In this paper we address the problem of selecting and scheduling several jobs on a single machine with sequence-dependent setup times and strictly enforced time window constraints on the start time of each job. We use short-term production targets to coordinate decentralised local schedulers and to make the objectives of specific areas in line with the chain objectives by maintaining a desired work in process profile in manufacturing environments. The existing literature in this domain is based on discrete-time approaches. We depart from prior approaches by considering continuous time. We introduce a two-step mathematical programming model based on disjunctive constraints to solve small problems to optimality, and propose an insertion-based heuristic to solve large-scale instances. We provide several variations of the insertion heuristic based on different score functions. The primary objective of these approaches is to maximise the total defined score for jobs while satisfying production targets for families of jobs in each shift. Further, our models minimise the maximum completion time of all selected jobs. The effectiveness, efficiency, and robustness of the proposed algorithms are analysed and compared with the existing literature.

This article addresses the problem of selecting and scheduling several jobs on a single machine to sustain the desired dynamic work-in-process profile. We consider sequence-dependent setup times between jobs and strictly enforced time window constraints on the start time of each job. We use working shift production targets to coordinate decentralized local schedulers and make them inline with the manufacturing chain goals. Based on the discretization of scheduling time horizon, we propose a two-step mixed-integer programming model and a new network-based heuristic. The primary objective of these approaches is to maximize the total defined score for jobs while satisfying production targets. The secondary objective is to minimize the maximum completion time of all selected jobs. The effectiveness, efficiency, and robustness of the proposed algorithms are analyzed and compared with two existing approaches over a wide range of simulated scenarios.

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We consider a general load balancing problem on parallel machines. Our machine environment in particular generalizes the standard models of identical machines, and the model of uniformly related machines, as well as machines with a constant number of types, and machines with activation costs. The objective functions that we consider contain in particular the makespan objective and the minimization of the ℓp-norm of the vector of loads of the machines both with possibly job rejection. We consider this general model and design an efficient polynomial time approximation scheme (EPTAS) that applies for all its previously studied special cases. This EPTAS improves the current best approximation scheme for some of these cases where only a polynomial time approximation scheme (PTAS) was known into an EPTAS. ⋆

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