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We review the literature about shop scheduling problems in manufacturing systems, revealing the concepts and methodologies that most impact the usage of scheduling theory in manufacturing environments. We focus our attention on the job shop and flow shop problems and their variants. We emphasize the interactions between the scheduling functions and manufacturing paradigms such as Industry 4.0, Computer Integrated Manufacturing, Computer‐Aided Process Planning, Advanced Planning and Scheduling, and Integrated Process Planning and Scheduling. We describe the main components and characteristics of the scheduling ecosystem, and we discuss how the scheduling interacts with the components that make it up and how it is affected by them. The metadata collected from the digital libraries on which the review was based (ScienceDirect, Scopus, and Elsevier) made it possible to characterize the historical evolution of the main concepts of the scheduling ecosystem in terms of scientific publications and research trends in the period 2000–2020. [ABSTRACT FROM AUTHOR]

In this paper, we propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing a solution of the multi-linear systems in the max-plus algebra. Necessary and suficient conditions for the interval multi-linear systems for weak solvability over max-plus algebra are obtained as well. Also, some examples are given for illustrating the obtained results. Moreover, we briey sketch how our results can be used in the max-plus algebraic system theory for synchronized discrete event systems. [ABSTRACT FROM AUTHOR]

Considering the technological advances of the industrial sector today, it appears that the management of energy resources has become increasingly prominent. Thus, to make this management more efficient, it is necessary to take into account the production planning and scheduling concept, since it allows influencing the scheduling of production at the level of cost and efficiency. Thus, the objective of this paper is to present a methodology that allows making the best possible scheduling of a textile production line to optimize it. This optimization is elaborated with the help of genetic algorithms, and, as it can be verified in this paper, it is possible to make an optimization of the production line at the level of energy cost or the level of energy consumption or optimization of both. Thus, the case study of this paper is based on a textile production line that produces a variety of products through three machines capable of performing numerous tasks, which can be done on more than one machine. Likewise, this production line enjoys photovoltaic production. This paper presents several case studies that allow for highlighting the impact of the methodology covered in the respective production line, where it is illustrated through different graphics.

The development and extending the classic models for approaching the real world conditions are always in consideration of researchers. For this reason, many efforts are made for generalization of the job shop scheduling problem. The stage shop scheduling problem is defined as a generalization of the mixed shop and a special case of the general shop. In a stage shop, each job includes several stages and each stage contains one or more operations. A stage is a subset of the set of the operations of a job so that these operations can be processed in any arbitrary order. In other words, the process of the operations of a stage cannot be initiated unless all the operations of the previous stage are completed. In this paper, two mixed integer programming models are presented for each of the problems "the stage shop scheduling with total weighted tardiness criterion" and "the stage shop scheduling with makespan criterion" (totally four models) and then the models are compared. For the comparison of the efficiency of the proposed models, some problem instances are generated. The computational results show that the second model is more efficient.

Agile assembly systems in automotive production are predominantly characterized by decoupled and independent workstations. This raises the question how such assembly systems can be evaluated and compared against the predominantly used ‪‪assembly lines. Job-shop-problems as a promising formulation do not yet offer a model that covers all the intended degrees of freedom. This research work thus presents an extended job-shop-problem and its validation while considering parallel and multifunctional workstations, sequence-dependent set-up times, routing and sequence flexibility as well as a multivariable objective function. The resulting model based on mixed integer linear programming contributes to the evaluation of agile assembly systems and supports the development of real-time capable algorithms for practical applications. [ABSTRACT FROM AUTHOR]

Beam scheduling is necessary for a multifunction radar(MFR) to perform multiple tasks and manage the resources of the radar efficiently. In this paper, we introduce the concept of the job shop problem to solve the beam-scheduling problem, and apply heuristic algorithms to enable reasonable beam allocation by the MFR. Then, we select three indicators, frame time, total weighed tardiness, and the number of targets dropped out, by considering realistic operation of the MFR. Based on the simulation results, we analyze the scheduling of each algorithm according to the number of targets and compare the performance of the algorithms. [ABSTRACT FROM AUTHOR]

This special issue of Algorithms is a follow-up issue of an earlier one, entitled ‘Algorithms for Scheduling Problems’. In particular, the new issue is devoted to the development of exact and heuristic scheduling algorithms. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. In the Call for Papers, we mentioned topics such as single-criterion and multi-criteria scheduling problems with additional constraints including setup times (costs), precedence constraints, batching (lot sizing), resource constraints as well as scheduling problems arising in emerging applications.

