Graph Al Euro g o G ri olthms d M f edoar l Routi 2010 ng Automa La ted ur eagui te d L ed Vehi ecture cles Rolf Möhring

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1 Graph Euro Algorithms Gold Medal for 2010 Routing Automated Laureate Guided Lecture Vehicles Rolf Möhring

2 My feelings Joy, thanks, and pride

3 Joy This is better than winning the soccer world cup

4 Thanks To my family Catharina Laura Raoul

5 Thanks to my group

6 Thanks to my research environment Study programs Business Mathematics, Industrial Mathematics Graduate programs (Graduiertenkollegs) Combinatorics, Geometry and Computation Berlin Mathematical School DFG Research Cluster (SPP) Algorithm Engineering BMBF Program Mathematics for Innovations in Industry EU Project Arrival Algorithms for Robust and Online Railway Optimization DFG Research Center MATHEON Mathematics for Key Technologies

7 Proud to be an Operations Researcher Mathematics Operations Research Computer Science Economics

8 My personal road in OR Mathematics RWTH Aachen Operations TU Berlin Research Computer Science U Hildesheim Economics U Bonn

9 The early years in Aachen (73-82) Project scheduling Deterministic Scheduling time-cost tradeoff decomposition scarce resources Stochastic Scheduling classes of policies optimality stability Franz-Josef Radermacher Computer Science, Ulm

10 Getting broader (80-96) structured (hyper-)graphs graph algorithms partial orders Project scheduling algorithms & software discrete optimization applications

11 PhD Gallery 1 of PhD students still in academia gn Dorothea Wagner 1986 CompSci Karlsruhe Stefan Felsner 1992 Math, Berlin Jens Gustedt 1992 CompSci, Nancy, F Rudolf Müller 1993 OR, Maastricht, NL From Mathematics to Andreas Schulz 1996 Information Security OR, MIT, USA Markus Schäffter 1996 CompSci, Ulm Wagner for ons Gustedt sitions AMD ms Markus Schäffter

12 Research Topics (80-96) An algebraic decomposition theory Interval orders: recognition, structure, jump number Treewidth, pathwidth, chainminors of networks Polyhedral structure of scheduling polytopes Complexity of rescheduling Scheduling with communication delays

13 Back to Operations Research ( now) Scheduling in production and traffic Routing in traffic, logistics and telecommunication

14 ung ngs nnemann Matchingproblem oblem oder äquivalent blem schinenbau PhD Gallery 2 of PhD students still in academia Matthias MüllerHannemann1987 CompSci, Halle Martin Skutella 1998 Math, Berlin Ekkehard Köhler 1999 Math, Cottbus Marc Uetz 2001 Math, Twente, NL Martin Oellrich 2008 CompSci, Berlin

15 Postdocs Christian Liebchen 2006 DB Schenker Nicole Megow 2006 CompSci, Saarbrücken Sebastian Stiller 2008 OR, MIT, USA Felix König 2009 Math, Berlin

16 Research Topics (97-now) Quadrilateral mesh generation Resource constrained project scheduling (RCPSP) Lagrangian relaxation LP-based approximation, also for stochastic case Discrete time-cost tradeoff Routing problems and flows over time Acceleration of shortest path calculations Train Timetabling Robust optimization Algorithmic game theory

17 Projects in traffic and telecommunication Embedding VPNs into the base net of the German Telecom Nova Traffic management and flows over time Navigation und Verkehrsdienste Constructing periodic timetables in public transport Coordinated traffic light control in networks

18 Projects in scheduling and logistics Routing of AGVs in the Hamburg harbor Ship Traffic Optimization for the Kiel Canal Turnaround scheduling in chemical plants Scheduling and logistics in steel production Optimizing throughput at a dairy filling line

19 Sequencing and Scheduling input of n items sequence them schedule them w.r.t. the sequence conditions may depend on entire subsequences cost depends on both

