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Northwest Corner Method Tutorial

Jul 12, 2024

Northwest Corner Method for Transportation Problem

Introduction

  • Objective: Find the initial basic feasible solution using the Northwest Corner Method.
  • Components of the problem:
    • Sources: F1, F2, F3
    • Destinations: A, B, C, D
    • The number (e.g. 60) in the grid shows the cost of transportation for one unit.
    • Supply capacity is given for each source.
    • Demand is given for each destination.

Steps in the Northwest Corner Method

  1. Start at the top-left corner (Northwest corner).
  2. Allocate units based on the minimum of supply and demand.
  3. Adjust supply and demand after each allocation.
  4. Cross out rows or columns where supply or demand is exhausted.
  5. Move to the next cell (always moving right or down).

Detailed Procedure

Step 1: Allocate from F1 to A

  • Supply (F1): 30
  • Demand (A): 35
  • Minimum: 30
  • Allocate: 30 units
  • Adjustments:
    • F1 supply: Exhausted
    • A demand: 35 - 30 = 5
  • Cross out row of F1

Step 2: Allocate from F2 to A

  • Supply (F2): 40
  • Remaining Demand (A): 5
  • Minimum: 5
  • Allocate: 5 units
  • Adjustments:
    • F2 supply: 40 - 5 = 35
    • A demand: Exhausted
  • Cross out column of A

Step 3: Allocate from F2 to B

  • Supply (F2): 35
  • Demand (B): 28
  • Minimum: 28
  • Allocate: 28 units
  • Adjustments:
    • F2 supply: 35 - 28 = 7
    • B demand: Exhausted
  • Cross out column of B

Step 4: Allocate from F2 to C

  • Supply (F2): 7
  • Demand (C): 32
  • Minimum: 7
  • Allocate: 7 units
  • Adjustments:
    • F2 supply: Exhausted
    • C demand: 32 - 7 = 25
  • Cross out row of F2

Step 5: Allocate from F3 to C

  • Supply (F3): 50
  • Remaining Demand (C): 25
  • Minimum: 25
  • Allocate: 25 units
  • Adjustments:
    • F3 supply: 50 - 25 = 25
    • C demand: Exhausted
  • Cross out column of C

Step 6: Allocate from F3 to D

  • Supply (F3): 25
  • Demand (D): 25
  • Minimum: 25
  • Allocate: 25 units
  • Adjustments:
    • F3 supply: Exhausted
    • D demand: Exhausted

Summary of Allocations

| Source-Destination | Units Allocated | Cost Per Unit | Total Cost | |--------------------|-----------------|---------------|------------| | F1 to A | 30 | 6 | 180 | | F2 to A | 5 | 5 | 25 | | F2 to B | 28 | 11 | 308 | | F2 to C | 7 | 9 | 63 | | F3 to C | 25 | 7 | 175 | | F3 to D | 25 | 18 | 450 |

Total Cost: 1076

Conclusion

  • The initial basic feasible solution utilizes the Northwest Corner Method with a total transportation cost of 1076.

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