Community

Hello, I'm trying to optimize a model I have created. Unfortunately I can only specify one function to optimize (minimize/maximize). However my model requires a number of parameters optimized and I'm struggling with how to define the optimization function. My process model involves a number of different processing "units" linked in a chain. The items move from one end of the process through these units. They are not all linked so different items can take different paths based on a probability. Each processing unit requires a number of different resources and takes a certain amount of time to complete. If there are insufficient resources when an item arrives at a unit it will queue up. What I need to find is the minimum number of resources required that has queues at a minimum whilst keeping throughput at a maximum. If my optimization function is "minimize queue lengths" then the optimizer will stop when it finds a configuration that has small queue lengths, but the resource numbers might be huge. If I use "minimize resource quantities" then obviously it will say zero resources is the best. So I have to combine minimize queue lengths with minimize resource quantities with maximize throughput. I'm assuming this will entail creating a function that takes queue length, resource quantity and throughput and adds a weight to each of them, combines them somehow and returns a single value. Is this the best approach? Does anyone have any other suggestions? This seems like it would be a fairly common problem to solve so I thought there might be a standard solution. Thanks - Joel