Exercise № 4

A powerful tool

 The right tool is crucial!

Experience and know-how are essential in any job. Choosing the right tool is not only crucial in manual trades. The tool you choose for professional decisions not only makes it easier for you to accomplish the forthcoming tasks – in many cases, it actually makes them possible in the first place.

Conversely, this means that the wrong tool can lead to problems: At worst, you end up investing too much time and energy without getting the results you were aiming for or you even end up causing damage.

This is precisely the case when it comes to planning issues. Of course you can solve your planning manually and devise a plan based on experience and estimation. However, once it reaches a certain magnitude, a procedure takes up too much time and too many resources which could have been saved if you had applied the right tool from the start.

In this exercise we demonstrate why it’s worth applying mathematics as an effective tool for your planning and how to use it properly.

Unit 1

Mathematical optimization – the right tool for your complex planning problems.

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Unit 2

Prescriptive Analytics: Venture a look into the future!

Go to unit

Unit 1

Unit 1:
Mastering planning problems

Defining the problem, finding the tool


What does complex actually mean?

Before you select the tool you want, it’s important to understand what the nature of the task is which needs to be solved. A significant aspect is the complexity of the planning problem. Basically, mathematical optimization is the right tool for complex planning problems. But what do we mean when we talk about complex?

5 factors

Which aspects can make a planning problem become complex? The following list includes the five important aspects that lead to complexity.

A problem that has only 10 possible solutions is so transparent that it’s easy to find the best one. The more possible solutions a problem has, the more complex it becomes.

If the production steps are consecutive and each change triggers a chain of other changes, then your planning becomes complex.

Restrictions such as deadlines that need to be met and available resources complicate the planning process.

If you would like your costs to be as low as possible and also keep your stocks low at the same time, then meeting both of these goals means your planning becomes complex.

Variables change constantly, restrictions are set or goals redefined. The problem must be solved fast so that the solution is in place before the conditions change once again, meaning that the solution you have no longer works.

The more of these aspects you have,  the more complex the planning problem becomes. Sometimes, it takes just one aspect to make planning become complex, even if it appears immaterial at first sight. Try it and see by planning your machine utilization based on our example below. Don’t worry: we’ve chosen delicious pralinés for our example.


Optimizing the
production of chocolate boxes

A chocolate factory produces 5 different assortments of pralinés. All 5 assortments are produced in the same amount.

  1. Production stage: production
  2. Production stage: packaging
  3. Production stage: decoration

After the pralinés have been made in production stage 1, they are packed into boxes during stage 2. In phase 3, the boxes are decorated with a ribbon or sticker. The production time for each assortment is different for each stage. Bear in mind that phase 2 can only start once phase 1 has been fully completed. In addition, the manufacturer wants his production to be as efficient as possible and a production stage should take up as little time as necessary.

Simply print out the production planning task, cut it out and lay out the plan. You’ll see that it isn’t as easy as it initially seems.

The answer is 24


»Things are easier if you use the right tool – in fact, the right tool makes many things possible in the first place«

Unit 2

Unit 2:
Prescriptive Analytics

A calculable future


What only mathematical optimization can do

Mathematical optimization is a multi-functional tool for all current planning tasks in day-to-day business. It becomes even more powerful when it is deployed for tasks in which we venture a look into the future and plan future events better.

These tools are called Prescriptive Analytics; like OPTANO. These allow recommendations for action to be calculated reliably for specific future events. Prescriptive Analytics run through different kinds of what-if scenarios. You can work out precisely which actions are needed to attain specific goals. It’s simply an ideal tool for the added value in your business.

There are many use case examples for such planning tasks: is it wise to open a new production facility? Which location would be most suitable for it? What effect would buying a new machine  have on my production?

It’s believed that only 30% of companies deploy Prescriptive Analytics at present. Therefore, it is worth exploring the limits of what they can do and venturing a look into the future together with OPTANO.


»If you know what you want to achieve, Prescriptive Analytics knows how«

Homework № 4

Homework № 4: How many grains of rice did Sissa get?

Finally! Homework that you actually enjoy doing! As mathematicians and software engineers, we love solving puzzles. This is why we would like you to solve a little brain teaser at the end of each exercise.

The legend surrounding the invention of chess involves the exponential growth of a problem: The Indian King Shihram was so taken with the game that he wanted to reward its inventor, Sissa, by granting him any wish, no matter how large. He replied: ” Master, give me one grain of rice for the first field on the chessboard, 2 grains for the second, 4 for the third and for every further field twice as many grains as that of the one before.” The king was insulted since he wasn’t aware of the magnitude of the wish.

Can you work out just how modest or greedy the inventor’s wish was? Send us the exact number of all the grains of rice that the king had to give to the inventor. Tip: Use math to solve the problem!


Send your answer


1st Prize:

A photoshoot styled on our campaign

If your name is drawn, you will have the opportunity to choose a theme of your choice for your personal photoshoot. It can be your hobby, a business issue, whatever you want. The only condition is that it is complex enough and fits on a 1x1m table. The photoshoot will take place in Bielefeld, Germany. Travel expenses within Germany as well as an overnight stay in a hotel are included in the prize.

2nd – 5th Prizes:

A hardback edition of  »Things Come Apart.« by McLellan

6th – 10th Prizes:

Game »Die Kunst Aufzuräumen«

Legal Notice:

Dissembled objects will not be reassembled. Further technical agreements concerning the photoshoot will be clarified with you in advance. The photo shoot will take place in Bielefeld. The winner and OPTANO will be assigned the rights to the finished product once the negatives have been handed over.

Legal Announcement

Conditions of Participation

This competition isn’t just for glory and prestige! Our first prize is a photoshoot in the style of our campaign. Conditions: You correctly answer all 10 of our fairly mind-boggling questions in our Exercise! Campaign. You can follow our campaign in our newsletter which you will receive as soon as a new exercise is online.

The competition closes in fall 2020.

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