**1.2 Preliminaries**

In the current section, we discuss some preliminaries of the terms we mention in the chapter.

The basic components of linear programming are as follows:

amounts of resources.

*Weapon Target Assignment*

*DOI: http://dx.doi.org/10.5772/intechopen.93665*

**1.6 Stochastic programming (SP)**

models.

**1.7 Types of SP problem**

shown in **Figure 1**.

**1.9 Software tools**

**181**

**1.8 Applications of stochastic programming**

• Decision variables (*x <sup>j</sup>*)—These are the quantities to be determined.

affect the cost, or, simply, the value that needs to be optimized.

• The objective function (1)—This represents how each decision variable would

• Constraints (2)—These represent how each decision variable would use limited

• Data—These quantify the relationships between the objective function and the constraints. *ci* is called profit or cost coefficients, *aij* are the constraint

coefficients and *bi* are the availability of resources or minimum requirement.

The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. For optimization under uncertainty stochastic programming is one of the best techniques. That is, stochastic programming is mathe-

Stochastic programming offers a solution by eliminating uncertainty and characterizing it using probability distributions. There exist many different types of stochastic problems. The most famous type of stochastic programming model is recourse problems. Another form of a stochastic problem is the chance-constrained programming problem. In this type of stochastic programming model, the constraints to be optimized depend on probabilities. The classification of SP problems is

Stochastic programming has been applied to a wide variety of areas. Some of the specific problems are part of the Stochastic Programming test set. Other applications are listed as follows: Manufacturing Production Planning, Manufacturing production capacity planning, Machine Scheduling, Freight scheduling, Dairy Farm Expansion planning, Macroeconomic modeling and planning, Timber management, Asset Liability Management, Portfolio selection, Traffic management, Optimal truss design, Automobile Dealership inventory management, Lake level management.

Nowadays computerized techniques are widely used to solve various types of problems in the world. Sometimes some problems become difficult to solve and time-consuming by hand calculation. So by using different software tools, we can

matical programs that include data that is not known with certainty but is approximated by probability distributions. Stochastic programming extends the scope of linear and nonlinear programming to include probabilistic or statistical information about one or more uncertain problem parameters. Similarly, when all the input data used in the mathematical formulation of the mathematical program is known with certainty then the corresponding models are called deterministic
