Exam sample 3

Pagina 1

Problem 3 You are the head of the dispatching department of a European energy company. Your company produces energy in the eastern part of Europe, specifically in Romania, Ukraine and Hungary. You can find the available energy supply in the three countries in the table below: Romania 3000 MW Ukraine 2500 MW Hungary 1500 MW Your company sells energy in some countries of western Europe, in the table below you can find the energy demand for the various countries: Italy 750 MW France 750 MW Germany 2000 MW Spain 1500 MW UK 2000 MW The costs of shipping a MW of energy grows linearly with the distance between countries, and are equal to 0.01 € 𝑀𝑊∗𝑚 The table of distances between nations is called dist_m, and it is stored in distances.gdx. This file is already present in the GAMS work directory. The table dist_m looks like this: Italy France Germany Spain UK Romania 1137 km 1870 km 1300 km 2500 km 2100 km Ukraine 1670 km 2020 km 1200 km 2860 km 2130 km Hungary 811 km 1250 km 700 km 1975 km 1450 km Your objective is to satisfy the energy demand on the market and minimizing the total shipping cost. Now: 1. Write a GAMS programme to solve this question. 2. Your department has refined the cost modelling equation, and discovered that the cost of shipping varies with the square root of the shipped power, and that the multiplicative constant is 0.25 € 𝑘𝑚 √𝑀𝑊 , Modify the model you’ve written above to account for this new cost function 3. You’ve been asked by the strategic planning department to analyze how the dispatching strategy will change in the next 10 years: specifically, you know that the shipping cost will decrease by 1 percent from 2020 until 2024, and by 5 percent from 2025 until 2029 (use the linear cost function)