Transportation Problem - Handbook

Type: LP (Linear Programming)

This handbook explains the Transportation Problem sample problem in the LP Black Box platform.

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The Problem

Scenario

Ship products from 2 warehouses to 2 stores, minimizing shipping costs.

Route	Cost per Unit ($)
Warehouse 1 → Store 1	4
Warehouse 1 → Store 2	6
Warehouse 2 → Store 1	5
Warehouse 2 → Store 2	3

Supply:

• Warehouse 1: 50 units
• Warehouse 2: 60 units

Demand:

• Store 1: 40 units
• Store 2: 50 units

Your Goal

Minimize total shipping cost while meeting supply and demand.

The Variables

Variable	Meaning
W1_S1	Units shipped from Warehouse 1 to Store 1
W1_S2	Units shipped from Warehouse 1 to Store 2
W2_S1	Units shipped from Warehouse 2 to Store 1
W2_S2	Units shipped from Warehouse 2 to Store 2

The Constraints

1. Warehouse 1 Supply: Cannot ship more than 50 units

   W1_S1 + W1_S2 ≤ 50

2. Warehouse 2 Supply: Cannot ship more than 60 units

   W2_S1 + W2_S2 ≤ 60

3. Store 1 Demand: Must receive at least 40 units

   W1_S1 + W2_S1 ≥ 40

4. Store 2 Demand: Must receive at least 50 units

   W1_S2 + W2_S2 ≥ 50

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How to Use

Step 1: Load the Sample

Select Transportation Problem from the dropdown.

Step 2: Solve

The solver finds the optimal shipping plan that minimizes cost while meeting all supply and demand requirements.

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Try It Yourself

• Add a third warehouse
• Change demand values and see how routes change

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This is a classic logistics optimization problem.