# The Transportation Problem: Features, Types, & Solutions

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• 0:03 The Transportation Problem
• 1:18 Types
• 2:36 Solutions
• 4:22 Lesson Summary
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Lesson Transcript
Instructor: Olga Bugajenko

Olga is a registered PRINCE2 Practitioner and has a master's degree in project management.

How do you calculate the cheapest way to ship goods between several warehouses and stores? In this lesson, you will explore the transportation problem and its solutions.

## The Transportation Problem

Imagine yourself owning a small network of chocolate retail stores. To run a successful business, you will also have to own or rent a warehouse where you will store the goods ready to be delivered whenever the stores need them. If you have only one warehouse, it will be supplying all your stores. However, as soon as you expand and open a second warehouse, you will have to make an important decision: which warehouse will deliver which goods to each of your stores? Depending on the choice you make, you might save or spend a significant amount of money.

The transportation problem is a distribution-type problem, the main goal of which is to decide how to transfer goods from various sending locations (also known as origins) to various receiving locations (also known as destinations) with minimal costs or maximum profit. As long as the number of origins and destinations is low, this is a relatively easy decision. But as the numbers grow, this becomes a complicated linear programming problem. Think about Walmart. In 2016, it had 5,229 stores and 166 distribution centers in the US! It would be impossible to calculate the optimal shipping routes without a computer algorithm.

## Types

Transportation problems can be classified into different groups based on their main objective and origin supply versus destination demand. Transportation problems whose main objective is to minimize the cost of shipping goods are called minimizing. An alternative objective is to maximize the profit of shipping goods, in which case the problems are called maximizing.

In a case where the supply of goods available for shipping at the origins is equal to the demand for goods at the destinations, the transportation problem is called balanced. In a case where the quantities are different, the problem is unbalanced.

When a transportation problem is unbalanced, a dummy variable is used to even out demand and supply. A dummy variable is simply a fictional warehouse or store. For example, if total supply at all warehouses is 35 units, but total demand at all stores is only 30 units, we create a fictional store with an additional demand of 5 units. The cost of shipping to the fictional store is usually zero. Now, the transportation problem becomes balanced.

It is worth noting that sometimes problems that are solved using the transportation method have nothing to do with an actual movement of goods. What is crucial for applying the method is to recognize the network of connected elements.

## Solutions

### Information Used to Solve Transportation Problems

Imagine yourself as an owner of two warehouses and three chocolate stores. To solve your transportation problem, the following data is required:

The supply at every origin (or warehouse)

• 50 boxes of chocolate in Newark's warehouse
• 35 boxes in Hagerstown

The demand at every destination (store)

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