Glossary · approach
Northwest Corner Rule
The simplest classical heuristic for generating an initial basic feasible solution of the transportation problem: starting at the top-left of the cost matrix, allocate as much as possible to the current cell and shift right or down until supply and demand are exhausted.
NWCNorthwest Corner Method
The Northwest Corner Rule is the simplest classical heuristic for producing an initial basic feasible solution to the transportation problem: start in the top-left (northwest) corner of the cost matrix, allocate as much as possible to the current cell (the minimum of the remaining supply or remaining demand), then move right (if supply remains) or down (if demand remains), and repeat until all row and column totals are met. The resulting solution is feasible but typically far from optimal — it ignores the cost matrix entirely and works only on position. The optimum is reached via MODI / Stepping-Stone or directly via Simplex. Pedagogical value: it shows the 'basic feasible start' concept underlying Simplex, and serves as a stepping stone to smarter starts such as Vogel's Approximation Method (VAM). Detailed in Bazaraa-Jarvis-Sherali (2010).
Örnek
3 plants (capacities 20, 30, 25 tons) × 4 customers (demands 15, 20, 18, 22 tons). NWC starts at the top-left: cell (1,1) gets min(20,15)=15 tons; then (1,2) gets min(5,20)=5 tons; (2,2) gets min(30,15)=15 tons; (2,3) gets min(15,18)=15 tons; (3,3) gets min(25,3)=3 tons; (3,4) gets min(22,22)=22 tons. A total of 75 tons is allocated; the initial solution is ready, then optimised with MODI or simplex.