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Critical chain buffer management (CCBM) has been extensively studied in recent years. This paper investigates a new formulation of CCBM, the multimode chance-constrained CCBM problem. A flow-based mixed-integer linear programming model is described and the chance constraints are tackled using a scenario approach. A reinforcement learning (RL)-based algorithm is proposed to solve the problem. A factorial experiment is conducted and the results of this study indicate that solving the chance-constrained problem produces shorter project durations than the traditional approach that inserts time buffers into a baseline schedule generated by solving the deterministic problem. This paper also demonstrates that our RL method produces competitive schedules compared to established benchmarks. The importance of solving the chance-constrained problem and obtaining a project buffer tailored to the desired probability of completing the project on schedule directly from the solution is highlighted. Because of its potential for generating shorter schedules with the same on-time probabilities as the traditional approach, this research can be a useful aid for decision makers. [ABSTRACT FROM AUTHOR]

This paper addresses the triangle width problem, which generalizes the classic two-machine flexible job-shop problem (FJSP) with tooling constraints. This new problem can be studied from three different angles: scheduling, matrix visualization, and vertex ordering in hypergraphs. We prove the equivalence of the different formulations of the problem and use them to establish the N P -Hardness and polynomiality of several of its subcases. This problem allows us to find more elegant (and probably shorter) proofs for several combinatorial problems in our analysis setting. Our study provides an elegant generalization of Johnson's argument for the two-machine flow shop. It also shows the relation between the question: "Is a matrix triangular?" and the "k-visit of a graph". [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose efficient algorithms for computing the energetic lower bounds of the cumulative sheduling problem. So we have to schedule in a minimal makespan a set of non preemptive tasks on a resource with a given capacity. A task has a release date, a processing time and a tail and requires a given amount of the resource capacity during its processing. The energetic lower bound is the largest value of the makespan such that the energetic reasoning check cannot detect unfeasability. We report some algorithms to practically compute this lower bound with efficient complexity. These algorithms rely on iterative augmentations of C max until the cumulative constraint or the energetic constraint is satisfied. Our Computational results show their practical efficiencies. [ABSTRACT FROM AUTHOR]

The generation maintenance scheduling deals with a time sequence of preventive maintenance outages for a given set of generation units in an electricity market subject to power system restrictions. Incorporating a leader–follower structure in generation maintenance scheduling models is essential because of the inherent conflict between the interests of an independent system operator (ISO) and generation companies (GENCOs). The present paper proposes a new preventive maintenance scheduling model for generation companies facing the risk of involving generation units' disruption and demand variations while ensuring the reliability of the power system. Each GENCO proposes the maintenance schedule of its generation units to the ISO in a non-cooperative manner intending to maximize its net profit. Then ISO reacts to the aggregated schedule according to the power system's reliability index. Thus, a new formula is developed to consider all the interactions between the power system's stakeholders. In this regard, a stochastic multi-leader one-follower approach is applied. The GENCOs are considered independent leaders at the upper-level and the ISO is considered a follower at the lower-level. Then an equivalent single-level counterpart model is presented for each leader. So, the whole problem is converted into multiple individual stochastic single-level models, and then the Nash Equilibrium concept is used to determine GENCO equilibrium strategies. The proposed methodology is evaluated using some modified IEEE reliability test systems. The numerical analysis confirms that the proposed model is more effective in cases with higher uncertainties. Moreover, the performed analysis demonstrated the importance of applying a bi-level approach to the problem. Finally, the superiority of the proposed approach compared to the existing one is confirmed. [ABSTRACT FROM AUTHOR]

