DECISION OPTIMIZATION IN THE MILITARY FIELD

Transcription

1 DECISION OPTIMIZATION IN THE MILITARY FIELD Vasile CĂRUŢAŞU, Daniela CĂRUŢAŞU Nicolae Balcescu Land Forces Academy Abstract Appointing optimal solutions in decision related problems is a difficult issue for which methods have been asserted, in certainty as well as in uncertainty conditions. These methods are useful in analysis, which imply finding the best solution, but, from a mathematical point of view, they don t offer a rigorous sustain. The usage of such instruments is necessary and useful for the commanders and major states in finding solutions for every training, military operations and combat stage. The continuous increase of the collected, processed and transmitted information volume implies the increase of the efficiency and troop leadership quality by implementing the decisional methods, by means of calculus techniques. The knowledge of such methods gives the command officer the chance to better direct and provide the proper scientific solution. Keywords: model, decision, certainty, uncertainty, optimal solution 1. Introduction Every day life is marked by decisions, irrespective of the activity that we perform and of the role that we play in society or family. But, when we find ourselves in a theatre of operations, and our decision can lead to the loss of subordinates lives, than, decision-making receives a special meaning. An arbitrary decision, without a proper study of the analyzed situation, can have disastrous consequences. Even more, in the military field, the decision made by leading factors has to depend on a solid scientific base. 111

2 This theory s evolution has targeted the elaboration of general methods that allow the generalization of the decision-making procedures. The utility theory aims at introducing a proper consequence comparison system for the different ways that a decident can act in association with a numeric value, known as utility. In the 60 s, a new decisional analysis approach appears once with the passing over to the multi-decisional problem solving. The French researchers, disregarding the utility term, provided for the optimal variant establishing, a method based on concordance and discordance indexes that can be determined by matrix methods. Another decisional process approach is the group decision theory that analyses the crossing over of the individual to the group options. All these researches aimed at finding objective methods of analyzing the variants placed in front of the decident and selecting objectively the optimal action variant. 2. Scenario We will focus on the analysis mode and decision-making in the case of the described tactical situation in Fig.1. 1 ST BASE 1 ST ZONE 2 ND ZONE 2 ND BASE 3 RD BASE C Fig

3 The enemy forces are situated in the 1 st Zone; they are equipped with 3 bulletproof transporters, anti armor, individual combat weapons, one self-propelled radar station for short distance and low altitude detection, and they intend to occupy a strategic position in the 2 nd Zone. The own forces dispose of 3(three) bases, situated as in Fig.1 and have the following: 1 st Base: a carrier in the G Golf; 2 nd Base: at approximately 2000 km from the 1 st Zone; 3 rd Base: at approximately 350 km from the 2 nd Zone and at approximately 250 km from the 1 st Zone. The three military bases placed in the structure of own forces are subordinate to a commandment situated in the 2 nd Base. The created tactical situation analysis and the performed analysis within the commandment have led to the following action variants: a) V1 air attack from the 1 st Base platform; b) V2 rocket attack from the 2 nd Base; c) V3 land attack from the 3 rd Base; d) V4 rocket attack combined with land attack; e) V5 air attack combined with land attack; f) V6 rocket attack combined with air attack. The weather forecast predicts instable weather for the period the military action is due to take place. The weather becomes a problematic aspect for the commander than when visibility decreases. The mission will be considered accomplished, if the enemy and its means are destroyed in proportion of at least 70%. The commandment analysis has to take in account the following criteria when making the decision according to the action variant: a) C1 time (hours); b) C2 number of people; c) C3 mission accomplishing costs (thousands of dollars); d) C4 mobility ( operating systems time / number of hours); e) C5 destruction capacity (number of strikes / surface). The information regarding the used criteria and the identified attack variants are synthetically arranged in the table below: 113

