Transportation Problem

Transportation Model for an optimal strategy for distributing a commodity from a group of supply centers to various receiving centers. Solved in C# Windows Form Application.

Reference to:

[1] Valentyn N Sichkar. Transportation Model for an optimal strategy for distributing a commodity from a group of supply centers to various receiving centers. Solved in C# Windows Form // GitHub platform [Electronic resource]. URL: https://github.com/sichkar-valentyn/Transportation_Problem (date of access: XX.XX.XXXX)

Description

The general transportation problem is concerned with determining an optimal strategy for distributing a commodity from a group of supply centers, such as factories, called sources, to various receiving centers, such as warehouses, called destinations, in such a way as to minimize total distribution costs.

Each source is able to supply a fixed number of units of the product, usually called the capacity or availability, and each destination has a fixed demand, often called the requirement.

Transportation models can also be used when a company is trying to decide where to locate a new facility. Good financial decisions concerning facility location also attempt to minimize total transportation and production costs for the entire system.

Task

There are 4 warehouse containing some number of units of the same type of product (see table 1), there is also 5 consumers depend on a certain amount of these products (see table 2). When shipping one unit from warehouse i to consumer j costs Pij arise. The magnitude of the costs is shown in the Table 3.

For the transportation K units from warehouse i to consumer j the total transportation cost is KPij. The task is to find a transportation plan in which the total transportation cost of all products to all consumers will be minimal.

Task for Transportation Problem

Checking for the balance

Finding the Initial Plan

Finding the Initial Plan - Iteration 2

Finding the Initial Plan - Iteration 3

Finding the Initial Plan - Iteration 4

Finding the Initial Plan - Iteration 5

Finding the Initial Plan - Iteration 6

Finding the Initial Plan - Iteration 7

Finding the Initial Plan - Iteration 8

Finding the Initial Plan - Found.png

Checking for the Non Empty Condition

The Whole Cost of the delivery

Improving the Initial Plan

Improving the Initial Plan Creating helper column and row

Improving the Initial Plan Calculating evaluations for the rest empty cells

Improving the Initial Plan Finding the largest value among the negative

Improving the Initial Plan Building circle

Improving the Initial Plan Finding minimum

Building new Initial Plan

To Find the Optimal Final Plan

Optimal Final Plan-Found

Results and Conclusions

MIT License

Copyright (c) 2017 Valentyn N Sichkar

github.com/sichkar-valentyn

Reference to:

[1] Valentyn N Sichkar. Transportation Model for an optimal strategy for distributing a commodity from a group of supply centers to various receiving centers. Solved in C# Windows Form // GitHub platform [Electronic resource]. URL: https://github.com/sichkar-valentyn/Transportation_Problem (date of access: XX.XX.XXXX)