Design and control of stochastic manufacturing systems

Diefenbach, Johannes

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URN: urn:nbn:de:bsz:180-madoc-634131
Document Type: Doctoral dissertation
Year of publication: 2022
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Stolletz, Raik
Publication language: English
Institution: Business School > ABWL u. Produktion (Stolletz 2010-)
Subject: 330 Economics
Keywords (English): assembly line balancing , operations research , newsvendor
Abstract: Many manufacturing systems are subject to uncertainty, which can be described using stochastic processes. These processes might be stable or change with the production quantity. This dissertation analyzes the design and control of such stochastic manufacturing systems. The first article investigates the balancing of an assembly line with stochastic task times and a constraint on the line reliability. We provide a sampling-based model formulation for generally distributed task times. We prove that any lower bound on the number of stations for the related deterministic problem can be transformed into a lower bound for this sampling formulation. We apply these bounds in a reliability-based branch-and-bound algorithm and show that they substantially reduce the required computation time. The second article analyzes the impact of the used sampling method and the sample size on the resulting performance measures and optimal decision by considering the performance evaluation of an M/D/1 queueing system and the optimization of an M/M/c staffing level numerically. The article suggests that managers should be aware that the distribution of the resulting performance measures or optimal solution derived from a sampling-based approach may not be symmetrical and that the chosen sampling method may have an impact on this behavior. The third article investigates the ramp-up of a new product or machine with stochastic and non-stationary yield. We formalize the problem as a Newsvendor problem and prove that any positive optimal ramp-up quantity will always be at least the demand. Furthermore, we characterize the optimal ramp-up quantity for the special case of stationary yield by a critical fractile. The optimal ramp-up quantity tends to be decreasing in the expected yield. However, a numerical analysis shows that an increase in the expected yield can lead to a higher optimal production quantity at first, before the production quantity decreases. There is a gap in the literature for each of the considered optimization problems under the considered assumptions. Future research could integrate the design and control decisions considered in this dissertation into a single optimization model.

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