Inserting and Setting Up Linear Optimization Blocks

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 - total advertising budget is not more than 500000 dollars.
x1 ≤ 300000 - not more than 60% of total advertising budget can be spent on internet advertising.
x2 ≥ 250000 - not less than 50% of total advertising budget should be spent on television advertising.
x3 ≤ 100000 - not more than 20% of total advertising budget can be spent on newspaper advertising.

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:

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:

Select the linear optimization block in the working area:

Click the Edit button on the Home ribbon tab.
Press F4.

Select the Edit item in the linear optimization block's context menu.

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 using the linear optimization block editing wizard , which is used to set up block parameters.

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.