I would like to get insights into methods that could be employed for tackling Maximization Problems that involve multiple constraints. One example would be the optimal usage of elevators in a building. Say, if the Power consumed by the elevator and Customer Dissatisfaction were two factors, and the Efficiency Index would be something like -
Assuming that there are a said number of floors and elevators, and with each of these elevators at a particular floor, and people waiting at different floors having different destinations; and we have the factors like Energy Consumption depending on factors like opening/closing of Elevator door or its movement across floors; and the customer dissatisfaction depending on factors like a customer getting serviced, wait time for boarding, halt at a non-destination, what would be the best way to break down these kind of problems??? The motive is to maximize the Efficiency Index.
E.I = 1/(P.C + C.D)
E.I = Efficiency Index
P.C = Power Consumed
C.D = Customer Dissatisfaction
Do these kind of problems fall into a particular category? Would appreciate any reference related to mathematical modeling of various real-world problems.