Replacement Theory in Operations Research

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

What data is required to apply this technique?

One needs two types of data in these situations. The first is the maintenance cost of the equipment, that is, how much are you spending each period (each month, each year depending on the useful life of the item). This also keeps our expenses in check and otherwise it is also a good habit to keep our expenses down. Second, it must have an approximate resale value corresponding to the respective period that is weekly, monthly, yearly, etc. These resale values ​​can be obtained by consulting experts in the respective fields or even nursing homes.

What is the theory?

The costs mentioned above have typical characteristics. The maintenance cost of items generally increases while their resale value decreases. This maintenance cost after a while can be huge and at the same time the resale value of that item can drop dramatically. This results in a total loss and most of the time in such cases we throw that item away or dispose of it. The replacement theory offers an optimal compromise between increased maintenance cost and decreased resale value. This optimal period, in which replacement can actually be done, is the sum of maintenance and depreciation in the original cost of the equipment.

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Consider the example of a Truck; the failure pattern here is progressive in nature, that is, as the life of the vehicle increases; its efficiency decreases. This results in additional expense in operating or maintaining this vehicle, and at the same time, its resale value (also called salvage value) continues to decline. The previous case makes this situation a typical case to apply the ‘Replacement Theory’.

Let’s look at a textbook problem. A trucking company purchased a truck for $100,000. The resale value of the truck continues to decline from $75,000/- in the first year to $20,000/- in the eighth year, while the maintenance cost of the truck continues to increase $3,000/-. – in the first year up to $25,000 /- in the eighth year. Determine the optimal substitution policy?