objective 2 :

N_1=24

N_2=17

N_3=6

Objective-3: Delaying In order to reduce the travel time and provide enough time to detect the vines, IPEC would like you to identify the roads that should be enlarged such that the shonest put to reach Airport from Mintaq-5 is prolonged or maximized Roads cannot be physically enlargod, so the idea is 1) to place barcades on the road to reduce the trad e 2) to completely shut down some of the roads for public age Let us say the trave time in minutes from city to city fist. From the past experiences, IPEC citimates that it will take soy per day per barricade to increase the travel time by sy mis on a given road. Furthermore, multiple barricades can be placed on a road. For example, spending $2cy on a road will result in barricades, which will increase the wolvesime on that road by 25 mins. That is, the travel time from Cato Ciny by building two barricades will be ty + 26 minutes "There is no actual cost in shutting down a road. However, it may create a panic and liness among the public. Thus, all the roads cannot be shut down from the airport in a given day. It is cstimated that closing most number of roads in a dus will be mitigate the panic among the public. Your tasks are as follows (3a) A toy example is given in the following figure, and the coresponding data is given in the excel workbook named Data on the shorted Q3. From the toy cumple, study the mechanics of the problem. Specifically, identify the infcsible and the best scenamos. 00 Figen Type de 5 des del 3b) From the experience obtained from the camp, bu da geral mathematical model that will maximize the shortest path from Mintaqa 5 l = 5) to the airport (i = 1). Use the following main indices and parameters in the model ne: the total number of nades (including cities and airport 1.): the indices used for the cities, j = 1.... Qys is equal to 1 if there is an arc from city to city, and others y travel time in minutes from city it without a barricades & additional travel time in minutes per barcade on the road from city to city A: maximum number of roads that can be shut down in a day You are allowed to use additional items like in s anlar p r . Clearly define the additional items, and link them appropriately before using them in the model. The model type can be MIP, NLP or MINIP. (3) Implement the mathematical model in GAMS Software of your choice). No need to solve the model. H ve, you must be able to come theme to check for any errors. Use the data given in the excel workbook named Data on the sheet titled Q3c. Objective-3: Delaying In order to reduce the travel time and provide enough time to detect the virus, IPEC would like you to identify the roads that should be enlarged such that the shortest path to reach Airport from Mintaqa-5 is prolonged or maximized. Roads cannot be physically enlarged, so the idea is: 1) to place barricades on the road to reduce the travel time 2) to completely shut down some of the roads for public usage Let us say the travel time in minutes from city i to city jis tij. From the past experiences, IPEC estimates that it will take SC per day per barricade to increase the travel time by 8 mins on a given road. Furthermore, multiple barricades can be placed on a road. For example, spending $2cy on a road will result in two barricades, which will increase the total travel time on that road by 28t, mins. That is, the travel time from City to City by building two barricades will be ty + 28 minutes. There is no actual cost in shutting down a road. However, it may create a panic and unruliness among the public. Thus, all the roads cannot be shut down from Mintaqa-5 to the airport in a given day. It is estimated that closing at most A number of roads in a day will be enough to mitigate the panic among the public. Your tasks are as follows: (3a) A toy example is given in the following figure, and the corresponding data is given in the excel workbook named Data-xx. xlsx on the sheet titled Q3a. From the toy example, study the mechanics of the problem. Specifically, identify the infeasible and the best scenarios. Figure: Tay example where morement from Node-5 to Node-1 is delayed. 3b) From the experience obtained from the toy example, build a general mathematical model that will maximize the shortest path from Mintaqa-5 (i = 5) to the airport (i = 1). Use the following main indices and parameters in the model: n: the total number of nodes (including cities and airport). 1.): the indices used for the cities, 1.j = 1..., n. (3a) A toy example is given in the following figure, and the corresponding data is given in the excel workbook named Data-xx. xlsx on the sheet titled Q3a. From the toy example, study the mechanics of the problem. Specifically, identify the infeasible and the best scenarios. Figure: Toy example were morement from Node-5 to Node-1 is delayed. 3b) From the experience obtained from the toy example, build a general mathematical model that will maximize the shortest path from Mintaqa-5 (i = 5) to the airport (i = 1). Use the following main indices and parameters in the model: n: the total number of nodes (including cities and airport). 