Optimization is the art of conducting an operation in the most elective manner.

The per-formance measures for processes mav varv.

This variation brings forth different objectives for optimization purposes. Furthermore, real life problems entail different limitations during decision making processes which require several set of constraints to conceive feasible solutions. Even though the optimization problems are predicted to be commonly used in industries, a major field that require these practices is energy systems planning.

An energy company starts a new project to locate energy production facilities to provide electricity to a region. The project includes k districts, each of which is a possible site for facilities. The project portfolio consists of only a coal facility. The electricity generated from the facilities is distributed

directly to the districts with a specified transmission line material. Cost of such a construction depends on the length of the utilized limes. The amount of electricity that can be produced by each coal facility is stint. However, the facilities can conduct overcapacity energy production. If the overcapacity is enabled for a facility, then the production level directly increases by a specific percentile. However, enabling the overcapacity option for a facility is subject to a cost. The company made a commitment to satisfy all demand. For that purpose, they are planning to

install solar-energy panels in districts, as an alternative to the energy generated by coal facilities.

These panels do not require any transmission line as they can only serve to the districts in which they are installed. Note that the coal facilities and solar panels are mutually exclusive. In other words, a district cannot use both sources. The company is reluctant to construct solar panels as they are being told by the engineering company that they are going to be charged a maintenance cost proportional to the maximum amount of energy that solar panels serve to a single district.

As a strategic decision, the company restraints the overcapacity usage. For that purpose, in case the facilities in second and fifth districts conduct overcapacity production, then the third and fourth districts cannot utilize the overcapacity option. Moreover, company also informs you that because of logistical constraints a coal facility in the first district should supply a similar amount of energy

to the second and third districts.

The company ought to treat the districts in an equitable manner while meeting the energy demands

That is, the districts in close proximity should be served by the same type of resources (either a

coal facility or solar panels).

PartA

Write an Integer Programming model that would reveal the optimal strategy for the energy company

whose aim is to minimize the total cost of the project while satisfying the energy demand of eachdistrict.

Part B

Due to the forecasts of supply chain bottlenecks, the company wants to be prepared against

possibility that they may fail to construct unlimited amount of solar panels. That is, it may not be possible to install solar panels to a large number of districts. To be prepared for a scenario like this what type of parameter(s), decision variable(s) and/or constraint (s) should be added to the

mathematical model? How would this bottleneck effect the cost of the entire operation?

Optimization is the art of conducting an operation in the most effective manner. The performance measures for processes may vary. This variation brings forth different objectives for optimization purposes. Furthermore, real life problems entail different limitations during decision making processes which require several set of constraints to conceive feasible solutions. Even though the optimization problems are predicted to be commonly used in industries, a major field that requires these practices is energy systems planning. An energy company starts a new project to locate energy production facilities to provide electricity to a region. The project includes k districts, each of which is a possible site for facilities. The project portfolio consists of only a coal facility. The electricity generated from the facilities is distributed directly to the districts with a specified transmission line material. Cost of such a construction depends on the length of the utilized lines. The amount of electricity that can be produced by each coal facility is stint. However, the facilities can conduct overcapacity energy production. If the overcapacity is enabled for a facility, then the production level directly increases by a specific percentile. However, enabling the overcapacity option for a facility is subject to a cost. The company made a commitment to satisfy all demand. For that purpose, they are planning to install solar-energy panels in districts, as an alternative to the energy generated by coal facilities. These panels do not require any transmission line as they can only serve to the districts in which they are installed. Note that the coal facilities and solar panels are mutually exclusive. In other words, a district cannot use both sources. The company is reluctant to construct solar panels as they are being told by the engineering company that they are going to be charged a maintenance cost proportional to the maximum amount of energy that solar panels serve to a single district. As a strategic decision, the company restraints the overcapacity usage. For that purpose, in case the facilities in second and fifth districts conduct overcapacity production, then the third and fourth districts cannot utilize the overcapacity option. Moreover, company also informs you that because of logistical constraints a coal facility in the first district should supply a similar amount of energy to the second and third districts. The company ought to treat the districts in an equitable manner while meeting the energy demands. That is, the districts in close proximity should be served by the same type of resources (either a coal facility or solar panels). Write an Integer Programming model that would reveal the optimal strategy for the energy company whose aim is to minimize the total cost of the project while satisfying the energy demand of each district. Part B Due to the forecasts of supply chain bottlenecks, the company wants to be prepared against a possibility that they may fail to construct unlimited amount of solar panels. That is, it may not be possible to install solar panels to a large number of districts. To be prepared for a scenario like this what type of parameter(s), decision variable(s) and/or constraint(s) should be added to the mathematical model? How would this bottleneck effect the cost of the entire operation? Optimization is the art of conducting an operation in the most effective manner. The performance measures for processes may vary. This variation brings forth different objectives for optimization purposes. Furthermore, real life problems entail different limitations during decision making processes which require several set of constraints to conceive feasible solutions. Even though the optimization problems are predicted to be commonly used in industries, a major field that requires these practices is energy systems planning. An energy company starts a new project to locate energy production facilities to provide electricity to a region. The project includes k districts, each of which is a possible site for facilities. The project portfolio consists of only a coal facility. The electricity generated from the facilities is distributed directly to the districts with a specified transmission line material. Cost of such a construction depends on the length of the utilized lines. The amount of electricity that can be produced by each coal facility is stint. However, the facilities can conduct overcapacity energy production. If the overcapacity is enabled for a facility, then the production level directly increases by a specific percentile. However, enabling the overcapacity option for a facility is subject to a cost. The company made a commitment to satisfy all demand. For that purpose, they are planning to install solar-energy panels in districts, as an alternative to the energy generated by coal facilities. These panels do not require any transmission line as they can only serve to the districts in which they are installed. Note that the coal facilities and solar panels are mutually exclusive. In other words, a district cannot use both sources. The company is reluctant to construct solar panels as they are being told by the engineering company that they are going to be charged a maintenance cost proportional to the maximum amount of energy that solar panels serve to a single district. As a strategic decision, the company restraints the overcapacity usage. For that purpose, in case the facilities in second and fifth districts conduct overcapacity production, then the third and fourth districts cannot utilize the overcapacity option. Moreover, company also informs you that because of logistical constraints a coal facility in the first district should supply a similar amount of energy to the second and third districts. The company ought to treat the districts in an equitable manner while meeting the energy demands. That is, the districts in close proximity should be served by the same type of resources (either a coal facility or solar panels). Write an Integer Programming model that would reveal the optimal strategy for the energy company whose aim is to minimize the total cost of the project while satisfying the energy demand of each district. Part B Due to the forecasts of supply chain bottlenecks, the company wants to be prepared against a possibility that they may fail to construct unlimited amount of solar panels. That is, it may not be possible to install solar panels to a large number of districts. To be prepared for a scenario like this what type of parameter(s), decision variable(s) and/or constraint(s) should be added to the mathematical model? How would this bottleneck effect the cost of the entire operation