"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 extensively studied mathematical properties of some challenging production planning problems, and established novel theory that has also the potential to expand to some other common mathematical models that address industrial problems. These theoretical results are also successfully implemented in various computational frameworks in order to maximize potential practical use.
The award objectives were generally met (and indeed gone beyond the objectives for the theoretical part, where some surprising results are still leading us to further analysis and results)"