Project Planning and Control (PPC) problems with stochastic job processing times belong to the problem class of Stochastic Resource-Constrained Multi-Project Scheduling Problems (SRCMPSP). A practical example of this problem class is the industrial domain of customer-specific assembly of complex products. PPC approaches have to compensate stochastic influences and achieve high objective fulfillment. This paper presents an efficient simulation-based optimization approach to generate Combined Priority Rules (CPRs) for determining the next job in short-term production control. The objective is to minimize project-specific objectives such as average and standard deviation of project delay or makespan. For this, we generate project-specific CPRs and evaluate the results with the Pareto dominance concept. However, generating CPRs considering stochastic influences is computationally intensive. To tackle this problem, we developed a 2-phase algorithm by first learning the algorithm with deterministic data and by generating promising starting solutions for the more computationally intensive stochastic phase. Since a good deterministic solution does not always lead to a good stochastic solution, we introduced the parameter Initial Copy Rate (ICR) to generate an initial population of copied and randomized individuals. Evaluating this approach, we conducted various computer-based experiments. Compared to Standard Priority Rules (SPRs) used in practice, the approach shows a higher objective fulfilment. The 2-phase algorithm can reduce the computation effort and increases the efficiency of generating CPRs.

This paper presents the development and mathematical implementation of a production scheduling model utilizing mixed-integer linear programming (MILP). A simplified model of a real-world multi-product batch plant constitutes the basis. The paper shows practical extensions to the model, resulting in a digital twin of the plant. Apart from sequential arrangement, the final model contains maintenance periods, campaign planning and storage constraints to a limited extend. To tackle weak computational performance and missing model features, a condensed mathematical formulation is introduced at first. After stating that these measures do not suffice for applicability in a restrained time period, a novel solution strategy is proposed. The overall non-iterative algorithm comprises a multi-step decomposition approach, which starts with a reduced scope and incrementally complements the schedule in multiple subproblem stages. Each of those optimizations holds less decision variables and makes use of warmstart information obtained from the predecessor model. That way, a first feasible solution accelerates the subsequent improvement process. Furthermore, the optimization focus can be shifted beneficially leveraging the Gurobi solver parameters. Findings suggest that correlation may exist between certain characteristics of the scheduling scope and ideal parameter settings, which yield potential for further investigation. Another promising area for future research addresses the concurrent multi-processing of independent MILPs on a single machine. First observations indicate that significant performance gains can be achieved in some cases, though sound dependencies were not discovered yet.

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