Optimization Models and Algorithms for Complex Production Planning Problems

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In order to satisfy their customers' demand on time and at the lowest cost, manufacturing companies must carefully plan their production activities in advance. Decisions have to be taken related to the production quantities and the timing. This is a complex task because of the many inherent trade-offs and constraints that must be taken into account and efficient production planning tools are therefore important in order to create a competitive advantage. My research will focus on mathematical optimization models and algorithms which help to capture these trade-offs while taking into account the many constraints in the production environment in order to obtain high-quality production plans within a reasonable amount of time. Many challenges remain. First, the production environment is becoming more and more complex and this needs to be captured in detail in the mathematical models. If this is not properly done, production is likely to become more costly than anticipated. Second, most production processes consist of several steps, where the output of one step becomes the input for the next step. The planning hence must be done for several levels simultaneously. Third, in a supply chain, the procurement of components, production and distribution are sequential activities. By coordinating these activities, global efficiencies can be achieved. The planning of these interrelated production and transportation activities, however, also becomes more complex. Finally, in most environments, uncertainty is an important factor that needs to be taken into account. Uncertainty typically relates to the demand uncertainty, but also supply uncertainty is an important issue in production planning. The main objective of my research program is to develop Mixed Integer Programming based models and exact and heuristic optimization approaches for production planning problems in which the core issue is to satisfy demand for several products. The detailed objectives directly relate to the four challenges. The individual projects within the research program will focus on a specific issue within each of the four broad challenges described. First, we will consider a production environment with separate capacity-restricted areas for stocking products. In addition to the traditional production decisions, inventory also has to be assigned to specific stocking areas. Secondly, we will consider a production system in which standard items (e.g. steel beams) have to be produced, which are next cut into customized pieces and finally assembled into final products. This leads to a combined lot sizing and cutting stock problem with three levels. Thirdly, we consider an assembly production system in which components have to be transported between facilities. Finally, we consider a production problem in which the procurement level of components has to be decided as well as the production levels for the final products when there is both demand and supply uncertainty.