Introduction

If you are reading this, chances are that you are on your way to becoming a manager. Or, maybe, you are striving to become a better one. It may also be the case that the very word manager sounds dreadful to you and conjures up images of unjustified bonuses; yet, you might be interested in how good management decisions should be made or supported, in both the private and public sectors. Whatever your personal plan and taste, what makes a good manager or a good management decision? The requirements for a career in management make a quite long list, including interpersonal communication skills, intuition, human resource management, accounting, finance, operations management, and whatnot. Maybe, if you look down the list of courses offered within master’s programs in the sector, you will find quantitative methods (QMs). Often, students consider this a rather boring, definitely hard, maybe moderately useful subject. I am sure that a few of my past students would agree that the greatest pleasure they got from such a course was just passing the exam and forgetting about it. More enlightened students, or just less radical ones, would probably agree that there is something useful here, but you may just pay someone else to carry out the dirty job. Indeed, they do have a point, as there are plenty of commercially available software packages implementing both standard and quite sophisticated statistical procedures. You just load data gathered somewhere and push a couple of buttons, so why should one bother learning too much about the intricacies of QMs? Not surprisingly, a fair share of business schools have followed that school of thought, as the role of QMs and management science in their curricula has been reduced,¹ if they have not been eliminated altogether.

Even more surprisingly however, there is another bright side of the coin. The number of software packages for data analysis and decision support is increasing, and they are more and more pervasive in diverse application fields such as supply chain management, marketing, and finance. Their role is so important that even books aimed at non specialists try to illustrate the relevance of quantitative methods and analytics to a wide public; the key concept of books like Analytics at Work and The Numerati is that these tools make an excellent competitive weapon.² Indeed, if someone pays good money for expensive software tools, there must be a reason. How can we explain such a blatant contradiction in opinions about QMs? The mathematics has been there for a while, but arguably the main breakthrough has been the massive availability of data thanks to Web-based information systems. Add to that the availability of cheap computing power and better software architectures, as well as smart user interfaces. These are relatively recent developments, and it will take time to overcome the inertia, but the road is clear.

Still, one of the objections above still holds: I can just pay a specialist or, maybe, learn a few pages of a software manual, without bothering with the insides of the underlying methods. However, relying on a tool without a reasonable knowledge of its traps and hidden assumptions can be quite dangerous. The role of quantitative strategies in many financial debacles has been the subject of heated debate. Actually, the unpleasing outcome of bad surgery executed by an incompetent person with distorted incentives can hardly be blamed on the scalpel, but it is true that quantitative analysis can give a false sense of security in an uncertain world. This is why anyone involved in management needs a decent knowledge of analytics. If you are a top manager, you will not be directly involved in the work of the specialists, but you should share a common language with them and you should be knowledgeable enough to appreciate the upsides and the downsides of their work. At a lower level, if you get an esoteric error message when running a software application, you should not be utterly helpless; by the same token, if there are alternative methods to solve the same problem, you should figure out what is the best one in your case. Last but not least, a few other students of mine accepted the intellectual challenge and discovered that studying QMs can be rewarding, interesting, and professionally relevant, after all.³

I will spend quite a few pages trying to convince you that a good working knowledge of QMs is a useful asset for your career.

• When information is available, decisions should be based on data. True, a good manager should also rely on intuition, gut feelings, and the ability to relate to people. However, there are notable examples of managers who were considered geniuses after a lucky decision, and eventually destroyed their reputation, endangered their business, and went to jail in some remarkable cases. Without going to such extremes, even the best manager may make a wrong decision, because something absolutely unpredictable can happen. A good decision should be somewhat robust, but when things go really awry, being able to justify your move on a formal analysis of data may save your neck.
• QMs can make you a sort of universal blood donor. The mathematics behind is general enough to be applied in different settings, such as supply chain management, finance, and marketing. QMs can open many doors for you. Indeed, throughout the book I will insist on this point by alternating examples from quite different areas.
• Even if you are not a specialist, you should be able to work with consultants who have specialized quantitatively. You should be able to interact constructively with them, which means neither refusing good ideas merely because they seem complicated, nor taking for granted that sophistication always works. At the very least, you should be aware of what they are doing.

I have met some people whose idea of applying QMs is collecting data and coming up with a few summary measures, maybe some fancy plots to spice up a presentation, and that’s it. In fact, QMs are much more than collecting basic descriptive statistics:

1. If QMs are to be of any utility to a manager, they should help her in making decisions. Unfortunately, modeling to make decisions is a rather hard topic.
2. By the same token, basic probability and statistics are not enough to meet the challenge of a complex reality. Multivariate analysis tools have been applied, but there is a gap between books covering the standard procedures and those at an advanced level.

We will try to bridge that gap, which is somewhat hard to do by just walking through a lengthy and dry list of theorems and proofs. I will illustrate a few toy examples, that will hopefully provide you with enough motivation to proceed.

We have emphasized the role of data to make decisions. If we knew all of the relevant data in advance, then our task would be considerably simplified. Nevertheless, We that even in such an ideal situation some quantitative analysis may be needed. More often than not, uncertainty makes our life harder (or more interesting). We deal with different examples in which we have to make a decision under uncertainty. The standard tools that help us in such an endeavor are provided by probability and statistics, which constitute a substantial part of the book. Nevertheless, we will show that some concepts, such as probability, can be somewhat dependent on the context. Indeed, many features of real life may make a straightforward application of simple methods difficult, and we will see a few examples. Finally, We will discuss how, when, and why QMs can be useful, while pointing out their limitations.