When Excel Solver reports “Solver could not find a feasible solution”, it means no set of decision variable values satisfies all constraints at the same time. This page shows how to diagnose infeasibility, how to fix it step‑by‑step, and how to interpret Solver’s behavior using a complete numerical example.

• Linear Programming & Optimization
• Parent Business Analytics
• Inventory & Supply Chain Analytics
• Decision Analysis & Simulation

1. What “Infeasible” Means in Solver

A model is infeasible when no combination of decision variables can satisfy all constraints simultaneously. Solver checks the feasible region first; if it is empty, Solver stops before even attempting optimization.

Common symptoms:

• “Solver could not find a feasible solution.”
• “No feasible solution found.”
• Solver returns the initial values unchanged.

2. Most Common Causes of Infeasibility

2.1 Conflicting Constraints

Two or more constraints contradict each other, making it impossible for any solution to satisfy all of them.

Example: \[ x \ge 10,\quad x \le 5 \]

2.2 Incorrect Inequality Direction

A “≤” that should be “≥” (or vice versa) can eliminate the feasible region entirely.

2.3 Missing Nonnegativity Constraints

Solver allows negative values unless you explicitly restrict them. Negative values can break constraints that assume nonnegativity.

2.4 Wrong RHS Values

A typo in a capacity or demand value (e.g., 80 → 8 or 800) can instantly make the model infeasible.

2.5 Integer or Binary Restrictions

A model may be feasible in continuous form but infeasible once integer/binary constraints are added.

3. Step‑by‑Step Process to Fix Infeasibility

3.1 Step 1 — Check All Constraint Formulas

• Ensure each constraint cell contains a formula, not a typed number.
• Verify references to decision variable cells are correct.
• Check inequality directions carefully.

3.2 Step 2 — Add Nonnegativity Constraints

• Set all decision variables to ≥ 0 unless negative values are allowed.

3.3 Step 3 — Check RHS Values for Typos

• Confirm capacities, limits, and requirements match the intended model.

3.4 Step 4 — Temporarily Remove Integer Constraints

• If the continuous model is feasible but the integer model is not, the issue is with integrality.

3.5 Step 5 — Test Feasibility Manually

• Try simple values (0, 1, 10) to see whether any combination satisfies all constraints.

4. Numerical Example: Fixing an Infeasible Solver Model

A company produces two products using machine time and labor. Solver reports “infeasible.” Here is the original (incorrect) model.

4.1 Incorrect Model (Infeasible)

Decision variables

• \(x_1\): units of Product 1
• \(x_2\): units of Product 2

Objective

Maximize: \[ Z = 40x_1 + 30x_2 \]

Incorrect constraints

• Machine time: \[ 2x_1 + x_2 \le 100 \]
• Labor (incorrect): \[ x_1 + x_2 \le 50 \] But the production required by the objective forces more than 50 hours of labor.
• No nonnegativity constraints.

The model becomes infeasible because the labor limit is too small to allow any profitable combination of \(x_1\) and \(x_2\).

5. Fixing the Infeasible Model

5.1 Correct the Labor Constraint

The intended labor availability is 80 hours:

\[ x_1 + x_2 \le 80 \]

5.2 Add Nonnegativity

\[ x_1 \ge 0,\quad x_2 \ge 0 \]

5.3 Use Simplex LP

Since the model is linear, choose Simplex LP in Solver.