Build integer models and inspect branching decisions. Test maximization or minimization cases with clear steps. Export results, node logs, and summaries easily today online.
| Item | Example Value |
|---|---|
| Objective | Maximize Z = 5x + 7y |
| Constraint 1 | 2x + y <= 14 |
| Constraint 2 | x + 3y <= 18 |
| X Bounds | 0 to 10 |
| Y Bounds | 0 to 10 |
| Integer Rule | x and y must be whole numbers |
Objective function: Z = c1x + c2y
Constraint form: ax + by <= rhs, ax + by >= rhs, or ax + by = rhs
LP relaxation: Solve the same model without the integer rule first.
Branching rule: If x or y is fractional, split into two new nodes.
Example branch: if x = 4.6, create x <= 4 and x >= 5.
Bounding test: Prune any node that cannot beat the current best integer solution.
This calculator solves small integer programming models with a branch and bound method. It works with two decision variables. It also accepts up to four linear constraints. You can test maximization and minimization cases. The page shows the LP relaxation, branching decisions, and final integer answer.
Many linear programming answers are fractional. Real planning problems often need whole numbers. You may need full machines, full workers, or full shipments. Branch and bound fixes that issue. It creates smaller subproblems. It then checks bounds and removes weak nodes. This reduces wasted search effort.
The result section appears directly below the header and above the form after submission. That keeps the answer visible at once. You can inspect the best integer point and compare it with the root LP relaxation. The node log also helps you understand pruning, fathoming, and branching depth.
Integer programming supports production planning, assignment models, budget allocation, scheduling, routing, and resource selection. A branch and bound calculator is useful in maths classes and operations research practice. It helps students see how a feasible region changes when new branch constraints are added to a node.
CSV export is useful for reports and audits. You can move node records into a spreadsheet and review each branch step. PDF export helps preserve a printable summary. Both options support classroom work, project documentation, and client reviews. The example data table also gives a quick starting point.
This page is best for bounded two-variable models where you want a clear explanation of the search process. It is simple to use, but still shows important branch and bound logic. That makes it a practical learning tool and a helpful quick solver for small integer optimization tasks.
Branch and bound solves an LP relaxation first. If the answer is fractional, it splits the model into smaller branches. It then uses bounds to remove nodes that cannot improve the best integer solution.
This page solves bounded two-variable integer programming problems with up to four linear constraints. It supports maximization and minimization models and allows <=, >=, and equality constraints.
The LP relaxation gives a bound for the original integer problem. It shows the best continuous solution before branching. That value helps decide whether a node is worth exploring.
Bounds keep the search region finite and practical. They also make enumeration and node generation more stable. Clear lower and upper limits improve the quality of the result and reduce unnecessary search.
Pruning means a node is removed from further search. This happens when the node is infeasible or when its bound cannot beat the current best integer solution.
Yes. The calculator accepts decimal values for coefficients, right-hand sides, and variable bounds. The final decision variables are still treated as integers during branch and bound.
No integer solution appears when all feasible points violate the whole-number rule or when the chosen bounds and constraints leave no valid integer combination inside the feasible region.
The CSV file stores the summary and node log for later analysis. The PDF option lets you save or print the current result page for notes, assignments, and reporting.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.