**1.12 Conclusion**

solve problems from small to large scale problem optimally in a short time. There are so many computer-based mathematical programming languages have been used worldwide. Some of the tools that are used to solve optimization problems are **LINDO, LINGO, AMPL, MATLAB, MATHEMATICA, MAPLE, MS EXCEL**

AMPL, an acronym for "A Mathematical Programming Language" is a comprehensive and powerful algebraic modeling language for linear and nonlinear optimization problems, with discrete or continuous variables. It is a language for solving high complexity problems for large scale mathematical computation. It was developed by Robert Fourier, David Gay and Brian Kernighan at Bell Laboratories [1]. By using AMPL, we can get the solution of a problem in which the model of the formulation with sets, variables, parameters, constraints, etc. are written in a mod. file and the data of the formulation are written in a dat. file. Then the solution is

LINGO is designed to solve a wide range of optimization problems, including linear programs, mixed integer programs, quadratic programs, stochastic, and general nonlinear non-convex programs faster, easier and more efficient. It provides a completely integrated package that includes a powerful language for expressing optimization models, a full-featured environment for building and editing prob-

First one is based on weapons assignment in which the engagement of a target by a weapon is modeled as a stochastic event. In this type of problem, we develop a general computer oriented algorithm so that we can solve this type of problems for small scales to large scales problems in a single framework. To show the effectiveness of our developed model we present numerical examples of WTAP and com-

**SOLVER** and **TORA,** etc. In this chapter, we use AMPL and LINGO.

*Concepts, Applications and Emerging Opportunities in Industrial Engineering*

found after running the program in the console window.

lems, and a set of fast built-in solvers.

pare our result with different existing results.

*1.9.1 AMPL*

**Figure 1.**

*Codification of SP problems.*

*1.9.2 LINGO*

**1.10 Motivation**

**182**

In this Section, we discussed the relevant preliminaries. In the next Section, we will review some literature about weapons assignment and chance-constrained problem.

In this section, we will review some admissible research articles on Weapon Target Assignment Problem. Since the 1950s, the optimal assignment problem of weapons to targets has always been concerned by many countries. The study of WTA problem can be traced back to the 1950s and 1960s when Manne [2] and Day [3] built the model of WTA problem. The present research work on WTA is focused on models and algorithms. In the research on models of WTA, the static WTA


#### **Table 1.** *Existing algorithms for several ye.*

models are mainly studied and the dynamic WTA are not fully studied indeed. In the research on algorithms of WTA, the intelligent algorithms are often used to solve the WTA problem.

There are so many proposed algorithms on WTA problem [4, 5]. So we present the summary of variant heuristic algorithms and the implementation of various WTA have been proposed for several years is shown in **Table 1**.
