Machine scheduling aims to optimize job assignments to machines while adhering to manufacturing rules and job specifications. This optimization leads to reduced operational costs, improved customer demand fulfillment, and enhanced production efficiency. However, machine scheduling remains a challenging combinatorial problem due to its NP-hard nature. Deep Reinforcement Learning (DRL), a key component of artificial general intelligence, has shown promise in various domains like gaming and robotics. Researchers have explored applying DRL to machine scheduling problems since 1995. This paper offers a comprehensive review and comparison of DRL-based approaches, highlighting their methodology, applications, advantages, and limitations. It categorizes these approaches based on computational components: conventional neural networks, encoder-decoder architectures, graph neural networks, and metaheuristic algorithms. Our review concludes that DRL-based methods outperform exact solvers, heuristics, and tabular reinforcement learning algorithms in terms of computation speed and generating near-global optimal solutions. These DRL-based approaches have been successfully applied to static and dynamic scheduling across diverse machine environments and job characteristics. However, DRL-based schedulers face limitations in handling complex operational constraints, configurable multi-objective optimization, generalization, scalability, interpretability, and robustness. Addressing these challenges will be a crucial focus for future research in this field. This paper serves as a valuable resource for researchers to assess the current state of DRL-based machine scheduling and identify research gaps. It also aids experts and practitioners in selecting the appropriate DRL approach for production scheduling.

Motivated by a plethora of practical examples where bias is induced by automated-decision making algorithms, there has been strong recent interest in the design of fair algorithms. However, there is often a dichotomy between fairness and efficacy: fair algorithms may proffer low social welfare solutions whereas welfare optimizing algorithms may be very unfair. This issue is exemplified in the machine scheduling problem where, for $n$ jobs, the social welfare of any fair solution may be a factor $\Omega(n)$ worse than the optimal welfare. In this paper, we prove that this dichotomy between fairness and efficacy can be overcome if we allow for a negligible amount of bias: there exist algorithms that are both "almost perfectly fair" and have a constant factor efficacy ratio, that is, are guaranteed to output solutions that have social welfare within a constant factor of optimal welfare. Specifically, for any $\epsilon>0$, there exist mechanisms with efficacy ratio $\Theta(\frac{1}{\epsilon})$ and where no agent is more than an $\epsilon$ fraction worse off than they are in the fairest possible solution (given by an algorithm that does not use personal or type data). Moreover, these bicriteria guarantees are tight and apply to both the single machine case and the multiple machine case. The key to our results are the use of Pareto scheduling mechanisms. These mechanisms, by the judicious use of personal or type data, are able to exploit Pareto improvements that benefit every individual; such Pareto improvements would typically be forbidden by fair scheduling algorithms designed to satisfy standard statistical measures of group fairness. We anticipate this paradigm, the judicious use of personal data by a fair algorithm to greatly improve performance at the cost of negligible bias, has wider application.

The article describes a special time-interval balancing in multi-processor scheduling of composite modular jobs. This scheduling problem is close to just-in-time planning approach. First, brief literature surveys are presented on just-in-time scheduling and due-data/due-window scheduling problems. Further, the problem and its formulation are proposed for the time-interval balanced scheduling of composite modular jobs. The illustrative real world planning example for modular home-building is described. Here, the main objective function consists in a balance between production of the typical building modules (details) and the assembly processes of the building(s) (by several teams). The assembly plan has to be modified to satisfy the balance requirements. The solving framework is based on the following: (i) clustering of initial set of modular detail types to obtain about ten basic detail types that correspond to main manufacturing conveyors; (ii) designing a preliminary plan of assembly for buildings; (iii) detection of unbalanced time periods, (iv) modification of the planning solution to improve the schedule balance. The framework implements a metaheuristic based on local optimization approach. Two other applications (supply chain management, information transmission systems) are briefly described.

Obvious strategyproofness (OSP) is an appealing concept as it allows to maintain incentive compatibility even in the presence of agents that are not fully rational, e.g., those who struggle with contingent reasoning (Li 2015). However, it has been shown to impose some limitations, e.g., no OSP mechanism can return a stable matching (Ashlagi and Gonczarowski 2015). We here deepen the study of the limitations of OSP mechanisms by looking at their approximation guarantees for basic optimization problems paradigmatic of the area, i.e., machine scheduling and facility location. We prove a number of bounds on the approximation guarantee of OSP mechanisms, which show that OSP can come at a significant cost. However, rather surprisingly, we prove that OSP mechanisms can return optimal solutions when they use monitoring — a novel mechanism design paradigm that introduces a mild level of scrutiny on agents’ declarations (Kovacs, Meyer, and Ventre 2015).

On the basis of an analysis of previous research, we present a generalized approach for measuring the difference of plans with an exemplary application to machine scheduling. Our work is motivated by the need for such measures, which are used in dynamic scheduling and planning situations. In this context, quantitative approaches are needed for the assessment of the robustness and stability of schedules. Obviously, any `robustness' or `stability' of plans has to be defined w. r. t. the particular situation and the requirements of the human decision maker. Besides the proposition of an instability measure, we therefore discuss possibilities of obtaining meaningful information from the decision maker for the implementation of the introduced approach.

Sequencing and scheduling'as a research area is motivated by questions that We review complexity results and'optimization and approximation algorithms The chapter is organized as follows. There are several survey papers that complement the present chapter. In this section, we will review the main points of this theory. NPcompleteness of a particular problem is strong evidence that a polynomial-lime algorithm for its solution is unlikely to exist. The wide applicability of the notion of NPcompleteness was observed by Karp, who proved that 21 basic problems are NPcomplete.