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38 changes: 16 additions & 22 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -1247,7 +1247,7 @@ This is a method to generate an initial feasible solution without considering tr

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### 🔹 Steps:
### Steps:

1. **Start in the top-left (northwest) corner** of the transportation table.
- This is always cell $begin:math:text$ x_{11} $end:math:text$.
Expand All @@ -1264,38 +1264,44 @@ This is a method to generate an initial feasible solution without considering tr
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## 💸 Least Cost Method (Método do Custo Mínimo)
## 💸 [Least Cost Method (Método do Custo Mínimo]():

This method takes into account the transportation costs to guide the initial allocation.

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### 🔹 Steps:
### ➢ [Steps]():

1. **Identify the cell with the lowest unit cost** in the cost matrix among the remaining unallocated cells.
2. **Allocate as much as possible** to this cell, without exceeding supply or demand constraints.
3. **Adjust the supply and demand** for the row and column of the allocated cell.
4. **Remove** (cross out) the row or column where supply or demand becomes zero. If both are zero simultaneously, cross out only one to maintain feasibility.
5. **Repeat** the steps until all supplies and demands are met.


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⚠️ Unlike the Northwest Corner, this method **considers the costs** and usually leads to a **better initial solution**, closer to the optimal.

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### 🔍 Link to Risk Analysis
### 🔍 [Link to Risk Analysis]():

- Unbalanced models simulate **shortage/surplus risks**.
- Dummy rows/columns help visualize **operational failures**.
- Solutions help identify:
- Where **stockouts** will occur
- How to **redistribute resources**
- Costs of **unserved demands**

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This makes the model highly applicable to **supply chain risk management, disaster response logistics, and critical infrastructure planning**.

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### 📐 Initial Basic Feasible Solution
### 📐 [Initial Basic Feasible Solution]():

A basic feasible solution must:
1. Satisfy **all row (supply)** and **column (demand)** constraints.
Expand All @@ -1306,18 +1312,22 @@ These principles ensure a **non-degenerate** starting point for iterative improv

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## 🧩 Summary
### 🧩 [Summary]():

The transportation problem provides a clear, visual way to:
- Model **linear resource flows**,
- Simulate **imbalances and failure points**,
- Optimize with **tailored algorithms**, and
- Integrate with **Simplex** and **risk frameworks** for smarter planning.
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It's a cornerstone of **Operational Research**, **Logistics**, and **Decision Science**.



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Expand Down Expand Up @@ -1370,22 +1380,6 @@ $x_1 \geq 0, \quad x_2 \geq 0\$
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## [Contribute]()
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