纸浆 - LP Objective function 配方

Question

I am working on solving a set covering problem for electric vehicle charging stations. My objective is to maximize the demand covered by the radius of a charging station.

I have two variables to make up the objective function. Yij denotes the demand location i is covered by the radius of charging station j. Similarly, Xj denotes if charging station j is open.

I am looking to create an objective function such as the following: Maximize OF = ((Y11 + Y21+ Y31 +.... Yn1) * X1) + ((Y12 + Y22+ Y32 +.... Yn2) * X2) +....

I tried the following, but am running into issues:

OptModel += lpSum(((Y[i,j] for i in range (I)) * X[j]) for j in range(J))

Any idea on how to formulate this?

Answer 1

It isn't clear from your description why Y is a variable? It sounds like it should be a parameter (known value) if the demand location is within the radius of some source.... There must be some other nuance as to why this isn't known. (If it can be calculated, do it and make it a parameter and your problem is solved.)

The statement you propose is illegal because you are multiplying variables together and that makes the statement non-linear. You need to reformulate....

You have an implicit "and" condition in there in that you only want to receive credit if both Y and X are true, so you will need an additional variable or be clever in how you relate X and Y because you can't multiply them.

Why don't you just add this constraint:

Y[i, j] <= X[j]    for each j

that would essentially change the meaning of Y to "in range of an operating charger".

Also realize if you sum up all of these Y vars (or as you appear to try to do in your objective) you will get double counting of any demand that can be charged from multiple stations--not sure if that is intent or not.