Master production scheduling under uncertainty with controllable processing times

Abstract

Master Production Schedules (MPS) are widely used in industry especially within Enterprise Resource Planning (ERP) Software. MPS assumes infinite capacity, fixed processing times and a single scenario for demand forecasts. In this thesis, we questioned these assumptions and considered a problem with finite capacity, controllable processing times and finally and most importantly, several demand scenarios instead of just one. We used a multi-stage stochastic programming approach in order to come up with maximum expected profit given the demand scenarios. We used controllable processing times, which are feasible in most of the scheduling practice in industry, to achieve a flexibility in capacity usage. We provided a non-linear mixed integer programming formulation for our problem. Afterwards, we analyzed two sub-problems to simplify the structure of the objective function and suggested alternative linearizations. We considered easier cases of our problem, proposed sufficient conditions for optimality and established the computational complexity status for two special cases. We conducted three experiments, to test computational performance of the formulations, to analyze the profit performance of the multi-stage solutions and finally, to analyze the effect of controllability on profit. Our computational studies show that one of the proposed formulations solves large instances in a very small amount of time. The second experiment suggests that the performance of multi-stage solutions is significantly better than the one of solutions obtained using single scenario strategies in terms of relative regret. Finally, the third experiment shows that controllability significantly increases the performance of multi-stage solutions.