You should add integer constraints (MILP) when fractional solutions are not realistic or would lead to an invalid decision, such as the number of workers, vehicles, or machines. Keep it as a pure LP when fractional values are acceptable and the integer restriction would provide little practical benefit, because LPs are generally much faster to solve. In practice, there is no fixed cutoff based only on the number of variables; the main line is whether integrality materially changes the decision. A useful approach is to first solve the LP relaxation, check whether the solution is already integer or whether rounding gives a practical solution, and then use MILP if the fractional result would significantly affect the real-world decision.

I would use MILP when the decision variables must be whole numbers or binary choices are important. If fractional values are acceptable and the LP gives a realistic solution, I would keep it as an LP to save computation time. In practice, I would choose MILP only when the integer constraints significantly affect the accuracy or practicality of the solution.

Modeling real-world supply chain or allocation problems means using mathematical models to decide how resources should be distributed efficiently. It can help businesses determine how much to produce, where to send products, or how to minimize transportation costs while meeting customer demand.

The main question is whether fractional solutions are acceptable in the real-world situation. If variables represent things that must be whole numbers, such as employees, machines, or vehicles, then adding integer constraints is usually necessary even though MILP takes more computation. If fractional values are reasonable or the difference between the LP solution and a realistic integer solution is small, keeping a pure LP can save significant computation time. In practice, there is no fixed numerical line; the decision depends on the importance of accuracy versus computational cost. A common approach is to solve the LP relaxation first, compare its solution with a feasible integer solution, and add integer constraints when the resulting difference in cost, profit, or feasibility is important enough to justify the extra computation.