I am trying to solve a Capacitated Facility Location Problem (CFLP) with a dynamic setup cost in
The problem statement is this:
- I have the transport cost
- The fixed operating cost (manual labor and other expenses) is known
- I know the dropping points with loads and all the details
- The per square ft. cost of rent of a place is known
- The size of the Facility will be a function of the load. So the rent will depend on how much load is getting allocated in that place.
Assuming the rent will vary like this:
rent= rent_per_square_ft * load* 0.10
Now, I have accommodated the first 4 conditions in my code. But I am not sure how the number 5 can be accommodated.
My model looks like this in
R(if it can be of any help):
#m is the number of potential facility/service center (SC) locations #n is the number of customer locations model <- MIPModel() %>% # 1 if customer i gets assigned to SC j add_variable(x[i, j], i = 1:n, j = 1:m, type = "binary") %>% # 1 if SC j is built add_variable(y[j], j = 1:m, type = "binary") %>% # Objective function set_objective(sum_expr(transportcost(i, j) * x[i, j], i = 1:n, j = 1:m) + sum_expr(fixedcost[j] * y[j], j = 1:m), "min") %>% # Every customer needs to be assigned to a SC add_constraint(sum_expr(x[i, j], j = 1:m) == 1, i = 1:n) %>% # If a customer is assigned to a SC, then the SC must be built add_constraint(x[i,j] <= y[j], i = 1:n, j = 1:m) %>% #The demand of customers shouldn't exceed SC capacities add_constraint(sum_expr(demand[i] * x[i, j], i = 1:n) <= capacity[j] * y[j], j = 1:m)
I am looking for any headway. Even any link to a relevant article might help.