Untitled

import pulp

# Define parameters
N = 4  # Number of instruments
P = 10  # Number of plates
M = 8  # Number of tasks
transport_time = 5  # Time for robot transport between instruments

# Define task durations for each instrument
task_durations = [
    [10, 15, 20, 25],  # Instrument 1
    [12, 18, 22, 27],  # Instrument 2
    [14, 20, 25, 30],  # Instrument 3
    [16, 22, 27, 32]   # Instrument 4
]

# Create ILP problem
prob = pulp.LpProblem("Plate_Scheduling", pulp.LpMinimize)

# Define decision variables
# Binary variable indicating whether plate p is processed on instrument n at time t
x = pulp.LpVariable.dicts("x", ((p, n, t) for p in range(1, P + 1) for n in range(N + 1) for t in range(1, M + 1)), cat='Binary')

# Define objective function: minimize total completion time
prob += pulp.lpSum(t * x[p, n, t] for p in range(1, P + 1) for n in range(1, N + 1) for t in range(1, M + 1))

# Constraints
# Each plate must be processed only once
for p in range(1, P + 1):
    prob += pulp.lpSum(x[p, n, t] for n in range(1, N + 1) for t in range(1, M + 1)) == 1

# Task precedence constraint
for p in range(1, P + 1):
    for t in range(1, M):
        prob += pulp.lpSum(x[p, n, t] for n in range(1, N + 1)) <= pulp.lpSum(x[p, n, t + 1] for n in range(1, N + 1))

# Instrument availability constraint
for t in range(1, M + 1):
    for n in range(1, N + 1):
        prob += pulp.lpSum(x[p, n, t] for p in range(1, P + 1)) <= 1

# Solve the problem
prob.solve()

# Output results
print("Optimal Schedule:")
for p in range(1, P + 1):
    for t in range(1, M + 1):
        for n in range(1, N + 1):
            if pulp.value(x[p, n, t]) == 1:
                print(f"Plate {p} on Instrument {n} at time {t}")

# Print total completion time
print("Total Completion Time:", pulp.value(prob.objective))