Sync with ME-projects

Author: Panitzin

economic_planning/DynamicModel.lp

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+\ Model EconomicPlanning
+\ LP format - for model browsing. Use MPS format to capture full model detail.
+Maximize
+  0.3 production[steel,3] + 0.6 production[coal,1]
+   + 0.2 production[transport,3] + 0.3 production[steel,2]
+   + 0.6 production[coal,2] + 0.2 production[transport,2]
+   + 0.3 production[steel,5] + 0.6 production[coal,3]
+   + 0.2 production[transport,1] + 0.3 production[steel,4]
+   + 0.6 production[coal,4] + 0.2 production[transport,5]
+   + 0.6 production[coal,5] + 0.2 production[transport,4]
+   + 0.3 production[steel,1] + 0.2 extra_cap[steel,3]
+   + 0.4 extra_cap[coal,1] + 0.1 extra_cap[transport,3]
+   + 0.2 extra_cap[steel,2] + 0.4 extra_cap[coal,2]
+   + 0.1 extra_cap[transport,2] + 0.2 extra_cap[steel,5]
+   + 0.4 extra_cap[coal,3] + 0.1 extra_cap[transport,1]
+   + 0.2 extra_cap[steel,4] + 0.4 extra_cap[coal,4]
+   + 0.1 extra_cap[transport,5] + 0.4 extra_cap[coal,5]
+   + 0.1 extra_cap[transport,4] + 0.2 extra_cap[steel,1]
+Subject To
+ balance1[coal]: 0.5 production[steel,2] + 0.1 production[coal,2]
+   + 0.4 production[transport,2] + stock[coal,1] + 0.7 extra_cap[steel,3]
+   + 0.9 extra_cap[transport,3] + 0.1 extra_cap[coal,3] = 190
+ balance1[steel]: 0.1 production[steel,2] + 0.1 production[coal,2]
+   + 0.2 production[transport,2] + stock[steel,1] + 0.1 extra_cap[steel,3]
+   + 0.2 extra_cap[transport,3] + 0.1 extra_cap[coal,3] = 120
+ balance1[transport]: 0.1 production[steel,2] + 0.2 production[coal,2]
+   + 0.2 production[transport,2] + stock[transport,1]
+   + 0.1 extra_cap[steel,3] + 0.2 extra_cap[transport,3]
+   + 0.2 extra_cap[coal,3] = 170
+ balance_t[coal,2]: - 0.5 production[steel,3] - 0.4 production[transport,3]
+   + production[coal,2] - 0.1 production[coal,3] + stock[coal,1]
+   - stock[coal,2] - 0.7 extra_cap[steel,4] - 0.1 extra_cap[coal,4]
+   - 0.9 extra_cap[transport,4] = 60
+ balance_t[coal,3]: production[coal,3] - 0.5 production[steel,4]
+   - 0.1 production[coal,4] - 0.4 production[transport,4] + stock[coal,2]
+   - stock[coal,3] - 0.7 extra_cap[steel,5] - 0.9 extra_cap[transport,5]
+   - 0.1 extra_cap[coal,5] = 60
+ balance_t[coal,4]: - 0.5 production[steel,5] + production[coal,4]
+   - 0.4 production[transport,5] - 0.1 production[coal,5] + stock[coal,3]
+   - stock[coal,4] - 0.7 extra_cap[steel,6] - 0.9 extra_cap[transport,6]
+   - 0.1 extra_cap[coal,6] = 60
+ balance_t[steel,2]: - 0.1 production[steel,3]
+   - 0.2 production[transport,3] + production[steel,2]
+   - 0.1 production[coal,3] - stock[steel,2] + stock[steel,1]
+   - 0.1 extra_cap[steel,4] - 0.1 extra_cap[coal,4]
+   - 0.2 extra_cap[transport,4] = 60
+ balance_t[steel,3]: production[steel,3] - 0.1 production[steel,4]
+   - 0.1 production[coal,4] - 0.2 production[transport,4] - stock[steel,3]
+   + stock[steel,2] - 0.1 extra_cap[steel,5] - 0.2 extra_cap[transport,5]
+   - 0.1 extra_cap[coal,5] = 60
+ balance_t[steel,4]: - 0.1 production[steel,5] + production[steel,4]
+   - 0.2 production[transport,5] - 0.1 production[coal,5] + stock[steel,3]
+   - stock[steel,4] - 0.1 extra_cap[steel,6] - 0.2 extra_cap[transport,6]
+   - 0.1 extra_cap[coal,6] = 60
+ balance_t[transport,2]: - 0.1 production[steel,3]
+   - 0.2 production[transport,3] + production[transport,2]
+   - 0.2 production[coal,3] - stock[transport,2] + stock[transport,1]
+   - 0.1 extra_cap[steel,4] - 0.2 extra_cap[coal,4]
+   - 0.2 extra_cap[transport,4] = 30
