Feasible Solution

A feasible solution is any set of decision variables that satisfies all the constraints in a linear programming or operations research model. In Intro to Industrial Engineering, it is the pool of valid options before you pick the best one.

What is Feasible Solution?

A feasible solution in Intro to Industrial Engineering is any proposed set of decision-variable values that satisfies every constraint in the model. If even one restriction is broken, the solution is not feasible, which means it cannot be used as a valid answer to the problem.

This comes up most often in operations research and linear programming. You might be choosing how many units to make, how much product to ship, or how to assign workers to tasks. The constraints describe the real limits of the system, such as labor hours, machine capacity, demand, budget, or supply. A feasible solution stays inside all of those limits at once.

A useful way to think about feasibility is that it is the filter before optimization. The model does not start by asking, "What is the best answer?" It starts by asking, "Which answers are allowed?" Those allowed answers make up the feasible region in graphical problems, or the feasible set in algebraic and spreadsheet-based models.

In a simple production example, suppose a factory can make product A and product B, but it only has 100 labor hours and 80 units of raw material. A plan like A = 20, B = 10 might be feasible if it stays within both limits. A plan like A = 50, B = 40 might look productive, but it is not feasible if it uses too many hours or too much material.

Feasibility also matters in the Simplex Method. Simplex moves from one corner point to another inside the feasible region, searching for a better objective value without leaving the valid set of solutions. In transportation and assignment problems, feasibility means the shipping or matching plan satisfies supply, demand, and assignment rules. If a route plan leaves a warehouse overfilled or a demand unmet, it fails the feasibility check.

One common mistake is confusing feasible with optimal. A feasible solution only needs to work. An optimal solution is the feasible one that gives the best value for the cost function, profit function, or other objective.

Why Feasible Solution matters in Intro to Industrial Engineering

Feasible solution is the gatekeeper concept for almost every optimization problem in Intro to Industrial Engineering. Before you can improve a process, you have to know which choices are actually allowed by the system.

That matters in production planning because real factories do not get to ignore limits. If a schedule uses more machine time than exists, or a shipment plan sends out more units than are available, it may look good on paper but it cannot be implemented. Feasibility keeps the math connected to the physical process.

It also makes the rest of operations research make sense. The objective function tells you what you want, such as lowest cost or highest profit, but the constraints define the space of possible answers. Once you can tell whether a solution is feasible, you can compare alternatives correctly and avoid chasing a plan that breaks the rules.

Feasible solutions show up again in transportation, assignment, and supply chain problems, where the model has to respect demand, supply, capacities, and assignment rules. In those settings, feasibility is often the first thing you check in a hand-solved problem, a spreadsheet model, or a solver output. If the solution is not feasible, the rest of the answer does not count.

How Feasible Solution connects across the course

Constraints

Constraints are the rules that a feasible solution has to satisfy. In an industrial engineering model, they might limit labor, budget, machine time, storage space, or delivery quantities. If you change the constraints, you change which solutions are feasible, so they are the real boundary around the problem.

Optimal Solution

Every optimal solution is feasible, but not every feasible solution is optimal. That difference matters a lot in optimization because the feasible region can contain many valid answers. The objective function is what lets you rank those valid answers and choose the best one.

Excel Solver

Excel Solver checks feasibility when it tries to solve a model. You give it variables, constraints, and an objective, and it searches for a solution that satisfies all the rules before optimizing the target value. If your model is set up wrong, Solver may return an infeasible result or no valid answer at all.

Transportation and Assignment Problems

In these problems, feasibility means meeting supply, demand, and assignment requirements at the same time. A transportation plan is feasible only if all outgoing shipments stay within supply and every destination gets the required amount. That makes feasibility the starting point for finding a minimum-cost plan.

Is Feasible Solution on the Intro to Industrial Engineering exam?

On a problem set or quiz, you usually use feasible solution in one of three ways: decide whether a proposed answer satisfies the constraints, identify the feasible region from a graph, or check whether a solver output is valid. If you are given a candidate plan, plug it into each constraint and see whether any limit is broken. If the course uses graphs, the shaded overlap region is the set of feasible solutions, and corner points inside it are the candidates for the optimum. In transportation and assignment questions, you may also need to verify that supply, demand, and one-to-one assignment rules are all met before you move on to cost calculations. If a problem asks for the "best" answer, start by finding a feasible one, because the best answer has to be allowed first.

Feasible Solution vs Optimal Solution

Feasible solution and optimal solution are easy to mix up. Feasible means the answer satisfies all constraints, while optimal means it is the best feasible answer for the objective function. You can have many feasible solutions, but only one or a few optimal ones depending on the model.

Key things to remember about Feasible Solution

• A feasible solution is any set of decision-variable values that satisfies every constraint in the model.

• Feasibility comes before optimization, because a solution has to be valid before it can be judged as best.

• In graph-based linear programming, feasible solutions live in the overlapping shaded region formed by the constraints.

• In transportation and assignment problems, feasibility means meeting supply, demand, and assignment rules at the same time.

• A common mistake is treating a high-profit or low-cost answer as correct even when it breaks a constraint.

Frequently asked questions about Feasible Solution

What is feasible solution in Intro to Industrial Engineering?

A feasible solution is any proposed answer to an operations research model that satisfies every constraint. It might be a production plan, shipping plan, or assignment plan, as long as it stays within the limits of the system. Feasibility is the first checkpoint before you can look for the best answer.

How do you know if a solution is feasible?

Check the decision variables against every constraint in the model. If all inequalities, equalities, and non-negativity rules are satisfied, the solution is feasible. If even one constraint is violated, the solution is infeasible.

Is feasible solution the same as optimal solution?

No. A feasible solution is just allowed by the model, while an optimal solution is the feasible one that gives the best objective value. You can have lots of feasible solutions, but only the best one is optimal.

What does a feasible solution look like in a graph?

In a linear programming graph, feasible solutions appear in the overlapping shaded region where all constraints are satisfied. The corner points in that region are usually the candidates you check for the optimum. If a point falls outside the shaded area, it is not feasible.