Replacement Models in Operation Research

In an organisation, replacement problems arise when fixed assets, such as machines, equipment and other tools, need to be replaced due to reduced efficiency, failure or breakdown. Sometimes, replacement takes place when more efficient equipment is available in the market or the maintenance of the existing equipment is incurring a huge cost on an organisation.

However, an organisation needs to decide when the replacement of new equipment would be economical. Replacement models help an organisation to determine when to replace equipment in a cost-effective manner so that the overall productivity of the organisation is not affected.

These models help managers to answer the following questions:

• At what time should equipment be replaced?
• Should the existing equipment be replaced, if the new equipment with better efficiency is available? If yes, then when?
• Should the time value of money be taken into account while replacing the equipment?
• What should be the replacement plan for equipment that is used in large quantities and may fail randomly (for example, light bulbs)?
• What kind of replacement policy should be in place for the human resource of an organisation?

An organisation uses different types of equipment. Some equipment deteriorates with time; for example, the efficiency of a car reduces with time. On the other hand, some equipment, such as electric bulbs, fails instantly and needs to be replaced immediately. An organisation cannot use the same replacement policy for every kind of equipment. Different equipment is replaced differently. Now, let us discuss how different types of equipment that deteriorate with time are replaced in the next section.

Replacement of Equipment That Deteriorates With Time

Generally, the simplest replacement model is used for equipment whose efficiency reduces gradually. As discussed earlier, the replacement decisions of such equipment are based on the economic life and monthly or annual operating costs of the equipment. These costs increase with time, while the salvage value of equipment reduces with time.

While using the simplest replacement model, an organisation needs to determine the optimal time for replacing equipment that deteriorates with time. For this, the average cost of the equipment needs to be determined. It is assumed here that time is measured in discrete units.

The following are the three components of the average cost of equipment:

• The purchase price of the equipment
• The salvage value of the equipment
• The maintenance cost of the equipment

Therefore, Total cost of equipment = Purchase Price – Salvage Value + Maintenance Cost

Now, if we assume:
C = Purchase price
S = Salvage value

Mt = Total maintenance cost for t period

Total cost after n years T (n) = C – S+∑M(t)

Similarly, the average cost A (n) can be expressed as:

A (n) = [T (n)/n]

An organisation should replace equipment in a period when there is minimum average cost of the equipment. Now, let us understand how to calculate the optimal time for replacing equipment that deteriorates with time, with the help of some examples.

Replacement of Equipment That Fails Completely

Apart from equipment that deteriorates gradually, an organisation also uses equipment that fails suddenly. Light bulbs and fluorescent tubes are the examples of equipment that fails all of a sudden. Such type of equipment does not involve maintenance cost, however, they fail without warning. In the case of equipment that fails completely, it is more economical to replace the equipment in a certain interval rather than replace it when it stops working.

However, if the interval of replacement is too short, the per unit replacement cost would be high. The cost of replacement per period decreases with increase in the interval between two replacements. However, in such cases, the cost of individual replacement increases as the number of individual failures increases.

Therefore, an organisation needs to determine the optimal interval of replacement in which there is minimum total cost of replacement.