You cannot win a war without a mathematician

33-year-old District Governor of Çınar, Zikrullah Erdoğan, has been appointed by President Erdoğan to the position of General Manager of Procurement Services at the Ministry of National Defense (MSB). The military rank equivalent of the position he was appointed to is that of a major general…

To become a major general, you serve in the army as a lieutenant, first lieutenant, captain, major, lieutenant colonel, and colonel. The vast majority of colonels are retired due to a lack of available positions. If your service record is good and there is a vacancy, you are promoted first to brigadier general, and then to major general. We are talking about approximately 40 years of military experience…

The politicization of the army is one of the most significant existential problems for a country. There are many reasons for the collapse of the Ottoman Empire, and the politicization of the army is among the top of those reasons.

A decision had been made within NATO for member countries to double their defense spending. It is clear that a significant portion of the budget will be allocated to defense in the coming period. I do not know if this appointment was made to control this. But this appointment disrupts the entire hierarchy of the army. You are bringing in someone without rank to replace someone with the rank of major general. Below that rank, there are brigadier generals, colonels, and majors. Time will tell whether the chain of command will be damaged. Much criticism has been made on this subject. I agree with all of it. I also want to draw attention to one more issue.

Procurement service in the army is not limited to conducting ordinary tenders. Procurement in the army means logistics, which is a scientific discipline in its own right… In university (Hacettepe Economics, pre-1980), we took a semester-long course on “Linear Programming.” Linear programming is a scientific discipline where mathematics and statistics are used together…

It is used in many areas of economics to achieve maximum benefit with minimum cost. But Linear Programming emerged as a result of the quest for how to use military logistics efficiently.

For military logistics and procurement, you must know the history of war. You must know the defense and attack tactics and strategies of all kinds of warfare. Then, with the scarce resources, scarce ammunition, and scarce human resources at your disposal, how much material and how many people will you use on which front? To answer this question, you must know mathematical solutions, operations research, and linear programming.

Let me summarize how linear programming was born…

The foundations of linear programming were laid in 1939 by the Soviet mathematician and economist Leonid Kantorovich. But its true emergence was during World War II with the American George Dantzig.

In 1947, Dantzig was racking his brain to solve resource planning and logistics problems for the US Air Force. What was the basic need? The US and allied armies were facing problems such as:

• Distributing limited fuel to different fronts,

• Most efficient use of ship and aircraft capacities,

• Ammunition shipment,

• Transport of soldiers and equipment,

• Planning production capacity according to war needs,

• Route optimization of naval convoys.

These were actually turning into the same mathematical question:

“How can maximum operational efficiency be achieved with limited resources?”

This is exactly what linear programming was developed for.

In this process, Dantzig developed the famous “Simplex Method.”

During World War II and the Cold War, it was used in military planning for issues such as supply lines, radar placement, bombing routes, and maritime transport. Starting from the 1950s, it began to be used in economics and corporations.

Today, the fate of wars is determined not only by the number of soldiers and weapons technology; but also by supply chains, ammunition continuity, maintenance-repair capacity, data processing, logistics algorithms, and production planning.

For this reason, structures like the MSB Procurement Services General Directorate are no longer just “bureaucratic institutions that conduct tenders”; they have become one of the state's strategic operation centers.

The real issue is having the right material, at the right time, on the right front, at minimum cost, and without interruption. This directly requires both military knowledge and experience, as well as knowledge and experience in mathematics, statistics, data analysis, engineering, risk management, and optimization.

Modern armies survive not only with weapons; but with data, optimization, and the right human resources. Wars are no longer won only by generals, but also by mathematicians.

AHMET, AYŞE, AND ZEYNEP

To solve this complex equation, a fun exam question that simplifies the matter used to be asked in the economics and industrial engineering departments of some universities. While we are at it, let's repeat the question to explain the subject more clearly. (To avoid gender discrimination, you can replace Ahmet with Neşe, and Ayşe and Zeynep with Ali and Veli among the characters in the question.)

Ahmet is a university student… He has 30 hours of free time per week and a budget of 700 TL. Ahmet has two female friends named Ayşe and Zeynep. He meets with both of them separately and is happy. How will he use his 30 hours and 700 lira spending budget optimally?

A meeting with Ayşe:

• Lasts 3 hours,

• Costs 40 TL,

• Provides 8 happiness points.

A meeting with Zeynep:

• Lasts 2 hours,

• Costs 60 TL,

• Provides 10 happiness points.

How many hours should Ahmet meet with Ayşe and how many hours with Zeynep so that he uses his 30 hours and 700 lira to provide maximum benefit?

You write the formula for this. The result is as follows…

• If he meets with Ayşe 4 times and Zeynep 9 times, he uses his 30 hours and 700 lira exactly.

• He allocates more time to Zeynep because the unit benefit-time-budget balance makes her more attractive.

• He uses both his time and money completely. He achieves maximum happiness.

SOLUTION METHOD FOR THE CURIOUS

In the formula, we use x for Ayşe and y for Zeynep. According to the available data, Ayşe provides 8 and Zeynep provides 10 happiness points.

Objective function:

Maximum happiness = 8x+10y

Constraints: A meeting with Ayşe is 3 hours, with Zeynep is 2 hours… Total time is 30 hours…

The budget for a meeting with Ayşe is 40 lira, and the budget for a meeting with Zeynep is 60 lira. Total budget is 700 lira… We took the constraints as equality for full utilization.

3x+2y= 30

40x+60y= 700

When we simplify and solve the equations,

We reach the result X = 4, Y=9.

If we verify it…

3(4)+2(9)=12+18=30 hours

40(4)+60(9)=160+540=700 lira…

Time and budget constraints have been fully utilized and 122 happiness points have been captured.

Total happiness: 8(4)+10(9)=32+90=122

Now the similar question is: With the resources and budget opportunities we have, where and in what quantities will we place the new missile defense systems (S-400s are in storage) to protect against possible threats? Airports, refineries, power plants, bridges, or military units?