# Optimization of transport

Optimization of transport used for transportation link planning and cost reduction. Is used mainly by companies whose business requires to transport large quantities of products such as cereals, coal, sand and cement. Optimizing of transport is also known under the term "transportation problem".

## Stages of the classical transportation algorithm

- determination of the initial basic solution by using the selected method, for example:
- method of the Northwest angle,
- method of the minimum element of a row or column of a cost matrix,
- method of the minimum element of the cost matrix.

- using the method of potentials it is necessary to check which solution is optimal. For this purpose it is necessary to use a measure of optimality:
*o = (ui + vj) – cij = 0*, where*cij= ui + vj* - in the case when the solution that we got is not optimal, it is necessary to find another solution.

## Elements of the transportation problem

- The supply of providers - the supply of providers is understood the number of suppliers
*m*with*am*products. - Consumer demand - the needs of buyers understood as the number of customers
*n*, which the company intends to provide the*bn*products.

- The matrix of transportation cost -
*kij*, where*i = (1,...,m)*and*j = (1,...,n)*, i.e. cost of transporting the product from the*i-th*supplier to the*j-th*recipient. - The traffic matrix -
*xij*, where*i = (1,...,m)*and*j = (1,...,n)*, i.e. quantity of products transported from the*i-th*supplier to the*j-th*recipient.

## Types of transportation problems

- closed - occurs when supply of providers equals the demand, if there is the following relationship
*ai = bj* - open - occurs when supply of providers does not equal customer demand, ie. when there is the following relationship:
*ai > aj*, this means that the supply of providers is greater than the needs of consumers.*ai < aj*, this means that the supply of providers is lower than the needs.

Form of classical transportation algorithm for closed transportation problems.

Limiting conditions for suppliers:

*xij = ai* where *xij* is transport matrix

Limiting conditions for recipients:

*xij=bj*

*ai = bj*

*cij xij –> min*

## Optimization of transport connections in logistics

The optimization of transport links from the point of view of logistics management should be understood as all efforts for the smooth flow of goods from the manufacturer to the individual customer. Companies are part of the "pipeline" or chain. The chain is formed by both suppliers, companies and customers.

Supply chain management aims to save costs and / or improved customer service. The objective of supply chain management is to give the company the best position in the global market and keeping it in spite of ongoing changes in customer needs and competition.

To optimize the transport using logistics supply chain, company should pay attention to all segments and links in chain sequence:

- Transport
- Storage - including: inventory management and warehousing.
- Packaging - affects the mean of transport used.
- Manipulation of materials
- Performance - time from an order by the customer until the delivery of goods ordered. We can distinguish following elements:
- Order adoption
- Order development
- Preparation of goods
- Delivery (transportation).

## References

- Aneja, Y. P., & Nair, K. P. (1979).
*Bicriteria transportation problem*. Management Science, 25(1), 73-78. - Danila, B., Yu, Y., Marsh, J. A., & Bassler, K. E. (2006).
*Optimal transport on complex networks*. Physical Review E, 74(4), 046106. - Ford Jr, L. R., & Fulkerson, D. R. (1956).
*Solving the transportation problem*. Management Science, 3(1), 24-32. - Gleyzal, A. (1955).
*An algorithm for solving the transportation problem*. Journal of Research of the National Bureau of Standards, 54(4), 213-216. - Munkres, J. (1957).
*Algorithms for the assignment and transportation problems*. Journal of the Society for Industrial and Applied Mathematics, 5(1), 32-38. - Scellato, S., Fortuna, L., Frasca, M., Gómez-Gardeñes, J., & Latora, V. (2010).
*Traffic optimization in transport networks based on local routing*. The European Physical Journal B, 73(2), 303-308.