Our products and services´s cover a wide range of applications. Below, we present some practical cases for which ESCISSION could provide optimal solutions efficiently
PRACTICAL CASE 1
How a Covid-19 pandemic develops
These prognosis techniques can also be used to study how a pandemic like Covid-19 develops and help planning ahead. They allow us to act in order to reduce the number of people infected and the deceased.
The Agents have to decide how to face a pandemic and one of the biggest concerns is how the data is analyzed, in particular, how the mortality rate is worked out only taking into account the total confirmed number of deceased and the number of diagnosed cases.
These calculations result in much higher mortality rates, creating a great public alarm. The most reliable data that can be accessed are the number of dead and the number of new cases, all provided by governments and, in some cases like the USA or Spain, the number os patients admitted in the hospital. Levering this information it would be possible to answer questions like: How is the virus spreading around the world? How are the different governments performing? Could we find a way of reducing the number of cases and deaths?
In order to reduce uncertainty, different models were considered in the analysis here presented, and it was concluded that the spread of Covid-19 follows the Verhulst equation, a logistic function developed in 1938. This model would help the system take preventive actions and act in a coordinated manner, making use of the resources available in the different regions.
One example of using stochastic optimization is the optimal management of reservoir systems in order to maximize the value of the hydroelectric energy produced, bearing in mind certain operational restrictions.
Managers have limited knowledge of how much water is discharged from rivers that feed into the reservoirs, the exact consumptive demands that must be met, or the price of energy, which fluctuates constantly. This context of uncertainty poses the following question: how should turbines be scheduled in order to maximize the expected benefit, whilst maintaining water levels in the reservoir within maximum and minimum limits, with a given probability of failure?
Uncertainty in the input and intermediate parameters (weather, hydrological processes, other consumption, energy prices, etc.) transforms what is a relatively simple mathematical programming problem into a stochastic optimization one, which requires more complex techniques.
practical case 3
Storage capacity and transportation expansion planning
Another example of when these techniques are used is logistics and storage planning as well as optimal management of freight transport. For instance, when a logistics company plans to build different storage and distribution centers for products at a set of potential locations in order to meet its customers' demands in the most cost-effective way.
Managers have to decide the most advantageous option even though the exact demands their customers have are not known, and they must make decisions that minimize capital investments and transportation costs in order to fulfil supply guarantee criteria; defining not only where the potential storage centers may be located, but also their capacity and the optimal routes for product distribution. In this framework of uncertainty, the following questions are posed: where should the new logistic centers be located and how big should they be; and what are the optimal routes for satisfying customer demand? All of this must be carried out at the lowest cost and in fulfilment of the service level agreements?
Once again, uncertainty in demand significantly changes the solution to this question, which is now representative of a stochastic optimization problem that requires specific tools and solvers.
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