When Excel Solver says “Solver could not find a feasible solution” or “Solver stopped at current solution”, it usually means the model has a structural issue: conflicting constraints, missing bounds, wrong signs, or a mis-specified objective. This page shows how to diagnose and fix Solver failures using a clear checklist and a complete numerical example.

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

1. The Five Most Common Reasons Solver Cannot Find a Solution

1.1 Conflicting or Impossible Constraints

If two or more constraints contradict each other, the feasible region is empty. Solver will immediately report “no feasible solution.”

Example: \[ x \ge 10,\quad x \le 5 \] No value of \(x\) satisfies both.

1.2 Missing Bounds on Variables

Solver defaults to allowing variables to be negative unless you explicitly set lower bounds. Many LP models assume nonnegativity, but Solver does not unless you specify it.

1.3 Wrong Inequality Direction

A “≤” that should be “≥” (or vice versa) can destroy feasibility or flip the feasible region.

1.4 Wrong Objective (Max vs. Min)

If you choose “Min” when the model is designed for “Max,” Solver may push variables in the wrong direction and fail to find a solution.

1.5 Nonlinear Formulas in a Linear Model

If your LP contains multiplication of decision variables, IF statements, or nonlinear functions, Solver’s Simplex method cannot solve it. You must switch to GRG Nonlinear or fix the formulas.

2. Step‑by‑Step Checklist to Fix Solver Failures

2.1 Step 1 — Check All Constraint Formulas

• Ensure each constraint cell contains a single formula, not a hard‑typed number.
• Verify the formula references the correct decision variable cells.
• Check that the inequality direction matches the model.

2.2 Step 2 — Add Bounds to Every Decision Variable

• Set all LP variables to ≥ 0 unless negative values are allowed.
• Add upper bounds if the model requires them.

2.3 Step 3 — Confirm the Objective Cell Is Correct

• Ensure the objective cell is a formula combining the decision variables.
• Choose the correct direction: Max or Min.

2.4 Step 4 — Use the Correct Solving Method

• For linear models: Simplex LP.
• For nonlinear models: GRG Nonlinear.
• For integer/binary models: Simplex LP + Integer Constraints.

2.5 Step 5 — Test Feasibility Manually

Plug in simple values (0, 1, or small integers) to see whether any combination satisfies all constraints. If none do, the model is infeasible.

3. Numerical Example: Fixing a Solver “No Feasible Solution” Error

A company produces two products using machine time and labor. Solver reports “no feasible solution.” Here is the original (incorrect) model.

3.1 Incorrect Model (Causes Solver Failure)

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): \[ x_1 + x_2 \ge 120 \] This forces production to exceed available labor.
• No nonnegativity constraints were added.

Because labor requires at least 120 hours but machine time limits production to at most 100 hours, the model is infeasible.

4. Fixing the Model

4.1 Correct the Labor Constraint

Labor availability is 80 hours, so the correct constraint is:

\[ x_1 + x_2 \le 80 \]

4.2 Add Nonnegativity Constraints

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

4.3 Use Simplex LP

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

5. Solving the Corrected Model

Solve the two binding constraints:

2x₁ + x₂ = 100
x₁ + x₂ = 80
  

Subtract the second equation from the first:

x₁ = 20
  

Substitute back:

20 + x₂ = 80  ⇒  x₂ = 60
  

Optimal solution:

• \(x_1 = 20\)
• \(x_2 = 60\)
• Profit: \[ Z = 40(20) + 30(60) = 2600 \]

Solver now finds a feasible and optimal solution because the constraints are consistent.

6. Additional Troubleshooting Tips

• Check for hidden text or spaces in constraint cells.
• Ensure all formulas use = and not typed numbers.
• Verify that integer constraints are applied only when needed.
• Use “Reset All” in Solver if the model becomes corrupted.

For more help with LP, Solver, and optimization modeling, explore:

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