Summary of operations research knowledge points (6)

A full set of operations research knowledge points

Chapter VI Transportation Issues

1. Transportation issues

The content of the transportation problem is actually between the supply point and several demand points. When transporting goods of the same variety, specification, quality, etc., choose the best transportation plan to achieve the goal of the lowest total transportation cost or the largest profit.

2. Transportation issues and special structures

Transportation problem: The
following mathematical model can be established.


If the specific transportation quantity of each grid is uncertain, it can be set as Xij, which represents the transportation quantity from the i-th place of production to the j-th place of sale. For different transportation quantities, it will be different The purpose of the total freight is to find all possible distribution plans for the transportation quantity that meet the required restrictions, and then select the optimal one that has the lowest total freight from these transportation plans.
The solution of the transportation problem: the specific transportation quantity that makes the total freight cost the lowest.

Each data in the unit freight table represents the freight incurred from transporting a unit of product from different origins to different sales locations. Cij is used to represent the
production and sales balance sheet and the unit freight rate table. The two tables can be combined into one table. Balance sheet

Third, the operation method on the table

The method can be divided into the following three steps:
(1) Find an initial plan
(2) Determine whether it is optimal according to the judgment standard
(3) If it is not optimal, improve the plan, and then repeat step (2) (3) Step until the optimal solution is found

Fourth, the transportation problem where the demand is equal to the supply

1. Build a transportation map
2. Find an initial transportation plan
   . A grid with numbers is called a number grid, or a stone grid, the number is m+n-1, and a grid with a variable of 0 is called a space or a non-stone grid.
3. Seek improvement plan

Five, step stone method

1. Calculate each space for improvement route and improvement index. To improve the route is to start from a certain space and seek the route that attempts to change the original transportation plan. The improvement index refers to the variable that will cause the total freight when the transportation volume of goods changes by one unit following the improvement route.
2. Draw the improved route on the transportation map (closed loop method)
3. Find the improvement route and improvement index of each other box
4. Establish an improvement plan

Six, the method of establishing an improvement plan

The methods for seeking improvement schemes mainly include closed loop method and modified distribution method.

1. Closed loop method
   Among all the blanks, select the blank with the largest absolute value of negative improvement index as the adjustment grid, and along the improvement route of the blank, select the smallest volume with the negative sign as the adjustment volume
2. Modified distribution method
   Modified distribution method is also called potential method. Make some improvements to the original transportation route, add a row on the top of the diagram, and a column on the left side of the diagram

Seven, modify the relationship between the distribution method and the closed loop method

1. The closed loop method is the basis of the revised distribution method
2. The closed loop method first seeks to improve the route and then the improvement index. The modified distribution law is the opposite

8. Transport problems where the demand is less than the supply

1. Fake a supply point
2. The supply of the dummy supply point = the total supply-the total demand
3. The unit freight from any supply point to a dummy demand point is 0

Nine, the transportation problem where the demand is greater than the supply

1. Fake a supply point
2. The supply of the dummy supply point = the total demand-the total supply
3. The unit freight from a dummy supply point to any demand point is 0. That is, the transportation volume cannot be shipped out at all, and it is a shortage of transportation volume.