Models in food technology, at the simplest level, are equations showing the relationship between two or more variables. Dunn (1986) defined a mathematical model of a process as a 'system of equations whose solution, given specified input data, is representative of the response to a corresponding set of inputs'.
Empirical and fundamental models are widely used in food processing.
Most models used in food technology are empirical. Two types of empirical model, response surface methodology (RSM) and dimensional analysis are widely used in food processing. RSM is a graphical representation of the statistical relationship between process output and independent variables, whilst dimensional analysis is a technique, which combines physical parameters that describe the problem in such a way to produce new, dimensionless, variables, and interactions (Levine, 1997). The Van Slyke yield equation, for calculating the theoretical yield of Cheddar cheese, is an example of a RSM type model. See the discussion area for questions and answers on the Van Slyke equation.
Fundamental models, or models based on theory, require knowledge of the underlying principles and mechanisms and the relationships between variables.
Advantages of mathematical modelling
• Modelling enables product or process knowledge to be expressed in simple statements thus reducing the apparent complexity of some problems and facilitating a solution
• Has the potential to reduce the cost of experimentation, by reducing the number of experiments needed to analyse a particular problem. E.g. use of factorial experimental designs
• Models can be extrapolated to unexplored or un-explorable regions. You can try this out with the Cheddar cheese grade prediction model.
• Allows alternatives to be considered which may be difficult, or expensive to test.
• Enables the sensitivity of a process to variables, and the design of optimal control strategies, to be studied.
The above statements have been adapted from Levine (1997).
Modelling in the food industry
The use of modelling in the prediction of cheese yield and quality is discussed in the sections on cheese yield and cheese quality. See also the sections on modelling Cheese grade prediction values and why one cheese is different than another. Because of the importance of ensuring food at the point of consumption is free of pathogens and their toxins, considerable research has been devoted to modelling microbial growth and toxin production in foods.
The section on Site models and calculators provides an introduction to a range of models and calculators that should enable browsers to evaluate how useful certain models are and to identify some of the design faults e.g. two simple models for predicting the growth of listeria in cheese are discussed in the article "Modelling the probability of Listeria monocytogenes growing in cheese" on this site.
Click here to review a Power Point presentation on modelling.
Use of models in problem solving
Problem solving is something that the technologist does every day in industry. We are going to explore what is involved in problem solving by studying problems that the author has investigated.
Essentially the approach that we will take is to:
Define, explain and move towards actually understanding what the problem is.
Based on this understanding, and your knowledge of food technology, including any relevant product or process models you will devise a plan to investigate the causes of the problem.
Implement your plan
Review your findings to determine whether you have arrived at a solution.
This may be a cyclical process, where you progress to a solution in a logical way by eliminating a number of potential solutions.
Questions that you might ask
• Are there any product or process models that might be relevant?
• Has this problem occurred before? If yes, was it investigated? What was the outcome? Where are the records?
• Do you know anyone who might have experience of this problem?
• What do the operatives, supervisors, and managers have to say?
• Look at the data. Are there any trends?
• How do you know that the records/ analyses/ responses to questions are accurate? Could the responses or results be incorrect, invented?
• Have there been any personnel changes/ problems?
• Is the crisis management plan relevant?