To ensure at most one project is chosen, use a simple sum limit:

x1 + x2 is less than or equal to 1

Here, x1 and x2 are binary choices (0 or 1). This restricts the total selection so you can pick one or neither, but never both.

To model mutually exclusive choices where selecting one project prevents another, you set the sum of their binary decision variables to be less than or equal to one. For conditional rules where one project depends on another, you constrain the dependent project variable to be less than or equal to the prerequisite project variable.

Binary variables enforce project rules by treating each choice as an on/off switch through simple algebraic constraints. For either-or or mutually exclusive choices, summing the variables of candidate projects and capping the total at one ensures that selecting one project automatically forces the other to remain off, preventing both from being chosen together. For conditional or if-then dependencies, setting a secondary project's variable to be less than or equal to the main project's variable keeps the secondary option locked off unless the primary project is turned on first. Finally, for maximum portfolio limits, summing the binary variables across a group of potential projects and setting the total to be less than or equal to a set limit guarantees that the number of active selections never exceeds your maximum allowance.

Set each choice as a binary variable (1 = select, 0 = not select): for mutually exclusive options, use  y₁ + y₂ ≤ 1  so picking one blocks the other; for conditional rules like "can only pick B if A is chosen", use  y₂ ≤ y₁  so B can never be 1 unless A is also 1.

This is what makes binary variables especially powerful in facility location, capital budgeting, project selection, scheduling, and other discrete decision problems.

Binary variables enforce "either-or" or conditional constraints by algebraically linking decision choices through linear inequalities. To express a strict "either-or" rule (or mutual exclusivity) where choosing one project prevents another—for instance, selecting either Facility A (y_A = 1) or Facility B (y_B = 1), but not both—you sum the binary variables and bound them by 1 (y_A + y_B \le 1), which permits choosing one, or neither, but eliminates the possibility of selecting both. To enforce a conditional requirement where Project B can only be built if Project A is selected first, you set y_B \le y_A, ensuring y_B remains zero whenever y_A is zero. These simple binary linear constraints allow optimization models to seamlessly encode complex logical dependencies, capital budgeting prerequisites, and geographic exclusions across potential facility locations.