What's Our Capacity

Decision-makers basically deal with two definitions of the capacity of a physical system which produces a product of goods or services. One is that the capacity is equal to the maximum quantity of output which the system can produce, considering only physical limitations on production. For example, one might be interested in the capacity of a system of power plants to produce electric power. This output level is, of course, limited by both the number and size of generators and the availability of fuel. This definition of capacity focuses solely on maximizing the output, and ignores other factors which may make achievement of such an output unlikely. For example, in some systems marginal costs may become very large when output approaches this capacity. This concept of capacity is often termed ultimate capacity.

The other basic definition of capacity recognizes that the cost may be far too large at the ultimate capacity for such a level of output to be practically or economically attainable. This suggests the other basic definition of capacity: the maximum output at which cost does not exceed a maximum acceptable value. This concept is termed economic capacity in economics literature and practical capacity in the engineering literature. The term cost is deliberately left vague, for the specific measure used varies with the situation, in some cases being average cost, in others marginal cost, etc.

These definitions all refer to the quantity of output of the system of interest. This naturally raises the question of how the output of an entire system is to be defined. In most cases where capacity has been estimated, there is usually defined – or assumed -- a single, homogeneous output of the system being considered. For example, in the case of a manufactured product, the quantity of output would be simply a count of that particular product produced. If there is only one product, or if the variations in the product are rather minor, such that one measurement can be applied to all of the different products, then there is no difficulty in defining a single measure of output. This is the case for the individual components of systems for which capacity is often estimated, as described previously. But in the case of an entire city system, the output is very heterogeneous, encompassing many links as well as other elements of the system. This necessitates a discussion of the system output in detail.

If we consider a city system from the perspective of a physical system, the product of that system probably is most appropriately considered as the delivery of things -- services or objects -- from one provider to an appropriate recipient. Thus, at the microscopic level of a service delivery by a provider of a single service, such as zoning, the product of the city system would be a change in zoning on the individual’s property. Along with this change in zoning come a number of concomitant changes. One is a change in all the possible future uses of the property. Usually, associated with zoning will be some other changes, some of which may reflect the reason for which the zoning is affected. For example, in the case of commercial zoning, it usually results in an increase in the value of the property and surrounding properties, offsetting the cost to society of affecting the previous uses. In addition, other features may change which make the zoning more or less desirable, such as possible deterioration or improving of buildings as a result of the zoning. Thus there may be changes in the state or condition of the property as a result of a government service delivery.

Similarly, the delivery of snow management will have features of ultimate, practically or economically attainable capacity. Waiting until there is enough snow to justify the mobilization of snowplows and employees for a period long enough to make practical and relatively economical a non-routine task. Other issues may be involved in timing delivery for a desired level of service. Such things as the rate and accumulation of snowfall, moisture content, temperature, time of day or night, wind direction and velocity as well as duration of the event are all factors that interact to create a unique aspect for each storm with the result that no two storms are ever identical. All these issues affect the timing and level of the service delivery. The basic definition of capacity recognizes that the cost may be far too large at the ultimate capacity for such a level of output to be practically or economically attainable.

From the viewpoint of the city system as a whole, the problem is that the output is heterogeneous, that is, there are many products. Each service is truly unique in some aspects although many of these may be unimportant in terms of overall measures of output or capacity. If categories of attributes can be specified such that every service can be classified into one category, then the output could be described by a measure giving the quantity of services in each category.