The director of the projects department needs to assign 5 projects from a company's portfolio between...

 

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The director of the projects department needs to assign 5 projects from a company's portfolio between the 3 project managers in the department. Each project manager i has a quota q; of the number of projects s/he can oversee. For each project j the director has determined, based on expertise and experiences of each project manager, a sets, of project managers that can be assigned to oversee that project. The director wishes to determine an assignment of projects to project managers that will not exceed their quotas, while ensuring that every project is overseen by a manager from its set S;. Table 3 on the next page indicates each project manager's quota in the second column and in the remaining columns a '1' identifies projects that can be assigned to each project manager ('0' identifies those that can't be assigned). Project Manager 1 2 Table 3: Data for Q6(b) Quota 3 2 1 3 Project Number 2 3 4 5 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 i. Formulate a Binary Integer Programming model for this problem and give detailed justifications for the variables & constants, constraints and objective function of the model. (12 Marks) ii. If a feasible solution to the problem was not possible given the memberships of the sets Sj, which constraint/s of the BIP model could be changed so that the director could find an assignment that maximised the number of projects assigned a project manager. Provide the new constraint/s with justification/s. (3 Marks) The director of the projects department needs to assign 5 projects from a company's portfolio between the 3 project managers in the department. Each project manager i has a quota q; of the number of projects s/he can oversee. For each project j the director has determined, based on expertise and experiences of each project manager, a sets, of project managers that can be assigned to oversee that project. The director wishes to determine an assignment of projects to project managers that will not exceed their quotas, while ensuring that every project is overseen by a manager from its set S;. Table 3 on the next page indicates each project manager's quota in the second column and in the remaining columns a '1' identifies projects that can be assigned to each project manager ('0' identifies those that can't be assigned). Project Manager 1 2 Table 3: Data for Q6(b) Quota 3 2 1 3 Project Number 2 3 4 5 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 i. Formulate a Binary Integer Programming model for this problem and give detailed justifications for the variables & constants, constraints and objective function of the model. (12 Marks) ii. If a feasible solution to the problem was not possible given the memberships of the sets Sj, which constraint/s of the BIP model could be changed so that the director could find an assignment that maximised the number of projects assigned a project manager. Provide the new constraint/s with justification/s. (3 Marks)

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i Formulate a Binary Integer Programming model for this problem and give detailed justifications for the variables constants constraints and objective function of the model Let xij be a binary decisio... View the full answer