I am looking for some optimization algorithm suggestion on resource allocation. Preferably in Python.

I have a given number of total resources, and I have to conduct a certain number of Experiments with these resources. Each experiment takes a given set of days, and different number of resources.

Seeking for ways of attacking this optimization algorithms, where the output is an optimized way of assigning the resources to each Experiment, so the total time to do the experiments does not go over a max limit.

If it is three to four, I should have written on a sheet of paper and replicated in a code. But with total Experiments greater than 50, I am struggling to come up with an algorithm. I am Ok, if you just share an article, that you believe would work for this problem.

I am presently using linprog but getting a constraint error, which I am not able to figure out.

import pandas as pd
from scipy.optimize import linprog

# # Define experiment data
# data = {
#     "Experiment": ["Experiment A", "Experiment B", "Experiment C", "Experiment D"],
#     "Unit A Required": [10, 20, 15, 10],
#     "Unit B Required": [5, 10, 10, 5],
#     "Days": [5, 3, 7, 2]
# }#
# # Create a DataFrame
# df = pd.DataFrame(data)

df = pd.read_excel('Book3.xlsx')

# Define total available units of each type
total_brazos = 11
total_z2_rack = 3

# Objective function: Minimize the total days
objective = df["Working Days"].tolist()

# Constraints: Allocated units must not exceed available units of Unit A and Unit B
constraints = [
    {"type": "eq", "fun": lambda x: sum(x[:len(df)]) - total_brazos},  # Total allocated Unit A
    {"type": "eq", "fun": lambda x: sum(x[len(df):]) - total_z2_rack}   # Total allocated Unit B
]

# Combine bounds for Unit A and Unit B allocations
bounds_a = [(0, unit) for unit in df["Brazos Req"]]
bounds_b = [(0, unit) for unit in df["Z2 Rack Req"]]
bounds = bounds_a + bounds_b

# Solve the optimization problem
result = linprog(
    c=objective,  # Coefficients in the objective function
    bounds=bounds,  # Allocation bounds
    constraints = constraints,  # Constraints
    method='highs'  # Use the HiGHS solver
)

# Display the results
if result.success:
    allocated_brazos = result.x[:len(df)]
    allocated_z2_rack = result.x[len(df):]
    df["Brazos Allocated"] = allocated_brazos
    df["Z2 Rack Allocated"] = allocated_z2_rack
    df["Used Days"] = df["Brazos Allocated"] * df["Working Days"] / df["Brazos Req"]
    print("Optimized Allocation:")
    print(df)
    print(f"Total Days Used: {sum(df['Used Days'])}")
else:
    print("Optimization failed!")

Excel used above