4 Table 1 C1 C2 C3 C4 C5 V1 2, ,7 V2 1, ,1 0,94 V ,5 0,5 V4 3, ,3 0,83 V5 4, ,72 V6 2, ,6 0,9 We will search for the optimal action variant using the moment method and the linear attribution method. 3. Mathematical Model 3.1. Moment Method (Deutch Martin) Applying the moment method, which consists of the alternative moment calculation, in columns and rows, and their increasing arrangement, the results in the table below are obtained: Table 2 C2 C3 C1 C4 C5 V ,8 0 0 V5 0,64 0, ,5 V4 0,71 0,58 0,65 0,32 0,75 V1 0,35 0,53 0,37 0,6 0,45 V6 0,21 0,41 0,48 0,44 0,9 V ,24 1 From the obtained information in this table, the conclusion is that the problem s optimal solution is V2. The most efficient way of attack is, according to this mathematical method, the one presented by the second action variant (V2): rocket attack from the 2 nd Base Linear attribution method (Hungarian method) We take in account the same problem and attribute the following importance to the criteria. The factors of our interest are: the destroying capacity generated by each variant, mission achievement costs and the time in which the target is destroyed. 114

5 Table 3 C1 C2 C3 C4 C5 V1 2, ,7 V2 1, ,1 0,94 V ,5 0,5 V4 3, ,3 0,83 V5 4, ,72 V6 2, ,6 0,9 P 0,2 0,1 0,2 0,1 0,4 We build up the B matrix: Table 4 C1 C2 C3 C4 C5 V1 V5 V3 V3 V5 V2 V2 V3 V4 V5 V1 V6 V3 V4 V5 V4 V6 V4 V4 V6 V1 V1 V4 V5 V5 V1 V6 V6 V2 V1 V6 V2 V2 V2 V3 V3 P 0,2 0,1 0,2 0,1 0,4 We ll calculate the B matrix elements, which are inscribed in Table 5: Table V1 0 0,1 0 0,3 0,6 0 V2 0, ,1 0,5 V3 0,3 0, ,5 V4 0 0,1 0,8 0,1 0 0 V5 0,3 0,2 0,1 0,4 0 0 V6 0 0,4 0,1 0,2 0,3 0 This matrix generates the following matrix: 115

6 Table V V V V V V From this last matrix we can obtain the information regarding the optimal solution. We have b21=1, b62=1, b43=1, b54=1, b15=1 and b36=1. Hence, we conclude that the alternatives order will be: V2, V6, V4, V5, V1, V3. In this case also, the most efficient attack is presented in the second action variant (V2): rocket attack from the 2 nd Base. 4. Scenario Solution From the analysis presented above, in good visibility conditions, the optimal action variant is the one suggested by the second action variant (V2): rocket attack from the 2 nd Base. A very important analysis case is the establishing of the optimal solution in low visibility weather conditions. Low visibility weather conditions have as consequences for the mission achievement, the following: Mission accomplishment time increasing; Mission achievement costs increasing; System operating time increasing; Destroying capacity increasing. The criteria weight remains unchanged, but the problem information, according to the mentioned criteria, are changed, this meaning that the values increase. Therefore, resolving this problem with the two methods, the optimal solution in low visibility conditions is V6. 116

7 5. Summary In good visibility conditions the V2 variant is the optimal solution. A rocket attack is efficient, and has a great capacity to destroy, compared to the other variants that the own forces dispose of. Hence, V2 is the optimal solution in the context with a short time to accomplish the mission, a reduced number of people that prepare and serve it, and a low mission achievement cost. In low visibility conditions the efficiency of any other attack is visibly decreased. The optimal variant is a rocket attack combined with air attack. V6 contains a great capacity to destroy, a relative low mission achievement cost and a good time to accomplish the mission. The changing of the importance coefficients according to the criteria, leads to solution modification, a study of changing the optimal solution regarding these changes being extremely useful. References [1] Căruţaşu, Vasile; Bârsan, Ghiţă; Aplicaţii ale modelării şi simulării acţiunilor militare, Land Forces Academy Publishing House, Sibiu, [2] Hampu, Alexandru; Cercetări operaţionale şi modelarea sistemelor militare, Land Troops Academy Publishing House, Sibiu,