Berry Stuart - Guide to Computational Modelling for Decision Processes Theory, Algorithms, Techniques and Applications

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Part I
Introduction to Modelling and Model Evaluation

This section introduces modelling techniques and constructs models to represent and analyse planning problems in business, industry and the management of facilities.

These constructed models are evaluated; can they be solved in a reasonable time using standard analytical techniques or should the solution be approached using heuristic methods or heuristic methodologies?

Springer International Publishing AG 2017

Stuart Berry , Val Lowndes and Marcello Trovati (eds.) Guide to Computational Modelling for Decision Processes Simulation Foundations, Methods and Applications 10.1007/978-3-319-55417-4_1

1. Model Building

Val Lowndes (Retired) 1

(1)

University of Derby, Kedleston Road, DE22 1GB Derby, UK

(2)

College of Engineering and Technology, University of Derby, Kedleston Road, DE22 1GB Derby, UK

(3)

Computer Science, Edge Hill University, St Helens Road, Ormskirk, L39 4QP Lancashire, UK

Val Lowndes (Retired)

Email:

Stuart Berry (Corresponding author)

Email:

Marcello Trovati

Email:

Amanda Whitbrook

Email:

• Section introduces the use of system dynamics in modelling and then uses this approach to construct models to describe real applications.
• Section introduces the concepts needed to construct models using available data, modelling using Big Data.
• Section introduces modelling using blackboard architecture; this provides a flexible, symbolic artificial intelligence (AI) method for the cooperative modelling and then solution of complex problems.

1.1 Introduction to System Modelling

The purpose of system dynamics modelling is to develop understanding and then the improvement of systems. The first stage in this process is the construction of a logical model (influence diagram) to describe a system.

This model can then lead to sets of equations describing the operation of the system. These can be used to simulate the system to gain understanding of its dynamic behaviour and to be able to evaluate alternative policies, leading to improvements within the system.

A series of small examples are used to introduce this modelling process. Where information is available, the behaviour predicted by these models is compared with reality, i.e. what has happened in reality.

1.1.1 Introducing Influence Diagrams

Modelling using influence diagrams is introduced through the following illustrative examples:

• Stock control model: used to illustrate the basic modelling notation.
• Spending/saving model: used to illustrate the construction of an influence diagram and to introduce the concept of positive and negative feedback loops
• House building, financial models and population modelling: so that the predictions from the models (positive or negative loops) can be compared with reality.
• Transport modelling: extending the work to demonstrate the effect of government policy on transport provision (the Beeching cuts for example).

Example A: Stock Control Policies

A company holds stocks of finished goods to be able to satisfy demand; when stocks are low, more newly manufactured items are added to the finished goods stock; in this example, the available stock (for use) is influenced by production and demand (see Fig. ).

Fig. 1.1

Production

The direction of the arrow from [despatched] to [production] indicating the production levels is influenced by the quantity of items dispatched, and the arc label (D) indicates the delays between each event.

Where

Demand	Influences	Number dispatched
Number dispatched	Influences	Production
Production	Influences	Available stock
Available stock	Influences	Number dispatched

The model constructed from this diagram will have the form:

The next stage gives examples to introduce approaches to the production of influence diagrams and the notation used to analyse the resultant model.

1.1.1.1 Categorising Dependencies (Links) in a Model

An initial (causal) analysis is used to categorise an influence diagram and hence the underlying model, essentially the causal analysis asks: (Fig. ).

Fig. 1.2

a Positive arc: if inflation rate increases then prices will rise. b Negative arc: if demand increases then stock levels will fail

If the input value increases, what is the effect on the output value? leading to the categorisation of the links as either positive (+) or negative () links.

Connecting between inflation rate and prices, as inflation rises, then so too do prices giving:

Connecting between demand and stock levels, as demand rises, it follows that stock levels will fall:

In carrying out this analysis always start withif the input rises starting with the opposite if the input falls can lead to double negative statements and some confusion in the following analysis.

1.1.1.2 Categorising a Model

Having categorised all the links, a loop in a model can fall into one of the two states: positive or negative feedback loops. In general, a negative loop indicates a goal-seeking model here there will be convergence, whereas a positive feedback loop indicates unrestricted growth or decay (Fig. ).

Fig. 1.3

Categorising feedback loops

• State 1, a positive feedback loop would lead to unconstrained growth or decline, while
• State 2, a negative feedback loop would lead to a steady-state solution (goal-seeking).

1.1.2 Model Evaluation/Validation, Comparing the Model with Historic Data

Here, a model is constructed and evaluated showing that its behaviour replicates the real situation.

Example B: House-Building Model

An initial model links house buying with house prices and housing stock giving a model with a negative feedback loop, ignoring the overall demand for housing (Fig. ).

Fig. 1.4

First house price model

Analysing Influences in the diagram leads to the consequent effects:

House prices

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