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Types and Development of Decision-Making Models
Quantitative Analysis · Chapter 2: Decision-Making Models and RiskSection 2.1 · lesson 5 of 5511 min · free with a free account
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In this lesson
Types and development of decision-making models.
- Name the four building blocks every decision model contains
- Distinguish descriptive, predictive and prescriptive models
- Match a problem to an algebraic, graphical, simulation or network form
- Walk the six-step build process and judge when simpler is better
Transcript
Everything said in the video, section by section (1,604 words). Read along, or search it.
Decision-Making Models and Risk
Choosing the Right Framework
A factory manager has to decide how many of two products to build this week. She has limited labour, limited material, and a profit target. Intuition can get her close. It cannot tell her how close. A decision model can. A decision model is a formal representation of a decision problem. It makes the structure explicit, and it makes the problem solvable. In this section you will learn what every model is built from, and how models get classified. You will walk the six steps that turn a vague question into a working model. Then you will build one yourself, and break it on purpose to see what it really depends on.
Foundation
What a Decision Model Actually Is
Start with what actually counts as a model. It does not have to be complicated. Even a single equation qualifies, provided four things are made explicit. An objective. Decision variables. Constraints. Parameters. Miss any one of those and you have a description, not a decision model. Here is why that matters in practice. Without an objective, nothing tells you that one decision beats another. Without decision variables, there is nothing you actually control. Without constraints, every option looks feasible, including the impossible ones. And without parameters, the model has no numbers to run on. Get all four onto the page and the problem stops being a debate. It becomes something you can solve.
Building Blocks
Objective, Variables, Constraints, Parameters
Let us take each block properly, because this vocabulary comes back all term. The objective function states what you are trying to achieve. Usually something to maximise, like profit, revenue or customer satisfaction. Or something to minimise, like cost, risk or waiting time. Decision variables are the quantities you genuinely control. How many units to produce, which routes to assign, what price to set. Everything else in the model either depends on those variables, or constrains them. Constraints are the limits a feasible decision has to respect. Labour hours, machine capacity, budget, legal requirements, physical relationships. Parameters are the numerical inputs the model holds fixed for a given run. Some come from data, some from estimates, some frankly from assumption. And deliberately changing a parameter is exactly how we test sensitivity later.
Models By Purpose
Descriptive, Predictive, Prescriptive
Models get grouped by the kind of question they answer. Three classes, and they line up in time. Descriptive models explain what is. Dashboards, financial statements, statistical summaries, customer segmentation profiles. They make no forecast and no recommendation. Their value is clarity. Predictive models estimate what will be. Next month's demand. The chance a customer churns. The expected default rate on a loan portfolio. Now here is the part people skate over. A predictive model tells you what is likely. It does not tell you what to do about it. That job belongs to prescriptive models, which pair an objective function with constraints. Production schedules, vehicle routes, investment portfolios, staff rosters. Linear programming lives here.
Model Forms
Four Structural Forms
Same purpose, very different shapes. Within those three classes a model can take four structural forms. Algebraic models are equations and inequalities, with variables and parameters linked mathematically. That covers linear programming, pricing models and break-even analysis. Graphical models show the answer as a picture. Feasible regions, decision trees, influence diagrams. Useful when a problem has few variables. Simulation imitates a system over time using random sampling. It is the right pick when relationships are complex or stochastic. Monte Carlo risk analysis, queuing systems, inventory policy testing. Network models use nodes and arcs for flows, paths or connections. Shortest path routing, project scheduling, supply chain flow. Choosing the form matters as much as choosing the purpose.
Model Building
The Six-Step Model-Building Process
Building a model is a process, not one act of writing equations. Six steps take a vague business question to something that runs. Step one, problem formulation. State the question precisely. What decision is being made? Who owns it? Where is the boundary of the system? Step two, data collection. Gather the costs, the capacities, the demand history. Note which inputs are reliable and which are only estimates. That note pays off later. Step three, model construction. Write the objective, define the variables, list the constraints. Step four, validation. Compare the output against historical data or known cases. If it does not reproduce reality reasonably well, you iterate rather than push on. That loop is the whole point of the process. Step five, sensitivity testing. Vary key parameters and watch the recommendation. A decision that flips on a tiny input change is fragile. Step six is implementation, and it never really ends.
