As organisations
move up Tom Davenports’ analytics maturity curve, they encounter new challenges
in using the insights from data analysis and optimisation models. Today, the majority of organisations use descriptive
analytics to create insights on what has happened. Also the use of diagnostic
analytics to understand why things have happened is becoming more common.
Moving up the curve towards predictive and prescriptive analytics is more difficult
and requires the development of more advanced analytical capabilities. Gartner surveys
indicate that about 13% of the companies are using predictive
analytics. Predictive Analytics provides these companies the capability to
identify future probabilities and trends. It will also support the discovery of
relations in data not readily apparent with traditional analysis. These
insights can be used to for example estimate future demand, which in turn supports
sourcing and production decisions. Predictive analytics enables organisations to
balance the decisions of today against the conditions that they face in the
(uncertain) future; it allows them to become proactive instead of reactive. Turning
these insights into robust decisions is however not always as straight forward
as it seems.

Let’s take
the example of a company that manufactures desks, tables and chairs. The desks
sell at €60, the tables at €40 and the chairs at €10. To make the furniture the company needs to
source wood and two types of labour, carpentry and finishing. Costs and
resource requirements for each type of furniture, including the demand, are shown
in the table below.

Given the demand,
a simple linear programming model will help the company to figure out that the
best decision is to produce 150 desks and 125 tables. It will require the
company to source 1950 feet of wood, 487.5 labour hours of carpentry and 850
labour hours of finishing. A net profit of €4,165 will result. In fact, a
simple per-item profit analysis provides the answer already as producing chairs
will not generate any profit. What is important to note is that in the above
approach the sourcing, production and selling decisions are made in one go. In
practice this might not be realistic.

Using predictive
analytics the company constructed the following scenarios for future demand for
desks, tables and chairs with the accompanying probability of occurrence.

Given these
scenarios the company wonders how this variability in demand will impact its sourcing
and production decisions. How to deal
with the various demand scenarios? The use of predictive analytics has created
more insight, but also increased the complexity of the sourcing and production
decisions. To find out what is best, the company decides to perform a sensitivity
analysis on demand using the LP model with the deterministic demand scenario.
The analysis shows that although the number of desks and tables produced in
each demand scenario differs, no chairs will be produced in any of the
scenarios. Given this observation, the company decides to go for expected demand
scenario, also a common way of dealing with multiple scenarios in practice. The
impact of this decision becomes apparent when we look at the profit for each of
the demand scenarios based on this decision. Expected profit for sure is not
what was expected! In the low demand scenario there is a significant loss
instead of a small profit, in the most likely scenario there is a slightly
lower profit while in the high demand scenario the upward potential doesn’t
materialize. So on average the company will be worse off than expected (wheredid we here that before?). The sensitivity analysis on demand didn’t
provide any clue that this could happen, it is therefore flawed. Stein Wallace indicates that key to better deal with uncertainty in this case is
to have a more thoughtful approach to creating the math model.

Key in
developing a better model is to understand when decisions are made and how they
are impacted by the uncertainty in demand. There are three possible situations.

- Demand is known before the sourcing and production decision
- Demand is known after the sourcing and production decision
- Demand is known after the sourcing decision but before the production decision.

If demand is
known before we need to decide what to produce and source, there is no
uncertainty on demand and therefore the first model will provide the optimal
production and sourcing decisions for every demand scenario (as shown in the
above table). When we need to decide both sourcing and production before we
know demand, these decisions must be weighed against all demand scenarios. The
production plan and corresponding sourcing decisions in this case will be set trading
off the sunk cost of producing furniture that can’t be sold with the upward
potential in revenue from the high valued demand scenario. The best decision in this case is to source
and produce 50 desks and 110 tables.

An
interesting situation arises when we need to source before we know demand but
can adapt the production decisions after demand is known. So if there is a
change in demand, the resources can be used to produce furniture for which
there is demand. The optimal solution to the model clearly shows this. Compared
to the second situation in which demand is known after the sourcing and
production decision the model in this case advices to acquire more resources.
Also in the low demand scenario it suggests to switch to the production of
chairs, which generates additional revenue. It’s a fall-back scenario which
justifies the more aggressive sourcing decision.

In practice
the input of mathematical models is assumed to be accurate and deterministic.
If accuracy of the data is a worry the conventional wisdom is to perform a
sensitivity analysis. With the rise of predictive analytics more and more
companies will start using the results of their predictive models in their decision
models. As predictions are in their nature uncertain, many of these companies
will turn to sensitivity analysis to analyse the impact of the uncertainty on
their decisions. Most commercial solvers offer this as a standard feature,
which is most convenient. However the above example shows that sensitivity analysis
can be seriously flawed. Careful analysis of how uncertainty influences
decisions will lead to models that better incorporate uncertainty and therefore
will result in better quality decisions. This requires companies not only to
invest in predictive analytics tools but in modelling skills as well.

This blog
is inspired by an article of Stein Wallace on sensitivity analysis in linear
programming which was published in Interfaces. If you want to experiment yourself a download of an Excel workbook is available.