This week’s Wiki-Wednesday topic is Mathematic Optimization, and that article is the source of all quoted text below. We are covering it because of the CombineNet/Procurement Leaders/A.P. Moller – Maersk event on taking strategic sourcing to the “next level”. For many companies, whether they have implemented a strategic sourcing solution or not, optimization functionality may take a little longer to make use of, both because it is a more complex part of the software but also because the categories that can truly make use of optimization are not low-hanging fruit.
You can read an excerpt from the Wikipedia page on mathematical optimization here, but I am going to take this opportunity to break it down and use examples from procurement/sourcing. The article starts with a straightforward definition of optimization as “the selection of a best element from some set of available alternatives”.
All sourcing projects require some kind of optimization in order to make an award. Your qualified bids are the “available alternatives” and your project goals and objectives determine which of them is “best”. Depending on the project, “best” may mean cheapest, most readily available, or most innovative. In many projects, that kind of optimization can be done without the assistance of a system other than Microsoft Excel.
In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.
When you get into more complex situations: thousands of “items” with hundreds of suppliers able to handle different combinations of your product/service requirements, the assistance of technology will be required.
“In multi-objective optimization […] adding more than one objective to an optimization problem adds complexity.”
Minimizing cost is the obvious factor in optimization problems, but in real scenarios there may be many other factors to consider. For example: Do you need to ensure that specific incumbent or diversity suppliers receive a portion of the business? Sometimes that means a dollar or quantity threshold and other times it may mean awarding a product to that supplier regardless of the other bids received. Transportation provides many good examples for optimization; large transportation RFPs are usually broken down into “lanes” or routes between two points. It may be necessary to dedicate a lane to a pre-selected supplier, and optimization solutions ensure that requirement is factored into the final award scenario.
“A design is judged to be "Pareto optimal" (equivalently, "Pareto efficient" or in the Pareto set) if it is not dominated by any other design: If it is worse than another design in some respects and no better in any respect, then it is dominated and is not Pareto optimal.”
Again, let me provide an example to tie this back to procurement execution. Often, large events that would make use of optimization engines are multi-round. There may be an RFP and then an RFQ or multiple rounds of RFQs. Handling the process this way allows procurement to make adjustments to the bid as necessary based on first round information and to incorporate a feedback cycle into the second round. The other benefit is that you may be able to eliminate suppliers that are not competitive based on the project’s objectives and can be removed from the process.
In the quote above, the “design” is a bid – a total bid, assuming there are a number of items being bid on by that supplier. If the optimization engine can help you identify suppliers that will not end up being awarded any business, it is in everyone’s best interests to thank them for their participation and move on to the next round without them. They avoid losing further time and you avoid dealing with additional training requirements and background noise.
“Optimization problems are often multi-modal; that is they possess multiple good solutions. They could all be globally good (same cost function value) or there could be a mix of globally good and locally good solutions. Obtaining all (or at least some of) the multiple solutions is the goal of a multi-modal optimizer.”
If you are lucky enough to be running an event where you receive a number of good solutions, optimization will again come to the rescue. It is unlikely that all good options will be at the exact same price point, but assuming they are close, you can go to your secondary objectives like incumbent status, diversity status, and internal stakeholder preference. By running multiple scenarios, you can calculate the cost variance associated with each to help make the final decision. Although the cost difference may be relatively small at the item level, but once you apply the same scenario over the total business the costs or savings add up. Knowing that number will help your stakeholders make an informed decision.
“The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.”
It is possible that despite the number of bids received one or more of your items will not be fulfilled. At a minimum, the optimization engine should be able to help you quickly identify those items so you can work during your negotiation and feedback cycles to fill them. Although optimization engines do most of the heavy lifting, you should never hesitate to double check surprising results “the old fashioned way”. Having an unfulfilled item is a good example. Make sure that none of the scenarios you have built are causing conflicts preventing the item from being awarded when there was an acceptable bid.