Calculator Inputs
Example Data Table
| Goal | Equation | Target | Priority | Under weight | Over weight |
|---|---|---|---|---|---|
| Output balance | 8x1 + 6x2 + 4x3 | 60 | 1 | 5 | 1 |
| Quality score | 3x1 + 5x2 + 4x3 | 35 | 1 | 4 | 2 |
| Cost control | 4x1 + 3x2 + 2x3 | 30 | 2 | 2 | 4 |
| Utilization | 2x1 + 4x2 + 3x3 | 28 | 3 | 3 | 1 |
| Constraint | Expression | Limit |
|---|---|---|
| Constraint 1 | 2x1 + x2 + x3 | ≤ 18 |
| Constraint 2 | x1 + 3x2 + 2x3 | ≤ 24 |
| Constraint 3 | x1 + x2 | ≥ 4 |
Formula Used
Achievementi = ai1x1 + ai2x2 + ai3x3
di- = max(Targeti - Achievementi, 0)
di+ = max(Achievementi - Targeti, 0)
Penaltyi = wi-di- + wi+di+
Minimize Z = P1(sum of priority 1 penalties), then P2, then P3, and so on.
bj1x1 + bj2x2 + bj3x3 ≤, ≥, or = cj
This page searches all feasible combinations inside your chosen ranges, applies hard constraints first, then compares weighted deviations by priority order.
How to Use This Calculator
- Rename the three decision variables so they match your model.
- Set minimum, maximum, and step values for each variable.
- Enter coefficients, targets, priorities, and deviation weights for every goal.
- Add three hard constraints with coefficients, operators, and right-side limits.
- Click Solve Goal Program to search the feasible space.
- Review the best variable combination, penalties, and priority subtotals.
- Inspect the graph to compare target values, achievements, and penalties.
- Use the CSV or PDF buttons to export the calculated result.
FAQs
1. What does this calculator solve?
It evaluates a multi-goal optimization model with three decision variables, four goals, and three hard constraints. The solver checks feasible combinations and selects the plan with the best lexicographic priority performance.
2. What are d- and d+ values?
d- measures underachievement below a target. d+ measures overachievement above a target. Goal programming uses these deviations instead of one direct objective, letting you penalize shortfalls and excesses differently.
3. Why are priorities important?
Priorities create an order of importance. The solver minimizes higher-priority penalties before lower-priority penalties. This matches real planning situations where some goals matter more than others.
4. What do underachievement and overachievement weights do?
These weights control how costly each deviation becomes. A larger underachievement weight strongly discourages falling below target. A larger overachievement weight discourages going too far above target.
5. Does this calculator use exact linear programming?
It uses grid search over the ranges you provide. That makes it simple and transparent for web use. Smaller step sizes improve precision, but they also increase computation time.
6. Why did the solver use a coarser step?
Very large search spaces can be slow in a single page. When combinations become excessive, the calculator automatically increases step size to keep the search practical while still providing a useful result.
7. What happens if no feasible solution exists?
You will see a message stating that no feasible solution was found. In that case, widen variable ranges, relax a hard constraint, or adjust targets and weights.
8. When should I use goal programming instead of linear programming?
Use goal programming when you must balance several targets at once, especially when perfect satisfaction is impossible. It is ideal for tradeoff analysis, resource allocation, and planning with ranked objectives.