Robuste und großumfängliche Netzwerkoptimierung in der Logistik

This thesis explores possibilities and limitations of extending classical combinatorial optimization problems for network flows and network design. We propose new mathematical models for logistics networks that feature commodities with multidimensional properties, e.g. their mass and volume, to capture consolidation effects of commodities with complementing properties. We provide new theoretical insights and solution methods with immediate practical impact that we test on real-world instances from the automotive, chemical, and retail industry. The first model is for tactical transportation planning with temporal consolidation effects. We propose various heuristics and prove for our instances, that most of our solutions are within a single-digit percentage of the optimum. We also study problem variants where commodities are routed unsplittably and give hardness results for various special cases and a dynamic program that finds optimal forest solutions, which overestimate real costs. The second model is for strategic route planning under uncertainty. We provide for a robust optimization method that anticipates fluctuations of demands by minimizing worst-case costs over a restricted scenario set. We show that the adversary problem is NP-hard. To still find solutions with very good worst-case cost, we derive a carefully relaxed and simplified MILP, which solves well for large instances. It can be extended to include hub decisions leading to a robust M-median hub location problem. We find a price of robustness for our instances that is moderate for scenarios using average demand values as lower bounds. Trend based scenarios show a considerable tradeoff between historical average costs and worst case costs. Another robustness concept are incremental hub chains that provide solutions for every number of hubs to operate, such that they are robust under changes of this number. A comparison of incremental solutions with M-median solutions obtained with an LP-based search suggests that a price of being incremental is low for our instances. Finally, we investigate the problem of scheduling the maintenance of edges in a network. We focus on maintaining connectivity between two nodes over time. We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and for the non-preemptive case, we show strong non-approximability results.Diese Arbeit untersucht Möglichkeiten, klassische kombinatorische Optimierungsprobleme für Netzwerkflüsse und Netzwerkdesign zu erweitern. Wir stellen neue mathematische Modelle für Logistiknetzwerke vor, die mehrdimensionale Eigenschaften der Güter berücksichtigen, etwa Masse oder Volumen, um Konsolidierungseffekte von Gütern mit komplementären Eigenschaften zu nutzen. Wir erarbeiten neue theoretische Einsichten und Lösungsmethoden von praktischer Relevanz, die wir an realen Instanzen aus der Automobilindustrie, der Chemiebranche und aus dem Einzelhandel evaluieren. Für die taktische Transportplanung mit zeitlichen Konsolidierungseffekte erarbeiten wir verschiedene Heuristiken, welche für unsere Instanzen die Optimalitätslücke zu 10% schließen. Wir geben Härteresultate für verschiedene Spezialfälle mit unteilbaren Gütern an, sowie ein dynamisches Programm, welches Lösungen mit optimalen Baumkosten berechnet; eine Überschätzung der realen Kosten. Für die strategische Routenplanung unter Unsicherheit entwickeln wir eine robuste Optimierungsmethode, welche Nachfrageschwankungen antizipiert, indem Worstcase-Kosten über einer beschränkten Szenarienmenge minimiert werden. Wir zeigen, dass das Gegenspielerproblem NP-schwer ist. Um Lösungen mit guten Worstcase-Kosten zu finden, leiten wir ein sorgfältig relaxiertes MILP her. Seine natürliche Erweiterung für Hubentscheidungen führt auf ein robustes M-Median Hub Location Problem. Wir finden einen moderaten Preis der Robustheit für Szenarien, die Durchschnittsnachfragemengen als untere Intervallgrenze verwenden. Trendbasierten Szenarien zeigen einen deutlichen Tradeoff zwischen historischen Durchschnittskosten und Worstcase-Kosten. Ein weiteres Robustheitskonzept stellen inkrementale Hubketten dar, welche Lösungen für jede Anzahl an Hubstandorten angeben, sodass sie gegen Änderungen dieser Anzahl robust sind. Ein Vergleich mit entsprechenden M-Median Lösungen, die wir mit einer LP-basierten Hubsuche erhalten, zeigt einen geringen Preis der Inkrementalität bei unseren Instanzen auf. Zuletzt untersuchen wir das Problem Wartungsarbeiten an Kanten in einem Netzwerk zu planen, um Konnektivität zwischen zwei Knoten zu bewahren. Wir zeigen, dass sich das Problem polynomiell in beliebigen Netzen lösen lässt, falls Wartungsarbeiten unterbrochen werden dürfen. Falls dies nur zu ganzzahligen Zeitpunkten erlaubt ist, ist es bereits NP-schwer. Für den Fall ohne Unterbrechungen zeigen wir starke Nichtapproximierbarkeitsresultate

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Predictive and Prescriptive Analytics for Managing the Impact of Hazards on Power Systems

Natural hazards and extreme weather events have the potential to cause significant disruptions to the electric power grid. The resulting damages are, in some cases, very expensive and time-consuming to repair and they lead to substantial burdens on both utilities and customers. The frequency of such events has also been increasing over the last 30 years and several studies show that both the number and intensity of severe weather events will increase due to global warming and climate change. An important part of managing weather-induced power outages is being properly prepared for them, and this is tied in with broader goals of enhancing power system resilience. Inspired by these challenges, this thesis focuses on developing data-driven frameworks under uncertainty for predictive and prescriptive analytics in order to address the resiliency challenges of power systems. In particular, the primary aims of this dissertation are to: 1. Develop a series of predictive models that can accurately estimate the probability distribution of power outages in advance of a storm. 2. Develop a crew coordination planning model to allocate repair crews to areas affected by hazards in response to the uncertain predicted outages. The first chapter introduces storm outage management and explains the main objectives of this thesis in detail. In the second chapter, I develop a novel two-stage predictive modeling framework to overcome the zero-inflation issue that is seen in most outage related data. The proposed model accurately estimates customer interruptions in terms of probability distributions to better address inherent stochasticity in predictions. In the next chapter, I develop a new adaptive statistical learning approach based on Bayesian model averaging to formulate model uncertainty and develop a model that is able to adapt to changing conditions and data over time. The forth chapter uses Bayesian belief network to model the stochastic interconnection between various meteorological factors and physical damage to different power system assets. Finally, in chapter five, I develop a new multi-stage stochastic program model to allocate and relocate repair crews in impacted areas during an extreme weather event to restore power as quickly as possible with minimum costs. This research was conducted in collaboration with multiple power utility companies, and some of the models and algorithms developed in this thesis are already implemented in those companies and utilized by their employees. Based on actual data from these companies, I provide evidence that significant improvements have been achieved by my models.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168024/1/ekabir_1.pd