## Stochastic optimization – the ideal planning instrument

A large number of optimization problems are characterized by the fact that decisions which have already been made can have various effects- depending on how random events develop in the future. A decision which is independent of these future developments, or at least one which is most likely to lead to a positive result, can be termed as “good”.

Yet how do we come to a decision which is, on average, the best for all future developments under consideration? One method which can be used here is stochastic optimization – a specialized procedure for modeling and solving optimization problems under uncertainty.

The way towards optimal planning

And this brings us to the third step on the road toward optimum planning under uncertainty: stochastic optimization.

Let’s sum up again by first going back two steps in our consideration – back to the starting point of the topic “Planning under uncertainty”. Here, possible uncertainties were highlighted in production planning, for example, and, with terms such as “robustness and flexibility”, results were provided to help solve the problem: Planning under uncertainty – how does it work?

Step 2, Scenario Generation,provides us with the first answers to the question: How do we actually make robust and flexible decisions – decisions which still lie in the future?

The scenarios created by scenario generation are the basis for the third step of planning under uncertainty – stochastic optimization.

The result – the optimum overall solution

Stochastic optimization deals with optimization problems where the uncertainty is determined by probabilities. This means: uncertain input data can be initially viewed as statistic information – e.g. by means of  past experience or based on expert knowledge.

So where can we find experts with a wide range of experience? More often than not among a company’s own sales force. This makes it really easy to determine different scenarios:

• Scenario 1:  sales forecast
• Scenario 2:   increase in sales by 10%
• Scenario 3:   decrease in sales by 10%

The same probability is allocated to all scenarios. If it is possible to determine even the statistical distribution of changes (or to obtain this information from experts), we can generate many scenarios rapidly and reliably and verify them with the relevant probabilities.

The main procedure in stochastic optimization is shown in illustration 1 – based on the example of a sales force. The optimization is performed for all scenarios combined. Therefore, the result is an overall solution which can handle every scenario under consideration and thus guard against uncertainty as best as possible.

Diagram 1 – A stochastic optimization procedure

### Stochastics in practice

In practice, stochastics is fast gaining ground in optimization procedures. A typical challenge concerns decisions on production capacity in network planning. When should I build up capacities? How many machines should I procure? What if the new machine stands idle because there is a temporary lull in orders? Or is it advisable to outsource orders – but then that means making a low profit?

### And the good thing about it is…

With stochastic optimization, you can make decisions which, on average, are highly successful. In this way, business success is not about gambling on a forecast; it’s about guarding against many possible future scenarios –  and that pays off.

### OPTANO and stochastic optimization

Scenarios form the basis for stochastic optimization. OPTANO offers extensive possibilities here; planners can create scenarios easily and without any technical restrictions. OPTANO differentiates here between the data used to make calculations, between master data and scenario-dependent data. Scenario dependent data is, above all, data which forms the basis of uncertainties and fluctuations. In the scenarios, data can be changed easily, the consequences which are caused as a result can be analyzed and stored separately.

After scenarios have been created for various data, it is interesting to compare these in order to establish which variant is more feasible. Defined key figures (e.g. KPIs – key performance indicators) can be used here.

OPTANO, with the possibilities it provides for scenario generation, makes a convincing impression!  Read our blog entry with more details on this topic: What-if scenarios in production planning