1.1. A history
Like logistics, operational research (OR) emerged in a military context. The term can be attributed to Watson-Watt1 around 1940, becoming more widely known because of Patrick Blackett2 who, during the Second World War, put together the first OR team to resolve air defense problems and then problems surrounding supplying troops.
Although not yet bearing the name, OR developed out of mathematics and problems relating to mathematical expectation or combinatorial analysis between the 17th and 19th Centuries. Blaise Pascal3 worked on the problems of decision making in uncertainty and Gaspard Monge4, considered the father of optimization, studied the problems of cuts, fills and defilades. In the early 20th Century, stock management, with the famous Wilson formula5, brought OR into the modern world.
After the Second World War, many large businesses started using OR, a phenomenon that was making sweeping progress. It would be taught at Massachusetts Institute of Technology from 1948 before spreading into countless other universities and higher education institutions throughout the world. Nowadays, OR is known as a decision support tool.
1.2. Fields of application, principles and concepts
OR can be found within countless services in a business. It is often invisible, like logistics, and the two work in close collaboration.
Its presence is, however, more regularly found in vertical applications such as scheduling and planning, production management, quality, purchase and supply, stock and storing management, conveyance, expedition and transport, commercial action, management control and human resource management.
Methodologically, the use of OR is supported by well-defined principles resulting in the conceptualization of an often transversal approach through the chain system of the business.
The approach can be divided into a number of phases:
- – identifying the problem;
- – modeling the problem;
- – solving the problem;
- – validating the solution;
- – implementing the solution;
- – improving the solution.
COMMENT. – Section 1.2.1 aims to clarify the general methodology to be implemented so as to formalize an OR problem as well as to define the specific vocabulary used by logisticians.
1.2.1. Identification
Identification is by far one of the most difficult phases. At this stage, one or more objectives and a set of constraints need to be defined.
While at first glance this may seem simple, on closer examination it quickly takes on a complexity that often lies beneath the surface. For instance, in the case of the transportation of a load from one place to another, it could be said that the aim is to reach the destination by spending the least amount possible on the delivery of goods. The constraints are the potential routes and their respective mileage, the choice of one or more suitable vehicles depending on the mass being transported, the consumption of these vehicles, the cost amortization per kilometer, etc. The delivery point at the destination, however, may have specific opening hours, its storage capacity may be limited, etc.
It is clear to see how the objective itself becomes a source of constraints. It may perhaps need to be redefined, with some of the previous constraints transforming into a new objective in reality, such as for instance, optimal transportation and delivery time.
Constraints are generally equalities or inequalities that constitute equation systems that are difficult to handle and solve. The objective is, in many cases, attached to a function whose maximization or minimization is required. This may also be the establishment and the verification of a relation. There are often numerous criteria that are poorly defined. The success of this initial phase – the identification of the problem – is crucial as it is where the future problem of the OR is formulated.
Since businesses have been implementing quality management by modeling each of their key actions on one or a number of processes, logisticians have been able to draw on these resources. Nevertheless, it is rare for everything to be formalized enough so that objectives and constraints can be correctly defined. Only an accurate and detailed analysis, as well as collaboration with those on the ground, will provide the elements required for the problem in question to be correctly modeled.
1.2.2. Modeling
At this stage, the logistician will formulate an elementary description of the project by defining a set of variable integrated into equations, inequalities, systems, functions or relations. The nature of these variables can be quantitative or qualitative.
All units (kg, L, g, m/s, h, square meter, square kilometer, cubed meter, °C, °F, W, Kwh, etc.) are possible and in a diverse range of formats: integer, decimal, real, rational, monetary, hourly, logical, binary, personalized, etc. They may be input, output or control variables. Constant and random values may intervene. A model is deterministic when the set of its parameters is known with certainty or stochastic when its parameters are uncertain.
Variables can represent the known or unknown values of a problem: they are often called alternative. They face restrictions that are developed and contained within constraints with a view to obtain a definite result or solution in the form of an objective function to be optimized.
A model is built based on a set of properties:
- – real properties that belong to reality;
- – formal properties that only belong to the model;
- – compatible properties that adapt the model so that it fits with reality.
Depending on the chosen or imposed properties, logisticians are able to generate a perfect model when their model only contains the properties existing in the limited perimeter of the problem or a complete model when all the existing properties are taken into account.
The model can consist of functions that meet a number or prerogatives:
- – explain the situation, present the causes and effects inherent to the problem;
- – provide a solution enabling the variables and constraints of the problem to be acted upon so as to obtain a...