This article aims to identify the mathematical models used for the treatment of Job Shop Problem. The research is based on an exploratory qualitative analysis of patent information deposited in publicly accessible database. The results demonstrate that the information contained in patents can help provide a scenario of mathematical models used the treatment of Job Shop Problem and identify opportunities for development or the creation of new products based on the identified mathematical models. [ABSTRACT FROM AUTHOR]

A class of hypergraphs, called $$B$$-tails, is introduced. It is shown that a certain hypergraph can be assigned to any job shop problem in such a way that minimal $$B$$-tails correspond to optimal schedules. An algorithm for searching for a minimal $$B$$-tail is described. [ABSTRACT FROM AUTHOR]

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Hyper-heuristics or 'methodologies to choose heuristics' are becoming increasingly popular given their suitability to solve hard real world combinatorial optimisation problems. Their distinguishing feature is that they operate in the space of heuristics or heuristic components rather than in the solution space. In Dispatching Rule Based Genetic Algorithms (DRGA) solutions are represented as sequences of dispatching rules which are called one at a time and used to sequence a number of operations onto machines. The number of operations that each dispatching rule in the sequence handles is a parameter to which DRGA is notoriously sensitive. This paper proposes a new hybrid DRGA which searches simultaneously for the best sequence of dispatching rules and the number of operations to be handled by each dispatching rule. The investigated DRGA uses the selection mechanism of NSGA-II when handling multi-objective problems. The proposed representation was used to solve different variants of the multi-objective job shop problem as well as the single objective problem with the sum of weighted tardiness objective. Our results, supported by the statistical analysis, confirm that DRGAs that use the proposed representation obtained better results in both the single and multi-objective environment overall and on each particular set of instances than DRGAs using the conventional dispatching rule representation and a GA that uses the more common permutation representation. [ABSTRACT FROM AUTHOR]

In this paper, a cost-based job shop problem (JIT-JSP) is proposed to model the multi-order processing procedure in a just-in-time (JIT) environment. The objective of JIT-JSP is to minimize three costs: workin-process holding cost of half-finished orders, inventory holding cost of finished orders and backorder cost of unfulfilled orders. A modified tabu search (MTS) method is developed to improve the schedule quality by searching the neighbourhood of a f9asible schedule iteratively. The MTS method is comprised of three components that help to ensure a morp effective searching procedure: neighbourhood structure, memory structure and filter structure. Computational results show that the MTS method significantly improves the initial schedule generated by an arbitrarily selected dispatching rule. [ABSTRACT FROM AUTHOR]

Following a recent paper by the same author, a priority list-based tabu search heuristic is compared with the leading schedule-based tabu search heuristic of Nowicki and Smutnicki. More search neighbourhoods are required to achieve a given average makespan, but each priority list neighbourhood is searched much faster than the corresponding neighbourhood in the space of feasible schedules. Priority list-based tabu search therefore outperforms schedule-based tabu search in terms of elapsed CPU time. [ABSTRACT FROM AUTHOR]

Dehydration plants are broadly characterized by a multi-product nature chiefly attributed to the utilization of different raw materials to be processed sequentially so that demand constraints are met. Processing of raw materials is implemented through a series of preprocessing operations that together with drying constitute the production procedure of a pre-specified programme. The core of the manufacturing system that a typical dehydration plant involves, is scheduling of operations so that demand is fulfilled within a pre-determined time horizon imposed by production planning. The typical scheduling operation that dehydration plants involve can be formulated as a general job shop scheduling problem. The aim of this study is to describe a new metaheuristic method for solving the job shop scheduling problem of dehydration plants, termed as the Backtracking Adaptive Threshold Accepting (BATA) method. Our effort focuses on developing an innovative method, which produces reliable and high quality solutions, requiring reasonable computing effort. The main innovation of this method, towards a typical threshold accepting algorithm, is that during the optimization process the value of the threshold is not only lowered, but also raised or backtracked according to how effective a local search is. BATA is described in detail while a characteristic job shop scheduling case study for dehydration plant operations is presented. [ABSTRACT FROM AUTHOR]

This special issue of Algorithms is a follow-up issue of an earlier one, entitled 'Algorithms for Scheduling Problems'. In particular, the new issue is devoted to the development of exact and heuristic scheduling algorithms. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. In the Call for Papers, we mentioned topics such as single-criterion and multi-criteria scheduling problems with additional constraints including setup times (costs), precedence constraints, batching (lot sizing), resource constraints as well as scheduling problems arising in emerging applications. [ABSTRACT FROM AUTHOR]