This paper considers several two-machine open shop problems with two agents. Each agent has an independent set of nonpreemptive jobs, and the objective is to find either a schedule minimizing a linear combination of the makespans of both agents, a schedule minimizing the makespan of one agent with the makespan of the other agent not exceeding a threshold, or all Pareto-optimal schedules with respect to the makespans of both agents. We present a number of results for the problems above, including a polynomial algorithm and a pseudo-polynomial algorithm for special cases, non-approximability, two approximation algorithms, and a fully polynomial-time approximation scheme. Finally, we run numerical experiments to show the effectiveness of the pseudo-polynomial algorithm and the approximation algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces the d-distanceb-matching problem, in which we are given a bipartite graph G = (S , T ; E) with S = { s 1 , ⋯ , s n } , a weight function on the edges, an integer d ∈ Z + and a degree bound function b : S ∪ T → Z + . The goal is to find a maximum-weight subset M ⊆ E of the edges satisfying the following two conditions: (1) the degree of each node v ∈ S ∪ T is at most b(v) in M, (2) if s i t , s j t ∈ M , then | i - j | ≥ d . In the cyclic version of the problem, the nodes in S are considered to be in cyclic order. We get back the (cyclic)d-distance matching problem when b (s) = 1 for s ∈ S and b (t) = ∞ for t ∈ T . We prove that the d-distance matching problem is APX-hard, even in the unweighted case. We show that 2 - 1 d is a tight upper bound on the integrality gap of the natural integer programming model for the cyclic d-distance b-matching problem provided that (2 d - 1) divides the size of S. For the non-cyclic case, the integrality gap is shown to be at most (2 - 2 d) . The proofs give approximation algorithms with guarantees matching these bounds, and also improve the best known algorithms for the (cyclic) d-distance matching problem. In a related problem, our goal is to find a permutation of S maximizing the weight of the optimal d-distance b-matching. This problem can be solved in polynomial time for the (cyclic) d-distance matching problem — even though the (cyclic) d-distance matching problem itself is NP-hard and also hard to approximate arbitrarily. For (cyclic) d-distance b-matchings, however, we prove that finding the best permutation is NP-hard, even if b ≡ 2 or d = 2 , and we give e-approximation algorithms. [ABSTRACT FROM AUTHOR]

In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several variants of this problem that are known to be N P -hard, while also proving N P -hardness for two variants whose complexity was unknown before. Using these results, together with constant-factor approximations for the makespan objective from the literature, we also introduce the first results on bi-objective approximation in the coupled task setting. [ABSTRACT FROM AUTHOR]

This paper studies a two-machine flow shop scheduling problem with availability constraints due to a breakdown on the first machine. The starting time of the breakdown is considered stochastic and follows a known probability distribution. A service-level constraint is introduced to model the guarantee with which the obtained schedule takes into account the stochastic nature of the breakdown's starting time. The objective is to find a solution that minimizes the makespan while satisfying the desired service level. The studied problem is strongly NP-hard. We develop two mixed integer linear models that linearize the non-linear model. Using interval modeling of the breakdown, we propose lower bounds and a valid inequality that are used to strengthen both models. When the lower bounds and the valid inequality are applied, the performance of both models is greatly improved by reducing the gap and reaching optimality for more instances. We also introduced two heuristics that exploit the proposed interval modeling. The computational results indicate that both models are able to reach optimality for the 10-job instances. Moreover, the comparisons results between both models with the two heuristics showed their effectiveness. [ABSTRACT FROM AUTHOR]

This paper provides two new perspectives on single-machine scheduling problems in which the objective involves penalties regarding late work. Both of this perspectives have been neglected in the previous literature. We begin by presenting a parameterized complexity analysis of the N P -hard problem of minimizing the total late work on a single machine. We do so with respect to the following four parameters: (i) the number of different processing times ( υ p ); (ii) the number of different due dates ( υ d ); (iii) the maximal processing time (p max) ; and (iv) the maximal due date ( d max ). We use results from the literature to conclude that the problem is hard with respect to (wrt.) parameter υ d and is tractable (i.e., solvable in FPT time) wrt. p max . We then provide two FPT algorithms showing that the problem is also tractable wrt. to υ p and d max . We continue by analyzing a single-machine scheduling problem with assignable due dates where the cost function to be minimized includes penalties due to weighted early and tardy work. We assume that each job can be assigned a different due-date, the value of which is subject to a job-dependent upper bound. We provide an efficient method to optimally assign due dates for a given job schedule. We then use this result to reduce the problem to a purely combinatorial problem, which we show is N P -hard in general, but solvable in either FPT time or polynomial time for some special cases. [ABSTRACT FROM AUTHOR]

In mass casualty incidents, patients need to be evacuated to nearby hospitals as soon as possible, and a surge in demand for emergency medical services then occurs. It would result in ambulance offload delays, i.e., no emergency operating room is available when the ambulance arrives at a hospital, and thus the patients cannot be treated immediately. In this paper, we aim to solve a combinatorial problem of patient-to-hospital assignment and patient surgery sequence considering patient deterioration and ambulance offload delay during a mass casualty incident. A mixed-integer programming model is proposed. The objective is to minimize the completion time of all patients' surgeries. For solving such a problem, some structural properties of our studied problem are derived, and a heuristic is developed to solve the single operating room scheduling problem considering ambulance offload delay and patient deterioration based on these structural properties. A hybrid Firefly Algorithm-Variable Neighborhood Search algorithm incorporating the heuristic method is proposed to solve it. Our proposed algorithm can solve the problem within a short computation time, and the computational results demonstrate the superiority of our proposed algorithm over the compared algorithms. [ABSTRACT FROM AUTHOR]

