Optimization Network Flow Models

Optimization

Network Flow Models

1. Systems Unlimited sells personal computers to universities and colleges on the East Coast and ships them from three distribution warehouses. The firm is able to supply the following numbers of computers to the universities by the beginning of the academic year: a) A network model is balanced if the total supply equals the total demand. Is this problem balanced? Explain. b) Formulate a linear program to minimize the cost of shipping as many computers as possible from the centers to the universities. Solve the model using excel solver and Which universities are left with unmet demand. c) Critique this model against the four main assumptions of linear programming. 2. Event Planner Expert(EPE) has six events scheduled for this Sunday. Employees of EPE have been divided into seven teams capable of handling these events. Information about the teams, the events, and the cost of assigning a particular team to a particular event are provided in the following table a) EPE thinks it would be best to assign teams to events using a greedy approach. For example, Team 1 would be assigned to Event B, Team 5 to Event A, etc. Continue in this manner to identify Donna’s solution. b) EPE’s CEO daughter, Pam, is an applied Physics major at Georgia Tech University. Pam thinks that optimization should be used to assign teams to events. Pam’s model minimizes total cost and her variables xij equal 1 if Team i is assigned to Event j and zero otherwise. Formulate Pam’s Model. c) Solve the model you created in part (b) using Excel Solver . Was EPE’s solution from part (a) optimal? Explain. d) Suppose Teams 2, 3, and 7 can each handle up to two events while the other teams can handle at most one. Formulate an integer linear program to find a cost minimizing solution for this modified scenario