Linear Programming - Operatinal Research - Human Resources Allocation

Description of the problem: - 50 Offices of a Company spread in country region. - 90 New employees - each location has specific numbers of tasks. - each employee can assigned a 24 tasks as max - in case one location has less than 24 tasks then the employee is allow to share more than one location to reach 24 tasks. - in case one location has more than 24 tasks then the location can has more than one employee assigned. We need to allocate these new 90 employees to the 50 Locations keeping in mind the following: 1- We need to take into consideration their location preference and their living area during the distribution of employees. 2- One of the constrains is that we need to make sure that all the employee should have Max load of work which is 24 tasks. in some locations maybe one location will have 12 tasks so we need to let that employee share two location in order to complete 24 Tasks. 3- when sharing locations we need to make sure that the employee is not assigned more than 3 locations and have not more than 24 tasks assigned. all the sharing location should be near to each other and the employee should not drive more than one hour. 4- Special cases is for the female employees, if they are expecting to have a Maternity leave which is 3 months off duty. This should be implemented in the model so that we can expect and predict the time when we will face the shortage ahead of time to cover that female location. The objective is to solve the problem by building Mathematical Linear Programming model: 1- Formulating the model with Objective function, Decision variable, and Constraints. 2- Solving the model with Excel and Gums Software. 3-Documentation - writing and explain the problem and the strategy of solving as a report. Develop a mathematical model of the problem that can be used to determine the right employee to the appropriate location based on the preferences and company needs. Also, you need to delvier the Mathematical Model with Solution + small report with a specific structure that I will provide. Time : Max two days.