Let us first of all understand the concept of the responsibility center as in the question four types of responsibility centers is used. Use of responsibility centers is one of the most established and widely used techniques in financial control. Responsibility accounting breaks a large organization into smaller, more easily manageable units known as responsibility centers. Each unit is looked upon as a small business. Managers bear an element of responsibility for the performance of their respective centers.

The principle of controllability applies to responsibility accounting. The presumption underlying controllability is that every dollar earned or dollar spent is under the control of, and can be traced to, at least one manager.

Responsibility accounting represents decentralization of a business enterprise. It is comparable to a political policy of shifting power from the federal government to state or even municipal government.

Types of responsibility centres and to determine the types of responsibility center a department should be:

1. Cost centers are those in which the manager and the center employees have control over costs, but not revenues or the level of investment. Thus if a department has only costs than it should be cost center. For example in a software manufacturing firm whose name is Indosys.
Cost centers are those which the manager and the center employees have control over costs, but not revenues or the level of investment. Here purchasing department (Of hardware and other technologies) is a cost center

2. Revenue center:
The center manager has control over revenues, but not costs or the level of investment, in a revenue center. The departments which have only revenues or are responsible for revenues only like :
There are three revenue centers based on geographies in the above company:

1 Sales Manager (America Exports),
2. Sales Manager (Asia )
3. Sales Manager (Australia )

3. Profit center:
The manager is responsible for both the revenues and costs. Thus he is responsible for the difference between the revenue and costs. In the above company, Here there are two broad products: Telecom software and Banking software are divided into profit center having separate divisions. Separate Product Managers are responsible for each division.

4. Investment center

Investment center is one in which the manager controls costs, revenue, and the level of investment. Level of investment represents expenditure on space, equipment, and other capital resources. It is like SBU, the profit centers can be converted into SBUs.

The metrics used to evaluate performance vary for each type of responsibility center. For a cost center, price variance is assessed. Price variance is the difference between the average price paid for a certain supply and the budgeted amount. The assumption is that the purchasing manager, through management of factors such as inventory and purchasing discounts, exerts some control over average price paid.
In a revenue center, sales price and sales volume are examined. In profit center profits are examined.
Investment centers may be assessed through a number of different metrics. One of the best known of these is return on investment.