Storage optimization problem: how to add new constraints to update LP variable limits based on new inputs
Alex Tian
Hello all,
I’m trying to solve an storage optimization problem using PULP in Python, where given daily prices I want to maximize the profit, say for the next year (365 days). I have defined a list of 365 variables “net_withdrawals” (positive number for withdrawals and negative if injections), and set an initial lower and upper limits in the declaration.
However, and I also have constraints defined that, the storage stock/inventory level at any time must be between 0 and maximum capacity, and so far so good. I’m having issue with adding another constraints to “futher“ limit the “net_withdrawals” variables for each day between a narrower range, based on the current stock level: e.g, withdrawal rate is halved and injection rate is doubled if the stock goes below 50% of the total capacity, and vice versa.
I can work out the current stock level, however as it is an Affine Expressions, I cannot seem to use if-else conditional statement to check his value and define the new limits for “net_withdrawals” variables. E.g.: total capacity is 1000, and I tried:
Optimization_model = pulp.LpProblem(Model - LP', pulp.LpMaximize)
periods = range(0, NUMBER_OF_DAYS)
net_withdrawals = [pulp.LpVariable("net_withdrawals_%s" % i, lowBound=-50, upBound=50) for i in periods]
For day in periods:
Stock_level -= net_withdrawals[i]
If stock_level < 500:
Optimization_model += net_withdrawals[i] < -25
Optimization_model += net_withdrawals[i] > 50
Else:
Optimization_model += net_withdrawals[i] < -50
Optimization_model += net_withdrawals[i] > 25
I’d like to add different constraints for
boundary limits based on different stock levels, e.g. 25%, 50%, 75% etc…
But I could not seem to get this basic logic
working.
Would anyone be able to suggest/advice?
I really appreciate it and thanks in advance.
Thanks.
Alex
