di Sergio Mauri

__What is this paper about?__

This paper is about “operational research” as in the British version of the subject or “operations research” as in the American one. From now on, it’ll be just O.R.. O.R. has a synonymous in “management science” (MS).

**Problem solving method.**

O.R. is the science used to solve a problem that impacts a Company or an organization. Here below the steps we have usually to take to face the occurring problem:

1. Collecting information

2. Formulate the problem

3. Mathematical modelling

4. Solving the Mathematical Model

5. Verification and Check

6. Implementation

__A brief history of O.R..__

This discipline is relatively new. It started in the UK in the late 1930’s. it was used to build an experimental radar equipment. It developed in the Second World War in UK to solve military problems. The O.R. is remembered especially for the role of Alan Turing, an english mathematician who, during the war, under the British Intelligence supervision, developed a system to decipher the so-called Enigma Code, tha nazis’ secret code. Turing was also the inventor of the first computer and was focused on recursiveness. So, the Turing’s Machine is a set of instructions able to compute it.

One more interesting chapter of the initial phase of this discipline is about Frederick Taylor, the “inventor” of taylorism, who introduced the O.R. in order to optimize the productivity of his factories, followed by Henry Ford in his’.

__Some types of mathematical models:__

- Revenue: price * quantity R(x) = p * x
- Costs = Fixed Costs + Variable Costs C(x) = FC + VC(x)
- Earnings = Revenue – Costs E(x) = R(x) – C(x)

Total Cost TC(x)

- Unit Cost = —————- UC(x) = ———-

Quantity x

Mathematical models have to be solved. Solving an optimization problem means to optimize the O.F. of the model itself. Then, we have to use a proper mathematical process in order to find the best solution. The mathematical processes are: graphic type (with maximum two decision variables); analytical type (applying algebraic methods or infinitesimal analysis methods) and iterative (if the procedures are repetitive).

__Attractive connections between Artificial Intelligence and Operational Research.__

The question we have to start with is: do Artificial Intelligence (A.I.) and Operational Research (O.R.) have something in common? In other words: are A.I. and O.R. , say Computer Science and Operational Research, connections?

They are complementary in the way that A.I. can be a tecnique that makes a better predictions about the data we feed into O.R. based optimization models. There’s even the other way around, rahter than A.I. models feeding into O.R. models, we have O.R. tecniques employed in A.I. based Machine Learning (M.L.) models. in M.L. In M.L. when you develop a model you are spontaneously faced with an optimization task. The task you are looking at is to build a model that makes the best prediction which is a natural optimization task and we can see the use of optimization tecniques in M.L. more and more.

In a much broader view of A.I. and O.R., when you think of A.I. as the area of computer science thai s concerned with building systems that show intelligent behabiour you could say that O.R. is A.I.. This does not emerge from from the classical research point of view, because traditionally there were two separate disciplines tha have indipendently developed tecniques that have usually a lot of things in common, but from the very general definition, building systems that do something intelligent , operational research could be classified as a part of A.I..