Integrated Sequencing and Scheduling in Coil Coating

Höhn, Wiebke; König, Felix G.; Möhring, Rolf H.; Lübbecke, Marco E.

doi:10.1287/mnsc.1100.1302

Cited by 23 publications

(27 citation statements)

References 24 publications

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“…In the context of applying 2-Union Independent Set to coil coating-a process in steel manufacturing- Höhn et al (2011) showed NP-hardness of 2-Union Independent Set on the so-called M-composite 2-union graphs (which arise in their application), and showed a dynamic programming based algorithm running in polynomial time for constant M, where the degree of the polynomial depends on M. They additionally provided experimental studies based on heuristics using mathematical programming.…”

Section: Known Resultsmentioning

confidence: 99%

“…Since 2-Union Independent Set is NP-hard (Bar-Yehuda et al 2006), there is little hope to find optimal solutions within polynomial time. Instead of following the route of approximation algorithms and heuristics (Spieksma 1999;Bar-Yehuda et al 2006;Höhn et al 2011), we aim for solving the problem optimally using fixed-parameter algorithms (Downey and Fellows 2013;Flum and Grohe 2006;Niedermeier 2006), a concept to date largely neglected in the field of scheduling problems (Marx 2011;Mnich and Wiese 2014). 2.…”

Section: -Union Independent Setmentioning

confidence: 99%

“…We have seen that on moderate values of γ ≤ 15, the algorithm can solve instances with up to 5.5 · 10 5 intervals in a time frame of about 5 min. However, in application data, like for example, from the steel manufacturing application of Höhn et al (2011), the number of colors can be much higher.…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…Examples for solving scheduling problems with (weighted) Independent Set on 2-union graphs include resource allocation scenarios (Bar-Yehuda et al 2006) and coil coating in steel manufacturing (Höhn et al 2011;Möhring 2011). Formally, we are interested in the following problem:…”

Section: Introductionmentioning

confidence: 99%

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Interval scheduling and colorful independent sets

Bevern

Mnich²,

Niedermeier

et al. 2014

J Sched

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Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent vertices). Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and strip graphs (edge-wise unions of an interval graph and a cluster graph), on which Independent Set remains NP-hard but admits constant-ratio approximations in polynomial time. We study the parameterized complexity of Independent Set on 2-union graphs and on subclasses like strip graphs. Our investigations significantly benefit from a new structural "compactness" parameter of interval graphs and novel problem formulations using vertex-colored interval graphs. Our main contributions are: 1. We show a complexity dichotomy: restricted to graph classes closed under induced subgraphs and disjoint unions, Independent Set is polynomial-time solvable if both input interval graphs are cluster graphs, and is NP-hard otherwise. 2. We chart the possibilities and limits of effective polynomial-time preprocessing (also known as kernelization). 3. We extend Halld\'orsson and Karlsson (2006)'s fixed-parameter algorithm for Independent Set on strip graphs parameterized by the structural parameter "maximum number of live jobs" to show that the problem (also known as Job Interval Selection) is fixed-parameter tractable with respect to the parameter k and generalize their algorithm from strip graphs to 2-union graphs. Preliminary experiments with random data indicate that Job Interval Selection with up to fifteen jobs and 5*10^5 intervals can be solved optimally in less than five minutes.Comment: This revision does not contain Theorem 7 of the first revision, whose proof contained an erro

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Section: Known Resultsmentioning

confidence: 99%

Section: -Union Independent Setmentioning

confidence: 99%

Section: Experimental Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interval scheduling and colorful independent sets

Bevern

Mnich²,

Niedermeier

et al. 2014

J Sched

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“…Tang et al [12] and Ouelhadj et al [13] studied the problem in a dynamic environment where unforeseen changes occur in the production system. Some researchers have also addressed planning and scheduling in downstream production lines such as hot rolling and cold rolling among which [14][15][16][17] can be pointed out. There are significant differences between our problem and theirs, e.g, ladle-, tundish-, and mold-related issues are irrelevant in their problems.…”

Section: Literature Reviewmentioning

confidence: 99%

A comprehensive solution for continuous casting production planning and scheduling

Yadollahpour

ArbabShirani

2015

Int J Adv Manuf Technol

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Production planning and scheduling in steelmaking-continuous casting (SCC) process consists of decision making about three important issues: consolidating orders into charges, grouping charges into casts, and scheduling the casts on machines. In contrast to earlier investigations that mostly focus on one of these issues, a comprehensive twophase approach is presented in this paper in order to solve the whole problem. In the first phase, a continuous-time formulation is developed to determine what casts in what sequences should be scheduled on which machines. The solution obtained is then used as an optimal framework to create the final schedule in the second phase where the assignment rules embedded in a heuristic algorithm are used to consolidate orders into charges and group charges into casts. This method has been successfully used for Mobarakeh Steel Company (MSC), the biggest steel enterprise in the Middle East. Computational experiments demonstrate that the proposed method substantially increases the productivity in MSC.

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