Category: Deterministic Decision Models

The portfolio optimization model that we have considered in Example 12.5 does not place any restriction on the composition of the portfolio. In practice, bounds are enforced, e.g., to limit exposure to certain risk factors; for instance, we might wish to limit exposure to emerging markets or to the energy sector. Another practical issue that is worth…

In the network optimization models of Section 12.2.4, we have taken the network structure as given. Hence, the decisions we had to make were tactical or operational, and just linked to flow routing. However, at a more strategic level, we have to make decisions concerning: As far as the last point is concerned, we have considered…

A classical example involving fixed charges is the lot-sizing model, which is essentially a generalization of the basic EOQ model to take into account multiple items, limited production capacity, and time-varying demand. To see why such a model arises, note that in the multiperiod planning models (12.26) and (12.27) we did not consider at all…

The knapsack model and its variants are pure binary programming models. In this section we get acquainted with a quite common mixed-integer model, arising when the cost structure related to an activity cannot be represented in simple linear terms. The fixed-charge problem is one such case. Let decision variable x ≥ 0 represent the level of an activity. The…

Let us consider a trivial model for capital budgeting decisions. We must allocate a given budget B of money to a set of N potential investments. For each investment opportunity, we know We would like to select the subset of investments that yields the highest total profit, subject to a limited budget B. This looks like a portfolio optimization model;…

As we have already pointed out, integer programming models may pop up when there is a need to restrict purchase or production decisions to integer quantities, maybe multiples of a standard batch. However, the most common reason for using such models is by far the inclusion of logical decisions. In this section we use a set…

Sometimes, we face management problems with quite complicated constraints, which seem to defy the best modeling efforts. Column-based model formulations are a formidable tool, which is again best illustrated by a simple example, namely, a stylized staffing problem. Imagine that we are running a post office, or something like that, with a lot of counters;…

An optimization model need not have a unique optimal solution. As we have pointed out in Section 12.1.1, the following can occur: Commercial solvers are able to spot infeasible mathematical programs, but, from a practical perspective, we cannot just report that, leaving the decision maker without a clue. It would be nice to provide her with…

Goal programming is one way of dealing with conflicting objectives, but it requires the assessment of weights and targets. Unfortunately, it may be very difficult, or even unethical, to figure out weights. As an example, consider the tradeoff between the cost of a production process and its pollution level. Sometimes, we would like to visualize…

The deviation variables that we have utilized in order to formulate alternative regression models as LPs have other uses as well. Let us consider a generic optimization problem over a feasible set S. A standard complication of real-life decision problems is that there is not just one criterion to evaluate the quality of a solution, but…