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Replacement Theory in Operations Research
Theory of substitution in operations research
It is used in the decision-making process to replace the existing equipment with us with a new one. It is like replacing our old refrigerator, moped, car or any machinery in the garage, workshop, etc. Some real examples of this situation are the decisions to buy a new TV, car, truck, lathe machine, even our house or apartment.
What data is needed to apply this technique?
Two types of data are needed in these situations. The first is the maintenance cost of the equipment, meaning how much you are spending each period (monthly, annually depending on the life of the item). This also keeps our spending under control and otherwise it is also a good habit to keep our expenses in check. Second, you need to 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 respective fields or even in old people’s homes.
What is the theory?
The costs mentioned above have typical characteristics. The maintenance cost of the items usually increases while their resale value decreases. This maintenance cost after a while can be huge, while at the same time, the resale value of this item can drop dramatically. This results in a total loss and most of the times in such cases we either throw that item away or discard it. Replacement theory provides an optimal balance between increased maintenance cost and decreased resale value. This optimal period, when the replacement can be effectively done, is the sum of maintenance and depreciation in the original cost of the equipment.
illustration
Consider the example of a truck; the failure pattern here is progressive in nature, i.e. as the life of the vehicle increases; its efficiency decreases. This results in additional expense in operating or maintaining that vehicle, and at the same time, its resale value (also called scrap value) continues to decrease. The above case makes this situation a typical case for applying the “replacement theory”.
Let’s look at a textbook problem. A trucking company bought a truck for $100,000. The resale value of the truck continues to decrease from $75000/- in the first year to $20000/- in the eighth year, while the running cost of maintaining the truck continues to increase by $3000/- in the first year until it reaches to $ 25000/- in the eighth year. Determine the optimal replacement policy?
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