Operations Research — Transportation models: What do we call a Transportation Problem in which the total supply available at all origins exactly equals the total demand required at all destinations (so no dummy source or dummy destination is needed)?

Introduction / Context:In Operations Research, the Transportation Problem allocates shipments from multiple origins (suppliers) to multiple destinations (customers) at minimum cost while respecting supply and demand constraints. A key diagnostic before solving is whether the problem is balanced or unbalanced, because that choice determines if we must add a dummy source or destination and which methods apply directly without modification.

Given Data / Assumptions:

• Total supply across all origins may equal or differ from total demand across all destinations.
• Costs per unit are known and nonnegative; capacities (supply/demand) are fixed.
• We are identifying the correct term when total supply equals total demand, exactly.

Concept / Approach:A Balanced Transportation Problem is defined by the equality: sum of supplies = sum of demands. When this holds, the model can be solved directly by methods like Northwest Corner, Least Cost, or Vogel’s Approximation to get a starting solution, and then optimized with Stepping Stone or MODI without introducing dummy rows/columns. If totals differ, the model is Unbalanced and requires a dummy source or destination to reconcile the totals before proceeding.

Step-by-Step Solution:

Verification / Alternative check:Attempt to set up the linear program. If all constraints can be written without slack from a dummy node and the equality condition holds, the instance is balanced by definition.

Why Other Options Are Wrong:

• Degenerate Solution: Refers to basic feasible solutions with fewer positive allocations than m + n − 1, not the supply-demand equality condition.
• Unbalanced Transportation Problem: Applies when total supply ≠ total demand.
• All/None: Incorrect because exactly one term fits the definition.

Common Pitfalls:Forgetting to add a dummy node when the problem is unbalanced; misclassifying degeneracy as balance/unbalance.

Final Answer:Balanced Transportation Problem