Binary variables complicate facility location decisions because opening a distribution center incurs a large fixed setup cost, creating a non-linear "all-or-nothing" cost step that continuous models cannot process.

Binary variables introduce fixed startup costs and all-or-nothing choices that disrupt smooth production plans. This creates a trade-off where paying a high upfront setup cost can lower overall shipping expenses by placing facilities closer to customers.

Binary variables complicate strategic supply chain decisions because they introduce discrete, yes-or-no choices—such as whether to open a specific distribution center (1) or not (0)—which turn linear problems into non-convex Mixed-Integer Linear Programming (MILP) models that cannot be solved using simple gradient methods and require computationally intensive algorithms like branch-and-bound. The fundamental trade-off lies between fixed facility setup costs and variable transportation costs. Opening fewer distribution centers minimizes fixed setup overhead but increases transportation costs due to longer shipping distances to customers. Conversely, opening more facilities reduces shipping distances and transportation expenses, but significantly drives up total fixed capital investment. Optimizing a supply chain network requires finding the precise balance where the combined sum of fixed facility costs and variable transportation costs is minimized.

Binary variables make the decision more complex because each distribution center can only be opened or closed. Opening a facility adds a fixed setup cost but may reduce transportation costs by being closer to customers. The trade-off is between paying higher fixed facility costs and saving on transportation expenses, so the model chooses the combination that gives the lowest total cost.