eThesis - School of Business electronic theses

The objective of this thesis is to add to the research in the field of production planning under uncertainty by extending a model from the existing literature addressing the stochastic capacitated lot-sizing and scheduling problem of a flow shop production system under uncertain demand and uncertain processing times. Furthermore, a calculation study is undertaken to gain useful insights for the application of the model.

The thesis is based on the model formulation of Ramezanian and Saidi-Mehrabad (Appl. Math. Model. 37 (2013) 5134-5147). They propose a stochastic model and transfer it into a deterministic one deploying chance constraint programming. In this thesis, their mathematical model formulation is extended to account for the usage of a service level restriction, additional uncertain parameters (setup times and capacities) and setup carry-over. These extensions, as well as four valid inequalities are then tested in a calculation study solving several artificial test instances for different model and parameter settings in IBM's ILOG CPLEX Optimization Studio.

The study reveals the strong influence of the characteristics of uncertain demand on total costs. In case demand, processing times and setup times are uncertain, only the distribution of and variation in demand influenced the resulting total costs noticeably. Moreover, the study shows that the total costs increase non-linearly with increasing safety level. Starting from a certain threshold (safety level of approximately 95%) increasing the safety level becomes disproportionally expensive. The effects increase with increasing problem size. Furthermore, the proposed valid inequalities do not lead to verifiable decreases in calculation times. Application possibilities of the model in practice are limited due to the large computation time requirements for small problem sizes already. Hence, future research should focus on developing efficient heuristic solution algorithms. Testing with real life instances is also necessary. Moreover, including other service level measures instead of a cyclic alpha service level and taking additional uncertainties (uncertain durability, material availability, costs, and input and output quantity and quality) into account are possibilities for future research.