What is Constraint-based Modeling in Prescriptive Analytics?

Every company operates within a large set of constraints, including annual budgets, material purchase contracts, resource capacity, hospital ward space, environmental regulations, customer order contracts, financial reporting regulations, and others. While these financial, physical and policy constraints can impact an entire organization, most planning processes are still done by department, business unit, geography or some other hierarchy. The need for true Integrated Business Planning (IBP) has never been greater.

No one would argue that major constraints, especially those impacting profits, are not important. Well understood and managed constraints, such as budgets, normally trickle down to various decision-making levels. However, companies often have many enterprise-impacting constraints, which are not always taken into account or followed.

This results in disconnects and inconsistencies in the decision logic process — often the case when organizations use a descriptive or predictive analytics modeling approach for planning decisions. Critical constraints are usually simplified or aggregated, and sometimes completely ignored!

What is a Constraint?

First, let's clarify what a constraint actually is. The classical and quite generic definition is something that limits or restricts something else. The key words being “limits” and “restricts."  There is no room for “sort of,” “kind of” or “partially”  a constraint must be binding. Constraints can take the form of rules, such as “no games can be scheduled on Monday nights,” or physical constraints, such as “the maximum capacity of the tank is 5,000 liters.”

A constraint is not a bias or a preference. Implementing a rule such as “games should be scheduled on Friday nights if possible” is not a constraint, it’s a preference.  A rule such as “customer ABC’s orders should be processed out of DC 123” is also not a binding constraint if viable alternatives are allowed to be considered.

Some industry pundits believe that using preferences and biases in the form of heuristic rules, in lieu of hard constraints, is perfectly acceptable but is it? What it comes down to is how important profitability, predictability, agility, and accountability are to the company’s management and their investors.

What is Constraint-based Modeling?

Constraint-based modeling is a scientifically-proven mathematical approach, in which the outcome of each decision is constrained by a minimum and maximum range of limits (+/- infinity is allowed). Decision variables sharing a common constraint must also have their solution values fall within that constraint’s bounds. A constraint-based modeling approach is most commonly — and effectively — used with optimization techniques, such as the use of linear and mixed-integer programming to maximize an objective function. 

Here’s a simple example: an auto manufacturer has two assembly lines, Line #1 for cars and Line #2 for trucks. However, the manufacturer has a single paint shop, which acts as a constraint for the entire plant. The company, in this case, wants to know how many cars and trucks it should make to maximize profitability. When an optimal solution is obtained, neither assembly line’s production can exceed the paint shop’s capacity.

While some approaches rely on averages (such as standard cost accounting) for true driver-based constraint modeling, all costs, rates, yields, and constraints will be defined in their natural units of measure (e.g., $/unit, Euro/hour and so on) for each step in the process. Imagine the problem as if you were actually watching the processes occur right in front of you. Once defined, it is then the solver’s responsibility to analyze natural behavior and apply all constraints to determine the optimal solution.

Conversely, constraint-based modeling is not hypothesis-driven (a.k.a. deterministic) modeling. No analyst using a constraint-based model should be able to predict the behavior of the entire model beforehand. Any “solution” that allows for this is not true constraint-based modeling.

True constraint-based modeling also calculates the opportunity value of the constrained decision. Company management should not settle for a report that states a machine’s capacity will be utilized for an entire 40 hour work week, and that, therefore, no additional production can occur. The best constraint-based modeling approaches will certainly provide that insight, but will also identify all profit-impacting opportunities.

For example, by adding an extra shift on a given machine, a company may be able to make an additional $100k per hour. Most traditional planning systems, like those for materials requirement, capacity, inventory or demand, simply will not calculate the true bottom-line opportunity value associated with a constrained decision. This is true for positive opportunity values constrained at an upper limit (usually in the form of time or market constraints), as well as negative opportunity values constrained at a lower limit (usually in the form of supply, labor or demand contracts).

Know What Questions to Ask

For prescriptive analytics software — used to answer the question “what should I do?”— constraint-based modeling is not an optional feature; it’s a core philosophical foundation. It must be able to not only define and apply critical customer-specific constraints but also, as mentioned previously, state the value of the constrained decision. This value can only be obtained by using established optimization techniques.

Software that supports constraint-based modeling comes in multiple flavors, from algebraic programming languages (which can model almost anything with the required expertise and time) to packaged applications (capable of solving targeted problems within an industry/function combination). The key for decision-makers within an organization is to know what questions to ask. Here’s a sample set:

  • Ask the vendor to describe how critical business constraints are defined, and if any shortcuts are taken in the process — remember the difference between constraints and heuristics.
  • Think globally — the value of constraint-based modeling grows exponentially with complexity. Make sure to ask how policy, regulatory and other types of non-physical constraints are represented.
  • Insist on understanding how financials are modeled — even if it's not necessary for your initial project, as soon as you meet with your CFO or CEO they will become critical.

By all means, if the project at hand is complex, put the vendor through a proof-of-concept (POC). Ask them to build a model with your data, and then optimally solve “what-if” scenarios during a live demonstration. This transparent approach will not only enable you to see how constraint modeling works but also provide a proper comparison of the various alternatives available.  

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