Transportation and Assignment Problems in Operations Research

Operations Research

Operations research is an interdisciplinary field that deals with mathematical modeling and statistical analysis of real-world problems. It involves the application of methods from various fields such as mathematics, economics, computer science, statistics, and engineering to create procedures and models that help make better decisions during wartime and peacetime. Operational researchers work in a wide range of industries including transportation, health care, manufacturing, telecommunications, defense, finance, and energy.

Two prominent areas within operations research are the Transportation Problem and the Assignment problem. These problems are often encountered in supply chain management and logistics planning.

Transportation Problem

The Transportation Problem is a classic optimization problem in which resources are distributed over several facilities to minimize the total cost. In this context, a facility refers to any organizational unit that produces goods or services; it could be a factory, warehouse, office, store, or even a group of stores. The problem involves minimizing the total cost of shipping goods from suppliers to customers.

The first major application of the Transportation Problem was in the U.S. Army during World War II when the problem of shipping goods from stockpiles to the ports needed to be solved. The first published account of the transportation problem was an article by George Dantzig in 1951. Dantzig's article provided the first algorithmic solution for the problem and also showed how to solve a general linear programming problem using the simplex method.

Assignment Problem

The Assignment Problem, also known as the Matching Problem, is another optimization problem in operations research. It is a combinatorial optimization problem in which there are a number of agents and a number of jobs, each agent can do only one job and each job can be done by only one agent. The assignment problem is to assign jobs to agents so that the total cost is minimized.

The Assignment Problem was formulated by the Hungarian mathematician János von Neumann in 1947. Neumann's original approach did not use linear programming but rather a method known as the Hungarian algorithm, also called the Kuhn–Munkres algorithm. The Hungarian algorithm is now widely used to solve the assignment problem and other problems related to the transportation problem.

In summary, operations research is a valuable tool for decision-making in various industries. The Transportation Problem and the Assignment Problem are two important applications of operations research in the field of logistics and supply chain management.