Is Optimization Just for Mad Scientists or the Manager Next Door? Could that be you?

There was a point in the past when, to many, the idea of “optimization” used to summon images of Greek letters juxtaposed in odd arrangements kept in black boxes that spewed out inscrutable results.  In some places, optimization was thought of as a subject best left to impractical theorists, sequestered in small cubicles deep in the bowels of the building to which few paths led and from which there were no paths out.   From that perspective, optimization was something that had to be reserved for special cases of complex decisions that had little relevance for day-to-day operations.

That perception was never reality, and today, growing numbers of business managers now understand that optimization and those who can make it work and leverage it intelligently are not just valuable assets, but absolutely necessary to achieving and sustaining competitive advantage.  Global competition mandates that managers not “settle” in their decisions, but that they constantly make higher quality decisions in less time.  Optimization helps decision-makers do just that.  The exponential increases in computing power along with advances in software, both tools and applications, have enabled the use of optimization in an ever widening array of business decisions.

Let’s consider a few fairly common decisions where optimization provides a powerful fulcrum for improved results. 

  1. Consider a paint manufacturer.  There will be several sequential manufacturing processes.  Each process is executed in a vessel or reactor.  The vessel or reactor must be cleaned between batches.  In the final operation, the paint must be packaged into relatively small containers from a large batch.  To what should the minimum and incremental batch sizes be set for each kind of paint in each successive operation so that the time between batches is minimized while the cost and risk of having too much product is also minimized?  Operations like this often work off of a product wheel where items are processed in a fixed sequence that repeats every so often.  In that case, the frequency of repeating the sequence must also be determined.
  2. What about a furniture maker with a limited supply of various types of wood that can make a wide variety of furniture styles and quality?  How should the supply of raw materials and manufacturing capacity be allocated to finished furniture pieces and sets in order to maximize profits, keeping in mind that there is limited demand for each type and piece of furniture?  That is not an easy problem to solve with paper and pencil, but one with which the production manager must grapple each day.
  3. What if you have a number of retail stores or shops?  You need to determine how much floor and shelf space to allocate to each product category, and perhaps, to each product with the goal of maximizing profit per square foot of floor space or linear foot of shelf space.  The problem is that there is limited demand for the highest margin products and demand is uncertain in any case.  This, again, is a perfect application for optimization.
  4. Suppose a hospital with limited X-ray, CAT-scan, MRI and other types of machines and technicians.  The hospital has a limited number of examining and other types of rooms as well as a limited number of doctors and other personnel with various special qualifications.  How should appointments and human resources be scheduled in order to minimize patient waiting time and maximize the use of costly capital equipment and well-trained, but expensive human resources?  That is a daunting challenge to face each day without optimization.
  5. Finally, consider a consumer goods manufacturer who must determine when to promote which products and for how much of a discount.  As in the other cases, the inability to make the best decisions can cost dearly.  In this case, the penalty may be manifested in lost sales opportunity because the promotion was not sufficiently enticing or associated with the right products.  On the other hand, the cost may come in the form of lost margin because while the promoted products sold out, the price was actually too low.

These are just a few examples of important, routine decisions that require the use of mathematics to give decision-makers the head start that they need to compete.  The use of mathematics can be also applied in other ways besides optimization such as statistical analysis and simulation.

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About Arnold Mark Wells
Industry, software, and consulting background. I help companies do the things about which I write. If you think it might make sense to explore one of these topics for your organization, I would be delighted to hear from you. I am employed by Opalytics.

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