How to improve the efficiency of operating rooms (ORs) has always been a challenging problem in the context of healthcare operations management. This paper focuses on the research of operating room scheduling under non-operatingroomanesthesia (NORA) mechanism, in the presence of the uncertainty of emergency arrivals. In particular, we examine the advantages of the NORA mechanism in comparison with traditional surgical anesthesia practice under different operating room settings. Operationally, the process is comprised of two stages: (1) initial scheduling and (2) rescheduling. In the first stage, the initial schedule for elective surgeries under NORA is first performed through our developed model. With experiments, it is shown that for different operating room settings, the NORA mechanism can significantly improve the operating room utilization in comparison with the traditional OR anesthesia process. In the second stage of rescheduling, our experiment results show that the rescheduling model can effectively address the disruptions caused by the random arrival of emergency patients. [ABSTRACT FROM AUTHOR]

We consider the problem of a project manager of a matrix organization responsible for the timely completion of projects arriving over time and requiring the usage of a set of resources under his/her purview. A project is defined by a set of activities, precedence relations between activities, resource requirements, a customer due date, and a priority (a weight). Arriving projects are released to a flow control system that monitors the progress of activities and schedules the set of available activities, i.e., activities that are ready to be processed, as appropriate. A critical feature of such control systems is the decision process for choosing the next activity to seize a given resource. This is the focus of this paper. In the past several decades, various heuristic priority rules have been proposed in the literature to support this type of decision in differing settings such as the job shop problem and the deterministic resource-constrained project scheduling problem. A gap exists with respect to testing the various rules all together in the more realistic dynamic-stochastic multi-project environment when the objective is to minimize weighted project tardiness. The purpose of this paper is to fill this gap. Results show that the priority rule “Weighted Critical Ratio and Shortest Processing Time” (W(CR+SPT))\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\hbox {W}(\hbox {CR}+\hbox {SPT}))$$\end{document} is the best performing rule with respect to minimizing weighted project tardiness. W(CR+SPT)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hbox {W}(\hbox {CR}+\hbox {SPT})$$\end{document} is shown to be a variant of the family of “Modified Due Date” rules first introduced by Baker and Bertrand (J Oper Manage 1(3):37–42, 1982). Repeated application of Duncan’s Multiple Range test demonstrates the robustness of our findings. For the environmental parameters (due date tightness, variation of expected activity durations, and utilization of resource), the W(CR+SPT)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hbox {W}(\hbox {CR}+\hbox {SPT})$$\end{document} rule is dominant with respect to weighted project tardiness among the eleven priority rules tested. Only when the number of resources is very modest (either 1 or 3 resources) or under a purely parallel resource network is W(CR+SPT)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hbox {W}(\hbox {CR}+\hbox {SPT})$$\end{document} not the dominant rule. In those cases, its variant W(CR+GSPT)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hbox {W}(\hbox {CR}+\hbox {GSPT})$$\end{document} is the best performing rule with respect to weighted project tardiness. [ABSTRACT FROM AUTHOR]

In enterprise project management systems, a program at the tactical level coordinates and manages multiple projects at the operational level. There are close relationships between multiple projects in a program, which are typically manifested as shared resources and precedence relationships. Most research efforts have concentrated on the resource sharing by projects, while the precedence relationships between projects have yet to be comprehensively investigated. In this paper, a bi-objective hierarchical resource-constrained program scheduling problem proposed, where both resource sharing and precedence relationships between projects are considered in a distributed environment. The problem contains two different sub-problems at the operational level and the tactical level, and they are modeled in the same way as two bi-objective multi-mode scheduling problems. Shared resources are allocated from the tactical level to the operational level, and once they are allocated to a project, they can only be re-allocated to other projects once the current project is finished. Subsequently, a two-phase algorithm based on NSGA-III is developed. The algorithm runs at the operational level and the tactical level in turn. According to the Pareto fronts of projects that are submitted from the operational level, the bi-objective program planning at the tactical level is conducted under the constraints of precedence relationships and shared resources. The results of computational simulations demonstrate the satisfactory performance of the improved algorithm. By coordinating the local optimization of projects and the global optimization of the program in a hierarchical framework, the method proposed in this paper provides an effective integrated scheduling method for decision-makers at various levels of a program. [ABSTRACT FROM AUTHOR]

