The article is devoted to the approach to performance assessment of systems and first of all business systems. In Russian “эффективность” is used as term for “performance”, “effectiveness” and “efficiency”. In English (as far as I know) this words also sometimes are used like a synonyms.

If you’ll ask any manager, what does he want from the organization, with the probability of 80% you’ll get the answer: “It must be efficient”. In Russian it’ll sound like “Организация должна быть эффективной” and does he mean effective, efficient or high level of performance you’ll never understand if you’ll not specify what does he mean.

Efficiency is one of the most used demands for the performance of a system. Efficiency is defined by the formula:

 (1);

where:

Ef – efficiency measurement;

R – result measurement;

C – resource consumption measurement.

So, lets agree that the efficiency is main feature of a system performance for some time and simulate some simple situation.

There is some department which result is defined like the increasing of profit volume for $10 million. It’ll be our result measurement. After we’ve planned our activity, calculated necessary resources management assigned the department budget – $2 million. So, for $1 we must get $5 result, our Ef=0,2.

After the end of the period we measure the result. And we see that the increasing of profit is only $1 million but the budget consumption is $200 thousand. So, Ef=0,2! We are efficient!! If the efficiency is main  measurement of performance – we have high level of performance. But…

Why my boss isn’t happy? His intuition says that the performance is low, because we’ve got only 10% of demanding result. Who cares about good efficiency when the effectiveness is low?

Does a system have required performance if spaceship falls in Pacific ocean instead of getting Mars orbit even if the consumption of resources is in proportion to distance?

Intuitively and logically it’s obvious that efficiency is necessary but not sufficient for appreciation of system performance.

Required performance demands simultaneous attainment of required efficiency and effectiveness.

The efficiency is defined:

 (2);

Absolute value of efficiency often has no sense. Most of all the assessment of efficiency  is related with the comparison of expected and actual efficiency.

 (3);

where:

Ec – efficiency measurement;

Ec_f  – actual efficiency measurement;

Ec_p – expected efficiency measurement.

The effectiveness if defined:

 (4);

where:

R – effectiveness measurement;

R_f – actual result measurement;

R_p – expected result measurement

Lets add one more entity – the resource consumption:

 (5);

where:

C – resource consumption measurement;

C_f – actual resource consumption;

C_p – expected resource consumption.

By the  (2), (3), (4), (5), efficiency is:

 (6);

Lets return to performance measurement. Our definition is:

performance is a way of functioning of system that provides necessary efficiency and simultaneously required level of effectiveness.

Ergo, performance is directly proportional to effectiveness (high measurement of effectiveness (4) means high performance) and inversely proportional to efficiency measurement according to (6) (low efficiency measurement (6) – high performance).

Ergo, performance is defined:

 (7);

where: k – proportion constant.

The special case of  the performance formula tested by author in real business practice may look like:

 (8)

The described approach to the performance assessment allows to get integral evaluation without taking into account relation of intermediate results, actions and resources. Undoubtedly, it is only high level measurement.

Application of formula (7) has some important limitations:

First, it concerns time like a resource which has the same importance like any other. But, every manager knows that time is the most deficit resource and it is very difficult to manage. Time couldn’t be added or accumulated in stock. That is why the formula (7) is valid to the cases of system performance assessment in fixed and comparable time intervals.

Second, formula (7) does not consider result dependence of composition and quality of resources used to it delivery. It’s generally not true in real life and real systems.

Classic managerial task is to balance a triangle “Time-limit – Quality (result scope) – Resource consumption” There is old managerial joke: “Cheap, qualitatively, within time-limit – you may choose any two of it”.
The reality shows that the answer is – “No”. If this assumptions were valid creators of new technologies would get immediate superiority in performance and deliver better results. But in  real market environment technological innovators themselves rarely wins, more frequent the winners are those who came second or third. Those followers often get more success and show more performance.Most often delivered result is an effect of a presence, quality and availability of resource in needed quantity and proper sequence. In this case resources are means of production or any other fixed assets, materials, information, people etc., except for the time available. Other words, every resource has some contribution to the result, i.e. result is an integral function of resource availability:

 (9)

The essence of function  f(c)  is a characteristic of system’s efficiency which is, first of all, determined by technologies used. Any technological innovations, implemented in system, should look toward increasing return on needed  resources.

The attention of the vast majority of managers who are preoccupied with the issues of performance is focused at this function. But this attention misses the very important aspect. Can the increasing of result be supported by the existing capacity of resources or adding resources? Is technological superiority the only basis for performance increasing?

The reason is simple: existing system is NOT ABLE to pass through itself proper volume of resources in available time-limit. Meanwhile, the delivery of the result in due time is very often is the main way to assess performance. Nobody sharpen the axes after the time they are needed!!!

For example. Olympic facilities in Sochi must be totally ready to 2014. If they will not be ready – no efficiency does matter in delivery of the result because the effectiveness rate will be zero (4). They must not be almost ready, they must be totally ready or the performance will be zero no matter how many resources were saved during the delivery.

Winners main advantage usually is the ability to pass through themselves more resources in order to deliver result in the same time as losers.

Company’s capability to provide itself with necessary resources may be described like further:

(10)

Here function ᵠ(t) is characteristic of resource permeability per unit of time.

Thus, the effectiveness of system is defined:

 (11)

Effectiveness is  function of system’s technological efficiency determined by the resource quality and availability and resource permeability in existing time-limits.

Technological efficiency  in business and social systems is in the focus of attention of entrepreneurs, most of decision makers are focused on this issue while resource permeability is often out of focus area. Meanwhile, it is one of the most important parameters that determines competitiveness and performance of a system. To author’s opinion in is critically undervalued.

When we design any system, we formulate hypothesis about nature and profile of functions f(c) and  ᵠ(t), based on retrospective analysis, intuition or expert evaluation or any other methods of decision making. According to this hypothesis we plan the expected performance of the system.

After finishing of a project or system starting we get actual measurements and can assess reliability of plan. So, formula (7) can be used for the assessment of reliability of our forecasts.

 

Conclusion:

1. Definition of performance as a way of functioning of system that provides necessary efficiency and simultaneously required level of effectiveness, allows to design a tool of quantitative assessment of performance (formula (7)).
2. In real systems effectiveness is determined, from one hand, resource composition, its quality and availability, when it’s necessary, and, from the other hand, resource permeability, i.e. system capability deliver resource in tame-limit.
3. Resource permeability management often is undervalued while finding ways to increase system performance.
4. Technological efficiency and resource permeability management is the basis ways of increasing performance of a system