20 Example 1: Slab logistics [König, Lübbecke, Möhring, Schäfer, Spenke 2007] different orders intermediate storage on stacks steel slabs arrive from casting Ongoing Industry Cooperation Integrated Steel Production 20-ton steel slabs each slab is unique casting previous processing fixed time windows 20-ton steel slabs each slab is unique material, size processing steps,... slabs arrive from Figure 5.1: Some coils of sheet metal. They comprise up to several hundred meters of sheet metal, and may weigh as much as twenty tons. casting scheduling = sorting with stacks previous processing fixed time windows intermediate storage on stacks intermediate storage on stacks slabs are moved by crane slabs are moved by crane Intractable Problems in Logistics State Space Exploration further processing or delivery shaping steel producers extremely diverse product portfolio: The coils used for home appliances, for instance, already have their typical white coating when bought from the steel supplier; the sheet metal used for car bodies already has an anti-corrosion coating before it arrives at the automotive plant for pressing; coils destined for building construction receive their coatings, which are very specific for technical as well as esthetic reasons, while still at the steel plant. Integrated Steel Production Task: Compile given stacks for transport/further processing. Coil Coating with Shuttles Ongoing Industry Cooperation material, size processing steps,... slabs arrive from 74 Steel producers and manufacturers of coating materials on the one hand, and distributors of pre-coated sheet metal on the other hand, have formed associations to promote the evolution of coil coating on national [82] and international [43] levels already in the 1960s. Progress in the development of new and improved coating materials and techniques fosters an ongoing diversification in pre-coated metal products, and in recent years there have been quite a few scientific publications on coil coating, e.g., [39, 80]. Yet, to the best of our knowledge, the present work is the first dealing with optimization in the planning process. As is typical for paint jobs, the coil coating process may be subject to long setup times, mainly for the cleaning of equipment, and thus very high setup cost. In order to reduce this cost, so-called shuttle coaters have been introduced. They possess two separate tanks which allow to hold two different coatings at the same time, see Figure 5.2. The advantage is twofold: The Task: Compile given stacks for transport/further processing. transport by cranes or vehicles in Logistics State Space Exploration IntroductionIntractable Problem Problems Formulation Introduction Problem Formulation

21 Sorting with stacks is hard... Natural side constraints stacking restrictions (size, temperature) limited number of stacks limited stack heights lead to PSPACE-complete problem in general

22 ... but rather easy in practice Use local search on state space every node corresponds to a state of the pile yard start node = current state targets = deliveries to next production stage

23 Greedy search in the state space generate start state generate all neighbors evaluate them go to the best

24 Greedy is fast and gives good quality bound for deviation from optimum number of moves in % 40% 34% 29% 23% 17% 11% 6% 0% lower bound obtained from relaxation solved by IP

25 Example 2: Coil coating [Höhn, König, Lübbecke, Möhring 2009] coils need to be sequenced run through coating line oven finish coater finish coater complex scheduling with shuttle coaters sling buffer sling buffer oven oven oven primer coater chem coater chem coater primer coater setups in the scheduling phase roller change roller change cleaning &roller change cleaning cleaning cleaning color tanks

26 Details about the scheduling phase Subproblem: given fixed-order coil sequence, find tank assignment with minimum total idle time tank 1 tank 2 tank 1 tank 2 Setup work necessary if color changes cleaning coil has larger width than predecessor roller change concurrent setup work on idle tank saves idle time

27 Graph model for the scheduling phase k shuttle coaters no parallel concurrent setup tank 1 tank 2 tank 1 tank 2 k shuttle coaters tank 1 tank 2 Practice Tank Assignment Problem with k coaters new ideas for efficient algorithm far too slow, even for small instances machine 3 Theory Max Weight Indep. Set in special 2-union graphs polynomial-time algorithm for fixed k dynamic programming strongly NP-hard time machine 1 machine 2

28 Combining sequencing and scheduling Sequence generation with a fast genetic algorithm Scheduling based on the insights from dyn. prog trivial lower bound TSP lower bound IP lower bound FIFO expert planner Quality testing by an IP relaxation

29 Example 3: Dairy production filling line [Gellert, Höhn, Möhring 2010] charges of products need to be sequenced run through a filling line complex scheduling due to cleaning Jobs specified by base, e.g. yoghurt, cream,... fruit (optional) package number of pallettes duration Setup/waiting due to package/fruit/base change or cleaning regular cleaning of line and tanks limited size of tanks minimum time lags

30 Details about the scheduling phase Guarantee maximum distance d clean between cleanings: clean clean 3 d clean preempt jobs replace setup already in the schedule clean clean clean clean 3 d clean clean clean clean clean clean Respect limited size of cream tank min dist min dist

31 Solving the two classes of constraints Can solve cleaning conditions fast via shortest paths Can solve sequence and job dependent minimum distances by a simple greedy scan Not clear how to do both together

32 Combining sequencing and scheduling Sequence generation with a fast genetic algorithm Scheduling based on the insights from analysis Quality testing by an TSP lower bound show optimality gap of 2% for a weekly production

33 Summary Combining sequencing and scheduling is at the core of many applications But We can help with a good analysis and good algorithms We do not understand the integration well yet Good IP models for lower bounds are very hard to obtain There is much work left to be done