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

Maintenance scheduling in a railway corricdor

We investigate a novel scheduling problem which is motivated by an application in the Australian railway industry. Given a set of maintenance jobs and a set of train paths over a railway corridor with bidirectional traffic, we seek a schedule of jobs such that a minimum number of train paths are cancelled due to conflict with the job schedule. We show that the problem is NP-complete in general. In a special case of the problem when every job under any schedule just affects one train path, and the speed of trains is bounded from above and below, we show that the problem can be solved in polynomial time. Moreover, in another special case of the problem where the traffic is unidirectional, we show that the problem can be solved in time $O(n^4)$

Proposed procedure for optimal maintenance scheduling under emergent failures

Production lines are usually subjected to emergent machine failures. Such emergent failures disrupt pre-established maintenance schedules, which challenge maintenance engineers to react to those failures in real time. This research proposes an optimization procedure for optimizing scheduling repairs of emergent failures. Three optimization models are developed. Model I schedules failures in newly idle repair shops with the objective of maximizing the number of scheduled repairs. Model II maximizes the number of assigned repairs to untapped ranges. Model III maximizes both the number of assigned failure repairs and satisfaction on regular and emergency repairs by resequencing regular and emergent failures in the shop that contains the largest free margin. A real case study is provided to illustrate the proposed optimization procedure. Results reveal that the proposed models efficiently scheduled and sequenced emergent failures in the idle maintenance shops, the untapped ranges between repairs of regular failures, and in the maintenance shop with the largest free margin. In conclusions, the proposed models can greatly support maintenance engineers in planning repairs under unexpected failures.

Strategies to Recover from Satellite Communication Failures

In natural and manmade disasters, inadequate strategies to recover from satellite communication (SATCOM) failures can affect the ability of humanitarian organizations to provide timely assistance to the affected populations. This single case study explored strategies used by network administrators (NAs) to recover from SATCOM failures in humanitarian operations. The study population were NAs in Asia, the Middle East, Central Africa, East Africa, and West Africa. Data were collected from semistructured interviews with 9 NAs and an analysis of network statistics for their locations. The resource-based view was used as the conceptual framework for the study. Using inductive analysis, 3 themes emerged from coding and triangulation: redundancy of equipment, knowledge transfer, and the use of spare parts to service the SATCOM infrastructure. The findings showed that the organization\u27s use of knowledge, and collaboration among NAs and nontechnical staff improved the organization\u27s ability to recover from SATCOM failures. The implication of this study for social change was the reduced cost of satellite services due to the efficient use of the bandwidth. These savings can be channeled into the purchase of vaccines, shelter, and the improvement in the quality of water and sanitation for displaced persons in humanitarian disasters, which improve the organization\u27s delivery of humanitarian services to the affected populations in the disaster

Scheduling maintenance jobs in networks

We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines. 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 in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions. Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation

Scheduling Maintenance Jobs in Networks

We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines. 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 in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions. Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.Comment: CIAC 201