**3.16 Comparison of media allocation result with other existing solution**

This hypothetical example was given and solved by using MS Excel [20] and meta-heuristic genetic algorithm [21] previously. We have used our proposed algorithm to solve the media allocation problem. The solutions obtained by using genetic algorithm [21] and MS Excel [20] are shown in **Tables 3** and **4**, respectively [22].

To check the efficiency of our model, we need to calculate the objective function for all the existing solution that is to be maximized. So the graphical representation


#### **Table 3.** *Media allocation solution by genetic algorithm.*

And, the linear constraints on the minimum required ads of media vehicles to

16 18 25 10

*x*<sup>11</sup> þ *x*<sup>21</sup> þ *x*<sup>31</sup> þ *x*<sup>41</sup> þ *x*<sup>51</sup> þ *x*<sup>61</sup> þ *x*<sup>71</sup> þ *x*81þ

*x*<sup>12</sup> þ *x*<sup>22</sup> þ *x*<sup>32</sup> þ *x*<sup>42</sup> þ *x*<sup>52</sup> þ *x*<sup>62</sup> þ *x*<sup>72</sup> þ *x*82þ

*x*<sup>13</sup> þ *x*<sup>23</sup> þ *x*<sup>33</sup> þ *x*<sup>43</sup> þ *x*<sup>53</sup> þ *x*<sup>63</sup> þ *x*<sup>73</sup> þ *x*83þ

*x*<sup>14</sup> þ *x*<sup>24</sup> þ *x*<sup>34</sup> þ *x*<sup>44</sup> þ *x*<sup>54</sup> þ *x*<sup>64</sup> þ *x*<sup>74</sup> þ *x*84þ

We develop a near optimization model which allocate media vehicles to predetermined target segments. As this media allocation problem is formulated by using weapon-target assignment problem with 60 decision variables. By using our algorithm, we have solved the Media Allocation problem in a short time. In this case, we only change the data values in the 'dat' file, use the same mod.file and run.

*x*<sup>91</sup> þ *x*10,1 þ *x*11,1 þ *x*12,1 þ *x*13,1 þ *x*14,1 þ *x*15,1 ≥16

*x*<sup>92</sup> þ *x*10,2 þ *x*11,2 þ *x*12,2 þ *x*13,2 þ *x*14,2 þ *x*15,2 ≥18

(12)

*x*<sup>93</sup> þ *x*10,3 þ *x*11,3 þ *x*12,3 þ *x*13,3 þ *x*14,3 þ *x*15,3 ≥25

*x*<sup>94</sup> þ *x*10,4 þ *x*11,4 þ *x*12,4 þ *x*13,4 þ *x*14,4 þ *x*15,4 ≥ 10

the four specified target audiences that must be engaged are:

Segment weights 2 3 4 1

**3.15 Solution of the media allocation problem**

file. The result is given in **Figure 8**.

**198**

**Media vehicles Morning time**

Number of ads required

*The probability of reaching target audiences.*

**Table 2.**

**(1)**

**Afternoon time (2)**

*Concepts, Applications and Emerging Opportunities in Industrial Engineering*

Somoy News (1) 0.21 0.12 0.12 0.23 8 BTV (2) 0.35 0.24 0.12 0.07 7 Channel I (3) 0.19 0.04 0 0.19 9 NTV (4) 0 0.26 0.19 0.13 5 ETV (5) 0.13 0.19 0.25 0 6 ATN News (6) 0.24 0.14 0.22 0.09 8 GTV (7) 0.09 0 0.18 0.28 3 Radio Today (8) 0.39 0.17 0.47 0 10 Radio Foorti (9) 0.24 0.31 0.14 0.43 15 Facebook (10) 0.1 0.23 0.03 0.35 12 Prothom Alo (11) 0.12 0.11 0.03 0.09 8 Ittefaq (12) 0.32 0.23 0.09 0.21 4 Billboard (13) 0.32 0.1 0.28 0.02 4 Printings (14) 0.23 0.12 0.08 0.03 4 E-mail (15) 0.29 0.07 0.04 0.32 4

**Prime time (3)**

**Night time (4)**

**Ad capacities**

### *Concepts, Applications and Emerging Opportunities in Industrial Engineering*


discussed two numerical examples and we have compared the results of the problems with previously solved results. We have observed that our proposed computational algorithm is easy to compute and gives a nearby optimal solution than other methods in a short time. We believe that AMPL program approach is a good and feasible alternative for the solution of this type class of problems. As further research, we may employ our developed AMPL program approach for the problem

This chapter is performed on two types of optimization such as the weapon's

In a warfare scenario, weapons allocation is very important. Since no exact algorithm is available to solve the WTAP, it is quite unavailable to estimate the quality of solutions produced by heuristic methods. The purpose of this chapter was to develop a new computerized algorithm to find a feasible solution in a reasonably fast time to help decision makers to make a proper assignment on the battlefield. We have developed a new computer-oriented algorithm by using AMPL to avoid the computational problems and solve this type of large scale problems. Our algorithm has been applied in two numerical examples of WTA problem and we have compared the complete outputs of the specified large scale problems with the outputs of the existing algorithms. We have concluded that our developed algorithm

Finally, we conclude that the programming language AMPL is an effective technique to compute different types of optimization problems which will reduce the computational time for large scale problems. Overall, we have developed computer-oriented algorithms to solve the mentioned applications of optimization

\* and Yaindrila Barua<sup>2</sup>

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

1 Department of Mathematics, University of Dhaka, Bangladesh

\*Address all correspondence to: mbabulhasan@yahoo.com

2 Daffodil International University, Bangladesh

provided the original work is properly cited.

with many targets, many weapons or advertising tools as well.

**4. Conclusions**

problems.

**Author details**

**201**

Mohammad Babul Hasan<sup>1</sup>

assignment problem.

*Weapon Target Assignment*

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

gives us the better result than others.

#### **Table 4.**

*Media allocation solution by MS excel solver.*

of the existing solutions of Media Allocation and objective function value for the corresponding results is shown in **Figure 9**.

In **Figure 9** it is clear that, our model gives the best result compared to other two methods. By analyzing the values of the objective function, we can see that the Genetic algorithm improved the solution using MS Excel by 0.004%. Thus, the AMPL algorithm employed in this study improved the previous solution using Genetic Algorithm and MS Excel Solver 0.033% and 0.037% respectively.

In this effort, we have proposed the AMPL program code as a meta-heuristic tool for the solution of all type of dynamic weapon-target assignment problem. We have