Assumptions
Which Assumptions Actually Matter
Every model simplifies reality. There is no way around that. A model that captured every detail would be as complex as the world itself. And just as hard to understand. So the goal is not to avoid assumptions. That is impossible. The goal is to know which assumptions matter. Here is the test, and it is a sharp one. An assumption matters when changing it would change the recommendation. Take a production model that assumes constant cost per unit. If cost actually rises with volume, the recommended production level may be wrong. That assumption is load bearing. Now suppose the cost is slightly off and the answer does not move. Then it is not load bearing, and it is not where your attention belongs. So list every assumption, then ask, if this were wrong, would my answer change?
Validation
Three Ways to Earn Trust in a Model
Validation answers one question. Can we trust this model? Three techniques, and they complement each other rather than compete. First, test against historical data. Run the model on a past period where you already know the actual outcome. If the output lands reasonably close to what really happened, confidence rises. Close within a tolerance the user accepts, not close in some absolute sense. Large gaps point to missing variables, or relationships that run the wrong way. Second, sensitivity analysis. Change one parameter at a time and watch the output. A stable model produces predictable, proportionate changes. A model that swings wildly on small changes is either capturing real instability, or built on weak structure. Third, expert review. Domain experts catch a forgotten constraint or a variable that does not exist in practice. It is a low cost, high value step, and it is the one no statistical test can replace.
Complexity Vs Interpretability
Why the Simpler Model Often Wins
There is a real temptation to add detail until the model looks impressive. Resist it. The simpler model is often the better one. Three reasons, and none of them are about elegance. First, trust. Decision makers must understand the model well enough to rely on its output. A model nobody can explain rarely influences a real decision. Second, data. Every extra parameter is another quantity somebody has to estimate. Bad data quickly swamps whatever you gained from the extra structure. Third, maintenance. As the business changes, every relationship has to be re-examined. Simple models survive change better. Accuracy does rise with complexity, but interpretability falls, and the sweet spot comes early. So start with the simplest model that could plausibly answer the question.
Worked Example
Building a Two-Product Production Model
Time to build one. A small factory, two products. A standard unit earns twenty dollars of profit, and a premium unit earns twenty-five. Each standard unit takes one hour of labour and two kilograms of material. Each premium unit takes two hours of labour and one kilogram of material. This week the factory has one hundred and twenty labour hours available. And one hundred and eighty kilograms of material. The question. How many of each should it produce to maximise profit? Let x be the number of standard units, and y the number of premium units. Maximise twenty x plus twenty-five y. Labour says x plus two y is at most one hundred and twenty. Material says two x plus y is at most one hundred and eighty. And both x and y must be at least zero, because you cannot build negative units.
Scenario A
Baseline: Checking the Corner Points
Now solve it. With only two variables you can solve this graphically. The constraints carve out a feasible region, and you check its corner points. The origin gives zero profit. A corner, but not a useful one. Ninety standard units and no premium gives eighteen hundred dollars. Sixty premium units and no standard gives fifteen hundred dollars. The interesting corner is where both constraints meet. Solve the two equalities together and you get eighty standard and twenty premium units. Profit is twenty times eighty, plus twenty-five times twenty. Two thousand one hundred dollars. Now notice something about that answer. Eighty plus two times twenty is exactly one hundred and twenty labour hours. Both constraints bind. The factory uses every labour hour and every kilogram, with nothing left idle.
Scenario B
Change One Parameter, Watch the Answer Move
Now break it on purpose. That is the real point of the exercise. Management revises one estimate. Each premium unit actually needs twenty per cent more labour. Two point four hours instead of two. One number changes. Labour becomes x plus two point four y, at most one hundred and twenty. Re-solve, and the recommendation moves. The corner shifts to eighty-two point one standard units, and fifteen point eight premium. Whole units round that down to eighty-two standard and fifteen premium. Profit falls to roughly two thousand and fifteen dollars, down about four per cent. Premium output drops because each premium unit now eats more of the scarce labour. So which assumptions were driving the result? Labour hours per unit, clearly. A small change there moved the schedule and the profit. Linear profit per unit is next. The model assumes price holds constant whatever the volume. And independent resource pools. If overtime costs more, the labour constraint hides a cost the model ignores. Even a four line model carries assumptions worth scrutinising, and that discipline is worth more than the equations.
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Quantitative Analysis (Math 250) is a self-paced online course of 55 video lessons in 13 chapters, from decision analysis and simulation to inventory and queuing models, project scheduling, linear programming and transportation models. It carries a NCCRS credit recommendation for 3 semester credits.
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