Multi-Item Production Planning: Theory, Computation and Practice

Production planning problems arise naturally in the context of the manufacturing companies, where decisions are to be made regarding when to produce and what to produce while considering interactions between different time periods (for example through inventories) and between different items (for example through shared machine/labor capacities). Due to its high savings potential and being such a key component of the manufacturing decision making process, production planning has been an active area of research for more than 50 years. Moreover, in the current economic climate and global competitive environment, UK manufacturing industries face the crucial choice of turning these challenges into opportunities. Although a wide body of academic and practical research is devoted to the topic, realistic industrial problems remain very challenging even with the tremendous advancements in the computer technologies, and therefore novel approaches are needed to maximize the potential benefits attainable.

Mathematical models are instrumental to study production planning problems, where decisions and limitations of the real system can be represented by a mathematical system of variables and equations. Although a significant proportion of the previous research was devoted to mathematical studies and attained important results, almost all of these previous studies are focused on non-realistic and simplistic problems. The first part of this project aims to address this gap, developing novel mathematical theory for subproblems present in realistic problems.

Recent computational technologies such as highly parallel computer infrastructures and GPU computing present immense opportunities for tackling problems that could not be attempted before. Moreover, such technologies are becoming available to the general public including small companies much faster and cheaper than in the past. Therefore, the second part of this project aims to develop computational models (based on the theoretical results of the previous part) appropriate for such infrastructures and test these extensively for various production planning problems, including some obtained from the industry.

Finally, the project will address specific production planning issues of the food and drink industry, which is the largest manufacturing sector in the UK with over 500,000 people employed. Identified as a key growth sector in Scotland by the "Government Economic Strategy", food and drink industry has been able to maintain the growth of exports even in the challenging economic climate, and has significant growth potential due to emerging markets. Production planning in this important industry has been neglected in the past, and this project will address this by working with an industrial partner in this area, developing customized tools for their challenges with the help of the theoretical and computational results of the previous parts.

The project has two main direct beneficiaries, who are the two industrial partners of the project. The impact on both of these beneficiaries will be primarily economic, as discussed in detail individually next. The plan for facilitation of the impact to each of these industrial partners is discussed in detail in the 'Pathways to Impact' document.

The first industrial partner, a dairy farmer co-operative in the UK, has been facing various issues in their production planning. This project will address these issues by academic expertise applied first-hand, where the project will improve the practice of production planning in the partner company. Ultimately, the final product to be used by the industrial partner is a customized software package developed with the knowledge obtained from this project and taking into account all the observations made in the production facilities, which will have a significant impact to the partner's operations in the coming years and increase its competitiveness with higher efficiencies in the production.

The second industrial partner, a production planning and scheduling software company in the UK, aims to protect its leader position by following the latest technologies and having a major release every year. To support this aim, this project will expose the latest mathematical and computational research to the partner, where all the key deliverables will be shared directly with the company. This will impact significantly the next generation software designed by the industrial partner and this early exposition will provide them an invaluable competitive edge.

In addition to these direct beneficiaries, other UK companies with production planning needs, in particular in food and drink, are seen as longer term and indirect beneficiaries of this project. As discussed in detail in the 'Pathways to Impact' document, various events such as workshops and training courses will be used to reach out to these beneficiaries, so that economic benefits can be realized with first-hand access to the knowledge generated through this project.

Finally, it is also worth noting that the project will impact the staff working in this project significantly, in particular the PDRA, giving them crucial personal development opportunities. These benefits include various technical and generic skills/experience, in particular various mathematical skills, computational skills such as HPC usage and software development experience, and access to real-world problems and industrial perspectives. This is a long-term impact indispensable to their future careers.