1.): the indices used for the cities, 4.j = 1, ..., n. Qupd is equal to 1 if there is an arc from city i to city), and otherwise 0. tij: travel time in minutes from city i to city, without any barricades. By: additional travel time in minutes per barricade on the road from city i to city j. A: maximum number of roads that can be shut down in a day. You are allowed to use additional items like: indices, nariables and/or parameters. Clearly define the additional items, and link them appropriately, before using them in the model. The model type can be MIP, NLP or MINLP. (30) Implement the mathematical model in GAMS (or any software of your cho to solve the model. However, you must be able to compile the model to check for any syntax crrors. Use the data given in the excel workbook named Data-xx. xlsx, on the sheet titled Q3c. Objective-3: Delaying In order to reduce the travel time and provide enough time to detect the vines, IPEC would like you to identify the roads that should be enlarged such that the shonest put to reach Airport from Mintaq-5 is prolonged or maximized Roads cannot be physically enlargod, so the idea is 1) to place barcades on the road to reduce the trad e 2) to completely shut down some of the roads for public age Let us say the trave time in minutes from city to city fist. From the past experiences, IPEC citimates that it will take soy per day per barricade to increase the travel time by sy mis on a given road. Furthermore, multiple barricades can be placed on a road. For example, spending $2cy on a road will result in barricades, which will increase the wolvesime on that road by 25 mins. That is, the travel time from Cato Ciny by building two barricades will be ty + 26 minutes "There is no actual cost in shutting down a road. However, it may create a panic and liness among the public. Thus, all the roads cannot be shut down from the airport in a given day. It is cstimated that closing most number of roads in a dus will be mitigate the panic among the public. Your tasks are as follows (3a) A toy example is given in the following figure, and the coresponding data is given in the excel workbook named Data on the shorted Q3. From the toy cumple, study the mechanics of the problem. Specifically, identify the infcsible and the best scenamos. 00 Figen Type de 5 des del 3b) From the experience obtained from the camp, bu da geral mathematical model that will maximize the shortest path from Mintaqa 5 l = 5) to the airport (i = 1). Use the following main indices and parameters in the model ne: the total number of nades (including cities and airport 1.): the indices used for the cities, j = 1.... Qys is equal to 1 if there is an arc from city to city, and others y travel time in minutes from city it without a barricades & additional travel time in minutes per barcade on the road from city to city A: maximum number of roads that can be shut down in a day You are allowed to use additional items like in s anlar p r . Clearly define the additional items, and link them appropriately before using them in the model. The model type can be MIP, NLP or MINIP. (3) Implement the mathematical model in GAMS Software of your choice). No need to solve the model. H ve, you must be able to come theme to check for any errors. Use the data given in the excel workbook named Data on the sheet titled Q3c. Objective-3: Delaying In order to reduce the travel time and provide enough time to detect the virus, IPEC would like you to identify the roads that should be enlarged such that the shortest path to reach Airport from Mintaqa-5 is prolonged or maximized. Roads cannot be physically enlarged, so the idea is: 1) to place barricades on the road to reduce the travel time 2) to completely shut down some of the roads for public usage Let us say the travel time in minutes from city i to city jis tij. From the past experiences, IPEC estimates that it will take SC per day per barricade to increase the travel time by 8 mins on a given road. Furthermore, multiple barricades can be placed on a road. For example, spending $2cy on a road will result in two barricades, which will increase the total travel time on that road by 28t, mins. That is, the travel time from City to City by building two barricades will be ty + 28 minutes. There is no actual cost in shutting down a road. However, it may create a panic and unruliness among the public. Thus, all the roads cannot be shut down from Mintaqa-5 to the airport in a given day. It is estimated that closing at most A number of roads in a day will be enough to mitigate the panic among the public. Your tasks are as follows: (3a) A toy example is given in the following figure, and the corresponding data is given in the excel workbook named Data-xx. xlsx on the sheet titled Q3a. From the toy example, study the mechanics of the problem. Specifically, identify the infeasible and the best scenarios. Figure: Tay example where morement from Node-5 to Node-1 is delayed. 3b) From the experience obtained from the toy example, build a general mathematical model that will maximize the shortest path from Mintaqa-5 (i = 5) to the airport (i = 1). Use the following main indices and parameters in the model: n: the total number of nodes (including cities and airport). 1.): the indices used for the cities, 1.j = 1..., n. (3a) A toy example is given in the following figure, and the corresponding data is given in the excel workbook named Data-xx. xlsx on the sheet titled Q3a. From the toy example, study the mechanics of the problem. Specifically, identify the infeasible and the best scenarios. Figure: Toy example were morement from Node-5 to Node-1 is delayed. 3b) From the experience obtained from the toy example, build a general mathematical model that will maximize the shortest path from Mintaqa-5 (i = 5) to the airport (i = 1). Use the following main indices and parameters in the model: n: the total number of nodes (including cities and airport). 1.): the indices used for the cities, 4.j = 1, ..., n. Qupd is equal to 1 if there is an arc from city i to city), and otherwise 0. tij: travel time in minutes from city i to city, without any barricades. By: additional travel time in minutes per barricade on the road from city i to city j. A: maximum number of roads that can be shut down in a day. You are allowed to use additional items like: indices, nariables and/or parameters. Clearly define the additional items, and link them appropriately, before using them in the model. The model type can be MIP, NLP or MINLP. (30) Implement the mathematical model in GAMS (or any software of your cho to solve the model. However, you must be able to compile the model to check for any syntax crrors. Use the data given in the excel workbook named Data-xx. xlsx, on the sheet titled Q3c