Why optimize? Or the autopsy of decision…

When you ask decision-makers how they make choices, they’ll often say something about “optimizing the solution” or making the “optimal” choice. These common expressions often reflect a complex process. Decision-makers must acquire information (often quantitative and sometimes in huge quantities); analyse, summarize, organize, and filter this information in order to identify the possible choices; and finally select an option. Decisions are often all the more difficult since the available data is frequently uncertain, polluted, or inconsistent.
In this process, decision-makers try to determine the consequences of the possible choices in order to compare them. Thus they inevitably face the “fear of regret”. Who never asked themselves, just before taking the leap, if there weren’t a better solution than the one they were about to choose?

We all strive to make the best possible choice, and therefore we establish a process (including questioning and hesitations) similar to what we call an “optimization algorithm”.

Consider the case of a company that has just acquired a competitor, and now has three warehouses instead of two to cover the territory and improve customer service. The Supply Chain Manager believes savings are possible by closing one of the three warehouses: each one has the capacity required to serve all customers. Which one to close? How to choose? What savings will result by closing this or that warehouse?

How do you decide?

Optimizing means choosing the best solution with sufficient guarantees that you are not making a mistake, or at least not by much, or by at most p%. At Eurodecision our business is to control and rationalize this process by applying quantitative methods. To achieve this goal, we use mathematical models considered authoritative by the decision-makers and their teams. We also leverage algorithms for constrained optimization that offer “proof of optimality”, or “a reasonable body of evidence that guarantees the optimality” of the proposed solution. This method involves choosing criteria (used to assess the solutions), determining the constraints (that tell us that not all solutions are possible: you can’t make a baby in a month by getting nine women pregnant), and all the basic decisions that make up each solution. When formulated in these terms, making the optimal choice means solving an algebra problem with many unknown variables: a constrained optimization problem.

Consider an R&D manager who needs to select three out of ten projects for funding, knowing he has a limited budget and will have to make trade-offs.
– Criteria might be the expected revenue from each project, how well the project fits in the company’s overall industrial investment strategy, the duration of each project, the number of people required to carry it out, etc.
– Constraints will probably include the total amount of the investment, the human resources available, and the deadline
– Decisions will include which projects to select and which people to assign to each project. 

In order to find the optimal solution (“the best choice”), our consultants use optimization algorithms. These are usually standard algorithms (such as simplex, branch & bound or the barrier method for problems related to Mathematical Programming), and sometimes we develop custom algorithms (for meta-heuristics or ad-hoc decomposition methods). Technically, the set of data/models/algorithms/restitution make up a decision support system, the software that decision-makers use to build their solutions.

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