Schedule Optimization with Python

[@JosephReynolds-o4j]

let's say you don't have fixed number of machines, and you're trying to determine the optimal number of machines to run based on demand

[@apm]

We've been researching topics related to design (number or size of machines) and schedule optimization. Here are a few papers (among many with this current topic): Hill, D., McCrea, D., Ho, A., Memmott, M., Powell, K., Hedengren, J., A Multi-Scale method for combined design and dispatch optimization of nuclear hybrid energy systems including storage, e-Prime - Advances in Electrical Engineering, Electronics and Energy, Volume 5, 2023, 100201, ISSN 2772-6711, DOI: 10.1016/j.prime.2023.100201 Mojica, J.L., Petersen, D.J., Hansen, B., Powell, K.M., Hedengren, J.D., Optimal Combined Long-Term Facility Design and Short-Term Operational Strategy for CHP Capacity Investments, Energy, Vol 118, 1, pp. 97-115, January 2017, DOI: 10.1016/j.energy.2016.12.009. I recommend that you also look at work by Ignacio Grossmann at CMU and Christos Maravelias at Princeton for additional contributions to combined scheduling and design optimization.

[@muhammadluthfi6887]

Thanks for the very insightful video. Im currently on the project of scheduling optimization of blending processes in refinery. is there any learn it further about it from the expert?

[@apm]

There is more information in these courses: apmonitor.com/me575 and apmonitor.com/do

[@xondiego]

Thanks for this video, a question is APMonitor and Gekko open source? let say if I work for a consultant and I want to use Gekko can I use it for free? otherwise how is the process for using gekko and APMonitor tools for optimization?

[@apm]

Yes, Gekko is freely available. The source is available from github.com/BYU-PRISM/GEKKO or install with "pip install gekko". It has the MIT License that allows any use, including commercial use.

[@codingspace1143]

Thanks for very useful video

[@evantale3191]

how should I modifies the code if I wanted to to schedule multiple task to the same type of machine that runs parallelly ? great video btw thankyou ! 😄🤝

[@apm]

Here is sample code from ChatGPT 4o: from gekko import GEKKO m = GEKKO(remote=False) # Number of tasks num_tasks = 5 # Number of parallel machines for Y and Z num_machines = 2 Y = {0: 10, 1: 20, 2: 15, 3: 40, 4: 8} Z = {0: 20, 1: 30, 2: 10, 3: 25, 4: 18} # Decision variables x = m.Array(m.Var, (num_tasks, num_tasks, num_machines), value=0, lb=0, ub=1, integer=True) # Ensure each task is assigned to exactly one time slot on any machine for i in range(num_tasks): m.Equation(m.sum([x[i, j, k] for j in range(num_tasks) for k in range(num_machines)]) == 1) m.Equation(m.sum([x[j, i, k] for j in range(num_tasks) for k in range(num_machines)]) == 1) # Time to process on Y and Z ty = m.Array(m.Var, (num_tasks, num_machines)) tz = m.Array(m.Var, (num_tasks, num_machines)) for k in range(num_machines): for i in range(num_tasks): m.Equation(ty[i, k] == m.sum([x[i, j, k] * Y[j] for j in range(num_tasks)])) m.Equation(tz[i, k] == m.sum([x[i, j, k] * Z[j] for j in range(num_tasks)])) # Delay time on Z d = m.Array(m.Var, (num_tasks, num_machines), lb=0) s = m.Array(m.Var, (num_tasks, num_machines), lb=0) for k in range(num_machines): m.Equation(d[0, k] == ty[0, k]) m.Equation(s[0, k] == 0) for i in range(1, num_tasks): m.Equation(d[i, k] >= tz[i - 1, k] - ty[i, k] + s[i, k]) # Minimize the total delay and slack m.Minimize(m.sum(d[:,k])) m.Minimize(1e-3 * m.sum(s[:,k])) # Solve the problem m.options.SOLVER = 1 m.solve() # Print the results print('Order of processing, rows=order, columns=product, depth=machine') print(x) print('Time on machine Y') print(ty) print('Time on machine Z') print(tz) print('Delay') print(d) For specific questions, please ask on StackOverflow with tag [gekko].

[@hassanlaqrabti4036]

Thank you professor

[@lazyac_]

thx does someone can help me with this?

[@apm]

Sure, the code examples are available at apmonitor.com/me575/index.php/Main/ScheduleOptimization. If you need help with a specific problem, please post your code to Stack Overflow or use ChatGPT to get help.

[@lazyac_]

Yes ChatGPT helped me! he used pulp library, i not sure about constraints he used but it works @@apm