I am working on a problem where I have an energy storage tank that can store up to 200 hours of energy. I also have the hourly electricity price data for an entire year, known in advance. My goal is to develop an algorithm in MATLAB/Python that determines the optimal charging and discharging schedule to maximize profit (revenue from selling minus cost of buying).

Here are the key details and assumptions:

• The tank can start in any initial state (empty, full, or partially full). If it starts with some charge, that initial charge is considered to have zero cost.
• Each unit of energy in the tank carries the price at which it was purchased.
• The tank capacity is limited to 200 units. I cannot exceed this limit when charging, and I cannot discharge when the tank is empty.
• When buying electricity (charging), the efficiency is 100%, so the full amount purchased goes into the tank at the given price.
• When selling electricity (discharging), I can only recover 60% of what is discharged as salable electricity (i.e., there is a 60% efficiency when selling energy from the tank).

I would like to know how to model and implement an algorithm in MATLAB/Python to solve this optimization problem. Any guidance on the approach—such as how to formulate it as a linear/integer programming problem or how to use MATLAB/Python’s optimization functions—would be greatly appreciated.

I expected to be able to map the problem onto a well-defined optimization model and then rely on solver capabilities to handle the complexity, rather than writing an exhaustive or heuristic search from scratch.

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