1.5.2 Quantitative Models
Quantitative, or computational, models are built with numbers, mathematical operators and formulations of linked algebraic expressions. We are interested in two types of model:
- analytical models, and
- simulation models.
Analytical models comprise formulations of equations that can be solved to produce unique, reproducible answers. Typically, such models are specified using simultaneous linear or non-linear equations. Algebra and calculus are used to find solutions. Once found, solutions can be substituted back into the original equations to confirm that they are fully satisfied.
Analytical models can be solved by capable non-experts able to produce solutions without the continued intervention of a subject-matter modelling expert. Once a problem has been formulated and the problem space clearly defined, it is possible for an intelligent and capable non-expert to produce solutions and implement remedial strategies. Generally speaking, it is the formulation of the problem that is most demanding. Examples include queuing problems, customer service, and other classical operations research problems such as the travelling salesman problem addressed using linear programming techniques.
Simulation models comprise formulations of equations that cannot be solved, at least not to produce unique and final answers. Through repeated simulations, representative modes of behaviour can be reproduced. These are compared with observed real-world behaviours. Typically, such models are used to investigate queuing problems, design problems involving many degrees of freedom, or feedback problems (especially those where feedback loop dominance may change with changing conditions.)
Unlike analytical models, it is not possible in simulation models to find unique sets of solutions that can be substituted back into the original equations to demonstrate that they satisfy them. Simulation models can involve large numbers of input variables, which in combination can produce widely varying outputs. The relationships between inputs and outputs can be challenging to interpret. Further, the structure of the model has to be adapted through an iterative process to produce progressively improved and (ultimately) highly more-representative sets of outputs.
These factors create the need for modellers to apply their skills to repeated iterations and modelling cycles. It is generally not possible to build a simulation model and then take it to be either complete or final. Remedial strategies developed from simulation modelling inevitably result in the problem’s structure being changed. In turn, this produces new behaviours and the model needs to be modified as a result. Simulation modelling can require continual attention by an individual or team with high levels of modelling and interpretive skills. When it comes to complex, dynamic problems, simulation modelling is closely linked to understanding and the development of double-loop learning. Modelling produces learning and enhanced understanding which, in turn, drives the need to revise the model(s) and to continue experimenting. This book explains and demonstrates how to build, test and interpret simulation models.