Weighted tardiness minimisation for unrelated machines with sequence-dependent and resource-constrained setups

AbstractMotivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimisation. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times, and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component – vital to guarantee the non-violation of the problem's constraints – which optimally allocates resources with respect to tardiness minimisation. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure are revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight due dates, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights.KEYWORDS: Parallel machine schedulingsequence-dependent setup timesweighted tardinessmetaheuristicstextile manufacturing Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementInstances, results and codes that support the findings of this work are available at https://github.com/svatikiot/Weighted_Tardiness_Experiments.Additional informationFundingThis research has been supported by the EU through the FACTLOG Horizon 2020 project, grant number 869951.Notes on contributorsIoannis AvgerinosIoannis Avgerinos is a Ph.D. candidate in combinatorial optimization at the Department of Management Science and Technology, Athens University of Economics and Business, Greece. He received the Bachelor's degree in geomatics engineering from National Technical University of Athens and the Master's degree in management science and technology from Athens University of Economics and Business. His research interests include combinatorial optimisation, decomposition methods and their implementation on transport and production scheduling problems.Ioannis MourtosIoannis Mourtos is a professor at the Department of Management Science and Technology, Athens University of Economics and Business. He studied computer engineering and informatics at University of Patras and operations research at London School of Economics and Political Science. His academic interests lie within combinatorial optimisation, polyhedral combinatorics and the integration of integer programming with constraint programming. His work has been applied to optimisation problems in manufacturing and logistics and has been supported by several EU-funded projects.Stavros VatikiotisStavros Vatikiotis is a Ph.D. candidate at the Department of Management Science and Technology, Athens University of Economics and Business. He studied electrical and computer engineering at National Technical University of Athens and holds a Master's degree in mathematical modeling from the School of Applied Mathematical and Physics Sciences, National Technical University of Athens. His research interests lie in the design of combinatorial optimisation methods and their applications on industrial production environments.Georgios ZoisGeorgios Zois is a research associate at the Department of Management Science and Technology, Athens University of Economics and Business. He studied computer science at University of Ioannina, logic, algorithms and computation at University of Athens and received his Ph.D. from University Pierre and Marie Curie (UPMC) on algorithmic problems for energy and temperature-efficient computing. His research interests lie in the design and analysis of efficient exact and near-optimal optimisation algorithms for real-life applications in the areas of logistics and manufacturing, including location optimisation and multimodal transportation problems, as well as resource-aware production scheduling and planning.