Attributes of variables

1 Performance measures in (chemical) supply chain models 

A prominent measure of overall success is the profit obtained with a given set of resources in a given time span. Basically, the profit depends on costs, revenues and assets employed, whereby those depend on system-internal and -external influences. In SC simulation the aim is to investigate the behaviour of the system and explain the relations between its components. Here, the focus is on studying internal relations under external disturbances. Let X 6 R denote the vector of controllable independent variables and y 6 R denote the vector of dependent response variables defined in the model building phase. Furthermore, e 6 R° denotes the vector of uncontrollable variables which are not considered in detail in the model but are captured as environmental effects. The function H -) describes the real relation between dependent and independent as well as environmental variables 

Typically, the function H -) is unknown and reflects the behaviour of the real system. Since the controllable variables x are often strategic decisions, experiments in reality are often too expensive. Hence, simulation models are developed mimicking the real system s behaviour. Formally, the simulation model can be seen as a function A -) such that 

AU these components influence the profit u of the real system, i.e. 

A regime of external conditions e has to be defined and integrated in the simulation model. This is referred to as a scenario. In common sense, a scenario comprises both, stochastic processes reflecting environmental conditions and the general structure of the modelled system. Typically, the focus of simulation is on the internal processes of a supply chain under a more or less specific environmental regime. E.g. in chemical industry an SC s revenues depend mainly on product prices that can be realized. Due to the highly competitive market for basic chemicals and the inflexibihty of (continuous) production processes in combination with immense capital commitment for production plants, the focus for optimization is on the internal processes of a chemical supply chain. 

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Availability of a well-designed and descriptive analytical plan that is appropriate given the design, level of measurement, attributes of variables, and underlying statistical assumptions. 

The outcomes of test and inspection can thus be classified by the level of measurement upon which they are based and the type of decision required. These outcomes in turn define the typical statistical methods used, such as prototype testing for decision 1 above. For in-process quaUty control (decision 3 above), nominal scale decisions lead to attributes control charts, while interval or ratio scales lead to variables control charts (Vardeman and Jobe 1998). The second type of decision above would lead to either attributes of variables sampling plans, although the whole concept of sampling a batch to determine its quality has largely been abandoned in favor of in-process quality control. 

At the beginning of the planning process, it has to be clarified which questions should be answered by the study. In most cases, the research questions are rather qualitative, unspecific statements than precise algebraic formulations. Hence, such statements have to be operationalized into mathematically manageable terms, l.e. measures have to be defined describing the aspects of the system under study that should be investigated. Such measures are called variables. In the context of experimental studies variables have a lot of attributes depending on their purposes. Table 4.9 shows an overview on the most common attributes of variables. 

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