ETF1100 Chap.10 Business Modelling and Optimisation
Business Modelling and Optimisation
Business Modelling and Optimisation translates a decision into variables, an objective and constraints before Excel Solver is used. The chapter checks inequality direction, units, non-negativity and integrality, verifies candidate solutions against every resource limit, identifies binding constraints and slack, and stress-tests whether a recommendation survives plausible changes in contribution, capacity or demand.
What this chapter covers
- 01
Decision variables with units
- 02
Objective functions
- 03
Resource and demand constraints
- 04
Feasible regions
- 05
Binding constraints and slack
- 06
Solver verification and sensitivity
Worked example · free
Formulate a product-mix model
- 1Write maximise Z = 30x + 45y.
- 1Check labour: 2(30) + 3(20) = 120, so it binds.
- 1Check materials: 30 + 2(20) = 70, so it binds.
- 1Check premium demand: 20 is below 30, leaving slack 10.
- 1Compute contribution = 30(30) + 45(20) = $1,800.
- 1Compare all feasible corners before declaring optimality.
Key terms
- Decision Variable
- A controllable quantity whose value the optimisation model chooses.
- Objective Function
- The numerical business outcome the model maximises or minimises.
- Constraint
- A mathematical limit representing capacity, demand, policy or another business requirement.
- Feasible Region
- The set of decisions satisfying every model constraint.
- Binding Constraint
- A constraint used exactly at the solution with no remaining slack.
- Slack
- The unused amount remaining before a nonbinding limit is reached.
Business Modelling and Optimisation FAQ
What should I define before opening Solver?
Write the decision variables with units, the objective and every constraint in words and symbols. Include non-negativity, integer, demand and capacity rules when relevant. Solver cannot discover a business restriction that was never entered into the model.
How do I verify an optimisation result?
Recompute the objective and substitute the decision values into every constraint. Confirm inequality directions, units, non-negativity and integrality, then identify binding limits and slack. A success message validates the entered mathematics, not the real business formulation.
Why should I run sensitivity checks?
Contribution, capacity and demand estimates can change. Resolve the model after plausible input changes to see whether the recommended mix remains stable. A solution that changes sharply after a small adjustment should be reported as sensitive rather than certain.
How are feasibility and optimality different?
A feasible solution satisfies every constraint but may not give the best objective value. An optimal solution is the best among all feasible choices under the model. Verify resource use and restrictions first, then compare objective values. Solver success cannot repair a missing constraint or an objective that represents the wrong quantity.
Exam move
Translate each case into words before building cells. Define decision variables with units, identify whether the objective is profit, revenue, cost or another quantity, and write every limit with the correct at-most or at-least direction. Check that coefficients use compatible units. In Excel, give variable cells clear names, calculate each constraint left-hand side separately and keep the limit beside it.
After Solver returns a result, recompute the objective and constraints manually, mark binding resources and calculate slack. Add integer restrictions when partial units are impossible rather than rounding later. Practise explaining what an extra unit of a binding resource could change and why a slack resource is not currently limiting. Stress-test one contribution, capacity and demand estimate at a time.
Close the answer with quantities to choose, the objective value, binding limits, unused capacity and a key assumption that management should monitor. For each case, create a formulation table listing the decision variable, unit, objective contribution and resource use. Translate words such as at most, at least, exactly and whole units into inequality, equality or integer restrictions before opening Solver.
Perform a dimensional check on every expression: objective terms must share one monetary or performance unit, and each constraint's left and right sides must use the same resource unit. Sketch a small two-variable feasible region and test one feasible and one infeasible point so constraints are understood as business rules rather than spreadsheet syntax.
In Excel, separate inputs, changing cells, calculated resource use and limits with clear labels; avoid embedding unexplained numbers in formulas. After solving, substitute the returned values into each constraint, compute slack and verify any integer or non-negativity rule. Compare all relevant corner points in a small linear example to confirm why the reported solution is best.
Save the baseline before changing capacity, contribution or demand, and record how the mix, objective and binding constraints respond. Treat a dramatic change after a small input movement as a sensitivity warning. Ask whether proportionality, additivity and divisibility are credible over the recommended range.
Finish with an operational statement naming actions, value, bottleneck, spare capacity and the assumption that deserves monitoring. Solver status is not the conclusion; a defensible formulation and verified business interpretation are.
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