+ balance_t[transport,3]: production[transport,3] - 0.1 production[steel,4]
+   - 0.2 production[coal,4] - 0.2 production[transport,4]
+   - stock[transport,3] + stock[transport,2] - 0.1 extra_cap[steel,5]
+   - 0.2 extra_cap[transport,5] - 0.2 extra_cap[coal,5] = 30
+ balance_t[transport,4]: - 0.1 production[steel,5]
+   - 0.2 production[transport,5] - 0.2 production[coal,5]
+   + production[transport,4] + stock[transport,3] - stock[transport,4]
+   - 0.1 extra_cap[steel,6] - 0.2 extra_cap[transport,6]
+   - 0.2 extra_cap[coal,6] = 30
+ balance5[coal]: - 0.5 production[steel,6] - 0.4 production[transport,6]
+   + production[coal,5] - 0.1 production[coal,6] + stock[coal,4]
+   - stock[coal,5] = 60
+ balance5[steel]: production[steel,5] - 0.1 production[steel,6]
+   - 0.2 production[transport,6] - 0.1 production[coal,6] - stock[steel,5]
+   + stock[steel,4] = 60
+ balance5[transport]: - 0.1 production[steel,6]
+   - 0.2 production[transport,6] + production[transport,5]
+   - 0.2 production[coal,6] - stock[transport,5] + stock[transport,4] = 30
+ steadyProduction[coal]: production[coal,6] >= 166.3967611336032
+ steadyProduction[steel]: production[steel,6] >= 105.668016194332
+ steadyProduction[transport]: production[transport,6] >= 92.30769230769229
+ capacityConstr[steel,3]: production[steel,3] - extra_cap[steel,3]
+   - extra_cap[steel,2] - extra_cap[steel,1] <= 350
+ capacityConstr[coal,1]: production[coal,1] - extra_cap[coal,1] <= 300
+ capacityConstr[transport,3]: production[transport,3]
+   - extra_cap[transport,3] - extra_cap[transport,2]
+   - extra_cap[transport,1] <= 280
+ capacityConstr[steel,2]: production[steel,2] - extra_cap[steel,2]
+   - extra_cap[steel,1] <= 350
+ capacityConstr[coal,2]: production[coal,2] - extra_cap[coal,1]
+   - extra_cap[coal,2] <= 300
+ capacityConstr[transport,2]: production[transport,2]
+   - extra_cap[transport,2] - extra_cap[transport,1] <= 280
+ capacityConstr[steel,5]: production[steel,5] - extra_cap[steel,3]
+   - extra_cap[steel,2] - extra_cap[steel,5] - extra_cap[steel,4]
+   - extra_cap[steel,1] <= 350
+ capacityConstr[coal,3]: production[coal,3] - extra_cap[coal,1]
+   - extra_cap[coal,2] - extra_cap[coal,3] <= 300
+ capacityConstr[transport,1]: production[transport,1]
+   - extra_cap[transport,1] <= 280
+ capacityConstr[steel,4]: production[steel,4] - extra_cap[steel,3]
+   - extra_cap[steel,2] - extra_cap[steel,4] - extra_cap[steel,1] <= 350
+ capacityConstr[coal,4]: production[coal,4] - extra_cap[coal,1]
+   - extra_cap[coal,2] - extra_cap[coal,3] - extra_cap[coal,4] <= 300
+ capacityConstr[transport,5]: production[transport,5]
+   - extra_cap[transport,3] - extra_cap[transport,2]
+   - extra_cap[transport,1] - extra_cap[transport,5]
+   - extra_cap[transport,4] <= 280
+ capacityConstr[coal,5]: production[coal,5] - extra_cap[coal,1]
+   - extra_cap[coal,2] - extra_cap[coal,3] - extra_cap[coal,4]
+   - extra_cap[coal,5] <= 300
+ capacityConstr[transport,4]: production[transport,4]
+   - extra_cap[transport,3] - extra_cap[transport,2]
+   - extra_cap[transport,1] - extra_cap[transport,4] <= 280
+ capacityConstr[steel,1]: production[steel,1] - extra_cap[steel,1] <= 350
+Bounds
+ production[coal,1] = 0
+ production[transport,1] = 0
+ production[steel,1] = 0
+ extra_cap[coal,1] = 0
+ extra_cap[steel,2] = 0
+ extra_cap[coal,2] = 0
+ extra_cap[transport,2] = 0
+ extra_cap[transport,1] = 0
+ extra_cap[steel,6] = 0
+ extra_cap[transport,6] = 0
+ extra_cap[coal,6] = 0
+ extra_cap[steel,1] = 0
+End

