In order to express average total cost per unit time as a function of the order size Q, we should consider all of the factors contributing to the overall cost. The first one that comes to mind is purchase cost. If the unit item cost is c, measured in money per item, we have to pay cQ whenever… Continue reading Task 1: representing the total cost function
Month: February 2023
A MOTIVATING EXAMPLE: ECONOMIC ORDER QUANTITY
Before getting into formal details of calculus, it is essential to arm ourselves with some motivation for doing so. In management science, we often want to relate decisions to cost or profit. This is necessary in order to find an “optimal” decision yielding the best performance in some well-specified sense. We should quote “optimal,” because… Continue reading A MOTIVATING EXAMPLE: ECONOMIC ORDER QUANTITY
Introduction
Calculus is a classical branch of mathematics, dealing with the study of functions. A function is essentially a rule for association of one or more input variables with an output value. For instance, we might be interested in relating a decision, say, how much to produce, to the business outcome, say, profit. We have seen… Continue reading Introduction
QUANTITATIVE ANALYSIS AND PROBLEM SOLVING
Even if the problem is too complex to rely on the decision proposed by the solution of a model, we should not underestimate the value of model building per se. The model building process itself is a valuable activity as it requires the following ingredients: If model building and model solving result in a solution… Continue reading QUANTITATIVE ANALYSIS AND PROBLEM SOLVING
Descriptive vs. prescriptive models
A quantitative model can be Typical examples of descriptive models that we cover in the book are All of these models are used to generate information that helps in coming up with a decision, but they are not aimed at generating the decision directly. Examples of prescriptive models whose output is the decision itself are… Continue reading Descriptive vs. prescriptive models
QUANTITATIVE MODELS AND METHODS
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… Continue reading QUANTITATIVE MODELS AND METHODS
The effect of organized markets: pricing a forward contract
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… Continue reading The effect of organized markets: pricing a forward contract
ENDOGENOUS VS. EXOGENOUS UNCERTAINTY: ARE WE ALONE?
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… Continue reading ENDOGENOUS VS. EXOGENOUS UNCERTAINTY: ARE WE ALONE?
Variations on coin flipping
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… Continue reading Variations on coin flipping
Squeezing information out of known facts
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… Continue reading Squeezing information out of known facts