Transportation models in Operations Research: Which of the following methods are used to obtain initial feasible or improved solutions in transportation problems?

Introduction / Context:
Transportation problems allocate shipments from multiple sources to multiple destinations at minimum cost while meeting supply and demand constraints. Several standard heuristics generate initial basic feasible solutions that are then improved via methods like MODI or stepping-stone.

Given Data / Assumptions:

• We are identifying commonly taught initial solution methods.
• Problem is balanced or can be balanced by adding dummy rows/columns.
• Costs are known and nonnegative.

Concept / Approach:
North-West Corner Method (NWCM) is simple and fast but ignores costs. Least Cost Method (LCM) considers costs when allocating. Vogel’s Approximation Method (VAM) uses penalties based on cost differences to produce a high-quality starting solution that often requires fewer improvement iterations.

Step-by-Step Solution:
List recognized methods: NWCM, LCM, VAM.Confirm each is applied to the transportation cost matrix.Select the comprehensive option: “All of the above.”

Verification / Alternative check:
Operations Research curricula and textbooks present these three as standard approaches for initial feasible solutions.

Why Other Options Are Wrong:
Choosing only one method disregards the breadth of common practice; all are valid depending on goals (speed vs. quality).

Common Pitfalls:
Forgetting to check degeneracy or balance; always validate and then improve the initial solution with MODI/stepping-stone.

Final Answer:
All of the above