Local search performance guarantees for restricted related parallel machine scheduling

We consider the problem of minimizing the makespan on restricted related parallel machines. In restricted machine scheduling each job is only allowed to be scheduled on a subset of machines. We study the worst-case behavior of local search algorithms. In particular, we analyze the quality of local optima with respect to the jump, swap, push and lexicographical jump neighborhood.operations research and management science;

Scheduling with processing set restrictions : a survey

2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Total Tardiness Minimization in a Single-Machine with Periodical Resource Constraints

In this paper we introduce a variant of the single machine considering resource restriction per period. The objective function to be minimized is the total tardiness.  We proposed an integer linear programming modeling based on a bin packing formulation. In view of the NP-hardness of the introduced variant, heuristic algorithms are required to find high-quality solutions within an admissible computation times. In this sense, we present a new hybrid matheuristic called Relax-and-Fix with Variable Fixing Search (RFVFS).  This innovative solution approach combines the relax-and-fix algorithm and a strategy for the fixation of decision variables based on the concept of the variable neighborhood search metaheuristic. As statistical indicators to evaluate the solution procedures under comparison, we employ the Average Relative Deviation Index (ARDI) and the Success Rate (SR). We performed extensive computational experimentation with a testbed composed by 450 proposed test problems. Considering the results for the number of jobs, the RFVFS returned ARDI and SR values of 35.6% and 41.3%, respectively. Our proposal outperformed the best solution approach available for a closely-related problem with statistical significance

Scheduling reentrant jobs on parallel machines with a remote server

This paper explores a specific combinatorial problem relating to re-entrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem is inspired by the logistics of a semi-automated micro-biology laboratory. The testing programme in the laboratory corresponds roughly to a hybrid flowshop, whose bottleneck stage is the subject of study. We demonstrate the NP-hard nature of the problem, and provide various structural features. A heuristic is developed and tested on randomly generated benchmark data. Results indicate solutions reliably within 1.5% of optimum. We also provide a greedy 2-approximation algorithm. Test on real-life data from the microbiology laboratory indicate a 20% saving relative to current practice, which is more than can be achieved currently with 3 instead of 2 people staffing the primary machines

Constructive heuristics for the unrelated parallel machines scheduling problem with machine eligibility and setup times

This work considers a scheduling problem identified in a factory producing customised Heating, Ventilation and Air Conditioning (HVAC) equipment. More specifically, the metal folding section is modelled as unrelated parallel machines with machine eligibility and sequence-dependent setup times. The objective under consideration is the minimisation of the total tardiness. The problem is known to be NP-hard so approximate methods are needed to solve real-size instances. In order to embed the scheduling procedure into a decision support system providing high-quality solutions in nearly real time, the goal of this paper is to develop fast, efficient constructive heuristics for the problem. Due to the lack of methods for this specific problem, some existing heuristics and one metaheuristic are selected from related problems and adapted. In addition, a set of heuristics with novel repair and improvement phases are proposed. The performance of the methods adapted and the proposals are compared with the optimal/approximate solutions obtained by a solver for an MILP in two sets of instances with small and medium sizes. Additionally, big-size instances (representing more realistic cases for our company) have been solved using the proposed constructive heuristics, providing efficient solutions in negligible computational times. Even if the adaptation of heuristics performs reasonably well, these are outperformed by the new heuristic proposed in this paper. In addition, when the new heuristic is embedded in the metaheuristic adapted from a related the problem, the results obtained are excellent in terms of the quality of the solution, even if the computational effort is somewhat higher.Ministerio de Ciencia en Innovación. “PROMISE

Faster Algorithms for Semi-Matching Problems

We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the weighted case, we give an $O(nm\log n)$-time algorithm, where $n$ is the number of vertices and $m$ is the number of edges, by exploiting the geometric structure of the problem. This improves the classical $O(n^3)$ algorithms by Horn [Operations Research 1973] and Bruno, Coffman and Sethi [Communications of the ACM 1974]. For the unweighted case, the bound could be improved even further. We give a simple divide-and-conquer algorithm which runs in $O(\sqrt{n}m\log n)$ time, improving two previous $O(nm)$-time algorithms by Abraham [MSc thesis, University of Glasgow 2003] and Harvey, Ladner, Lov\'asz and Tamir [WADS 2003 and Journal of Algorithms 2006]. We also extend this algorithm to solve the \textit{Balance Edge Cover} problem in $O(\sqrt{n}m\log n)$ time, improving the previous $O(nm)$-time algorithm by Harada, Ono, Sadakane and Yamashita [ISAAC 2008].Comment: ICALP 201