Inserting and Setting Up Linear Optimization Blocks

To work with the tool in Foresight Analytics Platform 10, use the new interface.

A linear optimization block is used to solve a problem of optimal use of limited resources.

In the problem controlling variables are resources, and criterion function is an entity that is subject to optimization. Problem solution is finding such values of controlling variables that satisfy the specified constraints and at which criterion function takes the maximum or the minimum value. Conditions, for which the problem is created, may change. To take into account these conditions without creating a new problem, criterion function coefficients are used that enable the user to account for influence of conditions change on criterion function calculation.

For example, a company advertises its products using the internet, television and newspapers. Each dollar spent on internet advertising increases revenue by ten dollars. Each dollar spent on television advertising increases revenue by seven dollars, and each dollar spent on newspaper advertising increases revenue by four dollars.

The are the following constraints in advertising budget distribution:

Total advertising budget is not more than 500000 dollars.
Not more than 60% of total advertising budget can be spent on internet advertising.
Not less than 50% of total advertising budget should be spent on television advertising.
Not more than 20% of total advertising budget can be spent on newspaper advertising.

The linear optimization block can be used to calculate an advertising budget model providing maximum revenue for the company.

Where:

Controlling variables are internet advertising budget, television advertising budget, and newspaper advertising budget.
Criterion function coefficients are the revenue obtained after each dollar spent on advertising.
Constraints are advertising budget distribution.
Criterion function - revenue.

Visualize this problem as formulas. The controlling variables x1, x2 and x3 are internet advertising budget, television advertising budget, and newspaper advertising budget. The following constraints are imposed on them:

x1 + x2 + x3 ≤ 500000 - full marketing budget does not exceed 500000 rubles.
x1 ≤ 300000 - No more than 60% of the whole marketing budget can be spent on internet ads.
x2 ≥ 250000 - At least 50% of the whole marketing budget should be spent on TV ads.
x3 ≤ 100000 - No more than 20% of the whole marketing budget can be spent on mass media ads.

Criterion function is getting maximum revenue:

10x1 + 7x2 + 4x3 → max

Where 10, 7 and 4 - criterion function coefficients for the controlling variables x1, x2 and x3 respectively.

To create a new linear optimization block:

In the object navigator:

Click the New Object > User Objects > Linear Optimization Block button in the Create group on the Home ribbon tab.
Select the Create > User Objects > Linear Optimization Block item in the object navigator's context menu.

After executing one of the operations the Insert Object - Parameters - Linear Optimization Block dialog box opens. Enter name of the created linear optimization block and change the automatically created identifier if required.

In the Calculation Algorithms extension:

Select the Linear Optimization Block item in the drop-down menu of the Calculation Block button on the Home ribbon tab.
Select the Create > Linear Optimization Block item in the working area's context menu.

To edit a ready linear optimization block:

In the object navigator select the function block and execute one of the operations:

Click the Edit button in the Open group on the Home ribbon tab.
Select the Edit item in the linear optimization block's context menu.
Press F4.

In the Calculation Algorithms extension select the linear optimization block in the working area:

Click the Edit button on the Home ribbon tab.
Select the Edit item in the linear optimization block's context menu.
Press F4.

To view criterion function, select the Criterion Function item in the linear optimization block's context menu. The Criterion Function Appearance dialog box opens.

Creating and editing is executed in the linear optimization block editing wizard, in which block parameters can be set up.

Setting Up Linear Optimization Block

Example of creating and Setting Up Linear Optimization

It is assumed that a meat trading company owns warehouses situated in different Moscow districts. It is required to calculate the optimal number of products to be stored in each warehouse taking into account:

In the example all data is entered by pasting from clipboard. It is done to speed up data entry in the example. When real linear optimization blocks are created, data is entered using keyboard.