Schedule Optimization with Python

Schedule optimization maximizes productivity, minimizes costs and reduces delays. It is widely used in manufacturing, logistics, transportation, construction, project management, and healthcare. By optimizing schedules, organizations can allocate resources effectively, improve delivery times, and meet customer demands efficiently, leading to increased competitiveness and profitability.
🎓Schedule Optimization apmonitor.com/...
Manufacturing facilities employ expert schedulers and tools to help visualize and plan for production cycles, scheduled downtime, transitions, etc. This example is a comparison of three methods for scheduling problems:
1. Exhaustive search
2. Heuristic (Johnson's Rule)
3. Integer Programming
Objective: Minimize the delay for the production of 5 products on 2 machines. Each product requires a different amount of time to process for each step. The example demonstrates Gekko for solving scheduling problems and compares to exhaustive search and heuristic method.
There are 5 products that require 2 processing steps on separate machines. The two machines (machine Y and machine Z) work one after the other. A product must go through machine Y first and after that through machine Z. Both machines can work simultaneously, but each machine cannot work on more than 1 product at a time. The factory needs to minimize the time of production of all given products. This is equivalent to minimizing the idle time of machine Z.
Product P0 P1 P2 P3 P4
Machine Y: 10 20 15 40 8
Machine Z: 20 30 10 25 18

[@codingspace1143]

Thanks for very useful video

[@hassanlaqrabti4036]

Thank you professor

[@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.

[@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.

[@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

[@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].

[@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