economic_planning/README.md

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+# Economic Planning
+
+This model is an example of an economic planning problem that a country may face. This problem is an input–output model 
+representing the interrelationships between the different sectors of a country’s economy. In such problems, the goal 
+is to determine different possible growth patterns for the economy. The input-output model is formulated as a linear 
+programming problem using the Gurobi Python API and solved with the Gurobi Optimizer.
+
+This model is example 9 from the fifth edition of Model Building in Mathematical Programming by H. Paul Williams on 
+pages 263-264 and 316-317.
+
+This modeling example is at the intermediate level, where we assume that you know Python and are familiar with the 
+Gurobi Python API. In addition, you should have some knowledge about building mathematical optimization models.
+
+https://gurobi.github.io/modeling-examples/economic_planning/economic_planning.html
+
+## Download the Repository
+
+You can download the repository containing this and other examples 
+by clicking [here](https://github.com/Gurobi/modeling-examples/archive/master.zip). 
+
+## Gurobi License
+
+In order to run this Jupyter Notebook properly, you must have a Gurobi license. If you do not have one, you can request 
+an [evaluation license](https://www.gurobi.com/downloads/request-an-evaluation-license/?utm_source=3PW&utm_medium=OT&utm_campaign=WW-MU-MUI-OR-O_LEA-PR_NO-Q3_FY20_WW_JPME_Economic_Plannng_COM_EVAL_GitHub&utm_term=Economic%20Planning&utm_content=C_JPM) 
+as a *commercial user*, or download a [free license](https://www.gurobi.com/academia/academic-program-and-licenses/?utm_source=3PW&utm_medium=OT&utm_campaign=WW-MU-MUI-OR-O_LEA-PR_NO-Q3_FY20_WW_JPME_Economic_Plannng_COM_EVAL_GitHub&utm_term=Economic%20Planning&utm_content=C_JPM) as an *academic user*.
+
+Copyright © 2020 Gurobi Optimization, LLC

economic_planning/StaticModel.lp

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+\ Model StaticModel
+\ LP format - for model browsing. Use MPS format to capture full model detail.
+Minimize
+ 
+Subject To
+ static_balance[coal]: 0.9 static_prod[coal] - 0.5 static_prod[steel]
+   - 0.4 static_prod[transport] = 60
+ static_balance[steel]: - 0.1 static_prod[coal] + 0.9 static_prod[steel]
+   - 0.2 static_prod[transport] = 60
+ static_balance[transport]: - 0.2 static_prod[coal]
+   - 0.1 static_prod[steel] + 0.8 static_prod[transport] = 30
+Bounds
+End