Mathematical programming is a powerful tool for supply chain management and production planning. It can also be used for job shop scheduling, next to other popular application domains such as network design and pricing. Application of mathematical programming to job shop scheduling can have major positive impact on a business but you should be aware of job shop scheduling challenges that might pop up along the way.
On SCDA we have e.g. demonstrated examples applying mathematical optimization to distribution network design, optimal distribution flow, and worker scheduling. E.g. read the following articles published by us in the past:
- Link: Prescriptive analytics for network design
- Link: Scheduling with Google OR Tools
- Link: Price and inventory optimization
- Link: Constraint programming with Google ortools
Job shop scheduling is another field that can benefit from mathematical optimization and constraint programming. The potential savings and improvements from a business point of view are huge. But there are major obstacles for successful commercial application of mathematical programming for job shop scheduling. Here are five major challenges that I have had to deal with in the past.
Complexity of model definition and computation
Production job scheduling problems can be extremely complex, with large numbers of variables and constraints. This can make it difficult to formulate an optimization problem that can be solved efficiently.
Dynamic constraints and conditions
Production job scheduling problems are often dynamic, with new jobs and changing constraints being introduced over time. This makes it challenging to develop a mathematical model that can adapt to changing conditions.
Imperfect quality of available data
To apply mathematical optimization to production job scheduling, a significant amount of data is required, including information about job requirements, machine capabilities, and scheduling constraints. Obtaining and maintaining this data can be difficult and time-consuming.
Enormous variety of capacity constraints
Production job scheduling often involves a large number of limited resources, such as machines, personnel, and materials. These resource constraints can make it challenging to develop an optimization model that can produce realistic schedules.
Cost of implementation
Implementing a mathematical optimization solution for production job scheduling can be costly and require significant technical expertise. Many companies may not have the resources or expertise to develop and implement such a solution.
Job shop scheduling challenges and simulation
Simulation can be a useful tool for overcoming some of the challenges associated with mathematical optimization in production job scheduling. There are 6 important simulation methods that supply chain managers and production planners should be aware of. I illustrated them in below figure:
Simulation methods can be combined (hybrid approach / multi-method approach), and they each have their strengths and weaknesses. Read more about the 6 important simulation methods here:
By simulating different scenarios, it is possible to gain insight into the impact of different scheduling decisions and identify potential problems before implementing changes in the real production environment. Simulation can be particularly useful in addressing dynamic nature, data availability, and resource constraints.
Moreover, simulation can be used to test and refine mathematical optimization models. By using simulation to test and refine the optimization model, it is possible to ensure that it is both accurate and effective in real-world conditions.
However, simulation also has its own set of challenges. For example, it requires significant technical expertise and computational resources to create an accurate simulation model. Additionally, simulation may not be able to capture all of the complexities and nuances of real-world production environments. Therefore, simulation should be used in conjunction with other tools, such as mathematical optimization, to achieve the best results in production job scheduling.
If you want to learn more about simulation and mathematical programming you can should read the following SCDA publications:
- Link: A webshop for simulation developers
- Link: Simulation-based capacity planning
- Link: Optimized SCM capacity scheduling
- Link: Open-cast mine simulation for better planning
- Link: Visual Components financial KPI simulation
- Link: Excellent job shop scheduling does not require fancy tools
Data scientist focusing on simulation, optimization and modeling in R, SQL, VBA and Python
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