipment with us with new one. It’s like replacing our old refrigerator, moped, car, or any machinery in a garage, workshop, etc. Some concrete examples of this are decisions to buy a new television, a car, a truck, a lathe, even our house or our apartment.

**What data is needed to apply this technique?**

Two types of data are needed in these situations. The first being the cost of maintaining the equipment, i.e. how much you spend each period (monthly, yearly depending on the life of the equipment). It also helps to control our expenses and if not, it is also a good habit to maintain our expenses. Second, you must have an approximate resale value corresponding to the respective period which is weekly, monthly, yearly, etc. These resale values can be obtained by consulting experts in the respective fields or even senior homes.

**What is the theory? **

The costs mentioned above have typical characteristics. The cost of maintaining items generally increases while its resale value decreases. This maintenance cost after a while can be huge while at the same time the resale value of that item can drop significantly. This results in total loss and most of the time in such cases we throw that item away or scrap it. The replacement theory provides an optimal trade-off between increasing maintenance costs and decreasing resale value. This optimum period, during which replacement can actually be made, is the sum of maintenance and depreciation in the original cost of the equipment.

**Drawing **

Let’s take the example of a truck; the failure pattern here is progressive in nature, i.e. the life of the vehicle increases; its effectiveness decreases. This leads to additional expenses for the operation or maintenance of this vehicle and, at the same time, its resale value (also called scrap value) keeps decreasing. The above case makes this situation a typical application of the “replacement theory”.

Let’s see a textbook problem. A transport company bought a truck for $100,000. The resale value of the truck continues to decrease from $75,000/- in the first year to $20,000/- in the eighth year, while the operating cost of maintaining the truck continues to increase by $3,000/- the first year up to $25,000. /- in the eighth year. Determine the optimal replacement policy?

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