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Motivated 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. [ABSTRACT FROM AUTHOR]

We examine the parallel machine scheduling problem where a set of jobs are to be processed by a set of unrelated parallel machines. We examine the most general among the variations for which an exact method has been proposed regarding makespan minimisation. This is because, apart from unrelated machines, we allow for (i) job splitting: each job's quantity can be split and processed by multiple machines simultaneously; (ii) sequence- and machine-dependent setup times: the setup time when job j succeeds k is different than the time when k succeeds j and varies also per machine m; and (iii) setup resource constraints: the number of setups that can be performed simultaneously on different machines is restricted. We present novel lower bound formulations and a heuristic that solves instances of up to 1000 jobs in a few minutes at an average gap of less than 20 %. Then, we propose a logic-based Benders decomposition, which, coupled with our heuristic, solves instances of up to 200 jobs and 20 machines to near optimality in less than two hours. Our method is used for a broad range of instances from textile manufacturing, thus yielding valuable managerial insights on makespan's versatility under varying machines or resources. [ABSTRACT FROM AUTHOR]

Featured Application: The outcomes of this work can be applied to forecast C5 content in debutanizer columns based on data obtained by a few pressure and temperature sensors. In addition, the proposed visualization can be used as a model global explanation, highlighting opportunities regarding feature selection, the most important features guiding the forecasts, and threshold values within which the forecasting model can operate. Refineries execute a series of interlinked processes, where the product of one unit serves as the input to another process. Potential failures within these processes affect the quality of the end products, operational efficiency, and revenue of the entire refinery. In this context, implementation of a real-time cognitive module, referring to predictive machine learning models, enables the provision of equipment state monitoring services and the generation of decision-making for equipment operations. In this paper, we propose two machine learning models: (1) to forecast the amount of pentane (C5) content in the final product mixture; (2) to identify if C5 content exceeds the specification thresholds for the final product quality. We validate our approach using a use case from a real-world refinery. In addition, we develop a visualization to assess which features are considered most important during feature selection, and later by the machine learning models. Finally, we provide insights on the sensor values in the dataset, which help to identify the operational conditions for using such machine learning models. [ABSTRACT FROM AUTHOR]

The diameter of the stable matching (stable marriage) polytope is bounded from above by [n/2], where n is the number of men (or women) involved in the matching; this bound is attainable. [ABSTRACT FROM AUTHOR]

Themany-to-many Stable Matching(MM)problemis defined on a set of workers and a set of firms and asks for an allocation of workers to firms that satisfies the firms' quotas and the preferences of workers for firms and vice-versa. This article proposes a time-optimal algorithm for solving theminimum-regret problemfor the MM, i.e. the problem of finding the MM solution in which the agent that is least well off is matched with the best possible set of agents of the opposite set. The proposed algorithm utilizes the notion of rotations and extends an analogous result for the Stable Marriage problem. [ABSTRACT FROM PUBLISHER]

The many-to-many stable matching problem (MM), defined in the context of a job market, asks for an assignment of workers to firms satisfying the quota of each agent and being stable, pairwise or setwise, with respect to given preference lists or relations. In this paper, we propose a time-optimal algorithm that identifies all stable worker-firm pairs and all stable assignments under pairwise stability, individual preferences, and the max-min criterion. We revisit the poset graph of rotations to obtain an optimal algorithm for enumerating all solutions to the MM and an improved algorithm finding the minimum-weight one. Furthermore, we establish the applicability of all aforementioned algorithms under more complex preference and stability criteria. In a constraint programming context, we introduce a constraint that models the MM and an encoding of the MM as a constraint satisfaction problem. Finally, we provide a series of computational results, including the case where side constraints are imposed. [ABSTRACT FROM AUTHOR]