Calculator Input
Enter coefficients, variable values, limits, and linear constraints. Submit to evaluate a decision-variable scenario against the model.
Formula Used
1) Objective Function
Z = Σ(ci × xi)
2) Linear Constraint
Σ(aij × xi) ≤, ≥, or = bj
3) Slack, Surplus, and Deviation
For ≤ constraints: Slack = bj − LHS
For ≥ constraints: Surplus = LHS − bj
For = constraints: Deviation = LHS − bj
4) Contribution Share
Contribution Share = |cixi| ÷ Σ|ckxk| × 100
5) Bound Utilization
Bound Utilization = (xi − Lower) ÷ (Upper − Lower) × 100
How to Use This Calculator
- Enter a scenario name, choose maximize or minimize, and set the decimal precision you need.
- For each decision variable, type a name, objective coefficient, selected value, and its lower and upper bounds.
- Fill each constraint with variable coefficients, choose the correct relation, and enter the right-side limit.
- Press Evaluate Decision Variables to compute objective value, feasibility, contributions, saturation, and slack or surplus.
- Use the graph, result tables, and CSV or PDF export buttons to compare scenarios and document your analysis.
Example Data Table
| Variable | Coefficient | Value | Contribution | Lower Bound | Upper Bound |
|---|---|---|---|---|---|
| x1 | 12 | 4 | 48 | 0 | 10 |
| x2 | 9 | 3 | 27 | 0 | 10 |
| x3 | 15 | 2 | 30 | 0 | 10 |
| x4 | 7 | 5 | 35 | 0 | 10 |
| x5 | 0 | 0 | 0 | 0 | 10 |
Example objective value: 140
Example C1: 2x1 + x2 + 3x3 + x4 ≤ 24, giving LHS = 22 and slack = 2.
Example C2: x1 + 2x2 + x3 + 2x4 ≤ 23, giving LHS = 22 and slack = 1.
Example C3: 3x1 + x2 + 2x3 + x4 ≥ 20, giving LHS = 24 and surplus = 4.
FAQs
1) What does this calculator evaluate?
It evaluates a user-entered linear decision model. It calculates the objective value, checks bounds, tests constraints, and reports slack, surplus, contribution share, and feasibility.
2) Does it find the optimal solution automatically?
No. This tool evaluates the variable values you enter. It is excellent for scenario testing, validation, and comparison, but it does not run a full optimization solver.
3) What is a decision variable?
A decision variable represents a controllable quantity in a mathematical model. Examples include production units, staff hours, shipment loads, or budget allocations.
4) Why are bounds useful?
Bounds define realistic limits for each variable. They help you verify whether a scenario stays within policy, capacity, demand, or mathematical restrictions.
5) What does slack mean in a constraint?
Slack shows unused capacity in a ≤ constraint. A larger slack means more room remains before the limit is fully consumed.
6) What is surplus in a ≥ constraint?
Surplus measures how much the left side exceeds the required minimum. It tells you how far a scenario is above the lower threshold.
7) Can I test minimization models?
Yes. Select the minimize option in the form. The calculator will still evaluate the same entered scenario, while labeling the model correctly for reporting.
8) What does contribution share tell me?
Contribution share shows how much each variable influences the total weighted objective. It helps identify dominant variables and compare tradeoffs quickly.