TP

1. Transportation Problem in
Operations Research
By: [Your Name]

2. Learning Objectives
• • Understand Transportation Problem concept
• • Link theory with real business logistics
• • Formulate Transportation Problem
• • Learn solution methods
• • Derive managerial insights

3. Why Transportation Problem is
Important
• • Transportation = 30–60% of logistics cost
• • Impacts profitability & service level
• • Widely used in FMCG, E-commerce, Cement,
Retail
• • Helps managers minimize cost scientifically

4. What is Transportation Problem?
• • Special type of Linear Programming Problem
• • Multiple sources → Multiple destinations
• • Objective: Minimize transportation cost
• • Subject to supply & demand constraints

5. Transportation Problem Structure
• Sources supply goods to destinations
• Each route has a unit transportation cost
• Decision: How much to ship on each route

6. Types of Transportation Problem
• 1. Balanced Transportation Problem
• Total Supply = Total Demand
• 2. Unbalanced Transportation Problem
• Total Supply ≠ Total Demand
• → Use Dummy Source/Destination

7. Mathematical Formulation
• Decision Variable:
• xᵢ = units shipped from source i to destination
ⱼ
j
• Objective:
• Minimize Z = ΣΣ cᵢ xᵢ
ⱼ ⱼ
• Subject to:
• Supply & Demand constraints

8. Solution Approach
• Step 1: Find Initial Basic Feasible Solution
(IBFS)
• • North-West Corner Method
• • Least Cost Method
• • Vogel’s Approximation Method (VAM)
• Step 2: Optimality Test (MODI Method)

9. North-West Corner Method
• • Start from top-left cell
• • Allocate maximum possible quantity
• • Move right or downward
• ✔ Simple
• ✘ Ignores transportation cost

10. Vogel’s Approximation Method
(VAM)
• • Calculate penalty for each row & column
• • Penalty = difference of two lowest costs
• • Allocate where penalty is maximum
• ✔ Near-optimal solution
• ✔ Preferred in practice

11. Optimality Test – MODI Method
• • Calculate u and v values
• • Compute opportunity cost (Δᵢ )
ⱼ
• • If all Δᵢ ≥ 0 → Optimal solution
ⱼ
• Managerial meaning: No further cost
reduction possible

12. Real-Life Business Example
• A company supplies goods from plants to
markets
• Transportation Problem helps decide:
• • Which plant serves which market
• • How much quantity to transport
• • Minimum total logistics cost

13. Managerial Insights
• • Supports cost-based decisions
• • Improves supply chain efficiency
• • Helps in capacity & network planning
• • Valuable tool for MBA managers

14. Limitations
• • Assumes linear transportation cost
• • Assumes certainty in supply & demand
• • Does not include real-time disruptions

15. Extensions & Analytics View
• • Transshipment Problem
• • Multi-objective Transportation
• • Fuzzy Transportation Models
• • Solved using Excel Solver, LINGO, Python

16. Key Takeaways
• • Transportation Problem links math with
business
• • Enables scientific logistics decisions
• • Right quantity + Right route = Cost efficiency

17. Thank You
• Questions & Discussion
• Let us optimize logistics the smart way!