Downloadable - About University

Applying simulation to a decision problem 185
Profit
Sales revenue Costs
Sales Price Fixed costs Variable costs
Figure 7.1 – Identifying the factors which will affect the profit earned by the commemorative
plate
profit of the commemorative plate. A tree diagram may be helpful in
identifying these factors, since it enables them to be subdivided until
the decision maker feels able to give a probability distribution for the
possible values which the factor might assume. Figure 7.1 shows a tree
for this problem. Of course, it might have been necessary to extend the
tree further, perhaps by subdividing fixed costs into different types,
such as advertising and production set-up costs or breaking sales into
home and export sales. It is also worth noting that subsequent analysis
will be simplified if the factors can be identified in such a way that
their probability distributions can be considered to be independent.
For example, we will assume here that variable costs and sales are
independent. However, in practice, there might be a high probability of
experiencing a variable cost of around $7 per plate if less than 10 000
plates are sold, while we might expect costs of around $5 if more than
10 000 are sold because of savings resulting from the bulk purchase of
materials, etc. It is possible to handle dependence, as we will show later,
but it does add complications to the analysis.
Stage 2: Formulate a model
Having identified the factors for which probability distributions can be
assessed, the next step is to formulate a mathematical model to show
how they affect the variable of interest, in this case profit. For Elite’s
problem the following model is thought to be appropriate:
Profit = (Price − Variable cost) × Sales − Fixed costs
Of course, this is only a model and therefore almost certainly a
simplification of the real problem. In practice, a large number of factors
and relationships which we have not included in the model may affect
profit. For example, at higher sales levels more breakages may occur