Author: haroonkhan

Hopefully, the examples in the previous sections have shown the relevance, as well as the limitations, of quantitative analysis for real-life business decisions. In the following chapters we cover a wide variety of tools, which could be somewhat confusing for the reader. Hence, it is a good idea to set a conceptual framework to classify…

An asset (e.g., a stock share) is sold now at a spot price S0 = $50, where t = 0 is current time. The spot price is the prevailing price at which the asset is exchanged at any moment. The spot price in one year is, of course, uncertain, but say that the expected price in one year is…

A colleague of mine draws the line between engineers (like myself) and economists as follows: In fact, the need for analyzing the interactions between noncooperative decision makers was the driving force for the development of game theory. We will consider related issues in Section 14.3, where we investigate the role of misaligned incentives when multiple stakeholders…

In this section, we consider the mother of all random experiments: coin flipping. This is a good way to get acquainted with probabilities, which are not necessarily relative frequencies, as well as with investments under uncertainty. We illustrate plain coin flipping first, and then some more interesting variations on the theme. Plain coin flipping Assuming that…

As we have remarked in the previous section, we often have to cope with the impossibility of gathering in advance all the information we need to make a decision, partly because of uncertainty about future events, and partly because some variable cannot be observed directly. However, this is no good reason not to do our…

In the product mix problem, we assumed perfect knowledge of future demand, but, unfortunately, exact demand forecasts are a bit of scarce commodity in the true world. Indeed, the standard trouble in supply chain management is purchasing an item for which demand information is quite uncertain. If we order too much, one or more of…

We often have to make decisions here and now, without complete knowledge about problem data or the occurrence of future events. In distribution logistics, significantly uncertain demand must be faced; in finance, several sources of risks affect the return of an investment portfolio. In all of these settings, the future effect of actions is not…

We solved the previous example by a simple rule: Let us pick the most profitable item and try producing as much as we can; if we hit a market limitation, consider the next most profitable item, and go on until we run out of resource availability. However, there must be something more to it. To…

A firm4 produces red and blue pens, whose unit production cost is 15 cents (including labor and raw material). The firm incurs a daily fixed cost, amounting to €1000, to run the plant, which can produce at most 8000 pens per day in total (i.e., including both types). Note that we are expressing the capacity constraint in…

Product mix decisions are essentially resource allocation problems. We have limited resources, such as machines, labor, and raw materials, and the problem calls for their optimal use in order to maximize profit, which is earned by producing and selling a set of items. The decision problem consists of finding the right amounts to produce for…