This paper addresses a parallel machine scheduling problem with non-anticipatory family setup times and batching, considering the task's stochastic processing times and release dates. The problem arises from a real-life ship scheduling problem in the oil and gas industry. We developed an Iterated Greedy simheuristic with built-in Monte Carlo Simulation to sample the stochastic parameters. We conducted experiments on a set of instances from the literature, considering two simheuristic variants and three uncertainty levels for the stochastic parameters. To highlight the advantages of using simulation to tackle the stochastic problem, the simheuristics are compared against a regular Iterated Greedy metaheuristic, yielding an improvement of up to 16.5% on the objective function's expected values, with a reduced impact on computational times. During a risk analysis, the Pareto set of solutions is generated to illustrate the trade-off between the expected objective value of the solutions and the conditional value at risk, providing decision-makers with a useful tool to select the schedules that better fit their risk profiles. We use an iterative mechanism to build confidence intervals within a certain confidence level during the method's simulation step, interrupting the procedure when it reaches the desired error. This strategy's advantage is highlighted in the computational experiments, which indicates that the number of replications of the simulation is instance and uncertainty level dependent. A periodic re-planning strategy is also used to evaluate the performance of the simheuristic, highlighting the advantages of using the proposed algorithm in a real-life usage situation. [ABSTRACT FROM AUTHOR]

A recent Journal of Scheduling paper by Chen and Zhang (J Sched, 2020. https://doi.org/10.1007/s10951-020-00668-1) proves that the problem of scheduling coupled tasks to minimize total completion time is NP-hard in the strong sense even for the case with all tasks having the same, though not necessarily unit, processing times. This note shows a simpler proof of that result, and strengthens it by proving that the problem is NP-hard in the strong sense even if all tasks are unit-time. [ABSTRACT FROM AUTHOR]

This paper considers an integrated approach to two common problems in a precision agriculture framework: management zone delineation and selective harvest scheduling. Our model minimizes the total costs of harvest operations, establishing planning and scheduling for selective harvest of each selected management zone. Therefore, this tool provides important information for decision making of farmers in the field. Our integrated model is contrasted with the hierarchical approach commonly used in the literature for these cases, where the result of zoning problem is an input to schedule the harvest problem. Both problems were solved through a complete enumeration of all the potential management zones and demonstrated the advantages of our proposed model over the hierarchical approach. Our model reached an average reduction of 10% in harvest operations costs for different instances in a case study. [ABSTRACT FROM AUTHOR]

Over the past couple of centuries, with the increase in the significance of the railways to the economy, the complexity of the railway network and consequently the decision making involved and the number of problems faced has only increased. Among the host of problems in railways management, one of the most important is the locomotive assignment problem (LAP). The LAP is as old as the railways itself. The objective of the LAP is to assign a fleet of locomotives at minimum cost to pre-scheduled trains subject to a host of constraints. Most of the models in literature either work on improving the efficiency of solving the LAP or attempt to solve the three levels of LAP separately. Our attempt in this paper is to arrive at a linear mathematical model that integrates the strategic, tactical and operational level aspects of the LAP. We also demonstrate that by the addition of a valid inequality, the lower bounds can be improved substantially resulting in a substantial reduction in solution times for the problem instances. Further, we develop a Dijkstra's algorithm-based heuristic to test the problem instances and compare the solution times and quality of solutions. Finally, we develop a case based on Southern Zone of the Indian Railways and test the heuristic to solve the LAP for this zone. [ABSTRACT FROM AUTHOR]

This paper proposes two models for the Technician Routing and Scheduling Problem (TRSP), which are motivated by a telecom provider based in Saskatchewan, Canada. The proposed TRSP models are distinguished from existing models by their ability to address two key issues: overnight and lunch break scheduling. The models aim to scheduling a set of technicians with homogeneous skill levels and different working hours for the purpose of providing services with different service times and time windows to a diverse set of widely spread communities. As the large-sized experiments of this problem categorized into NP-hard problems, a metaheuristic-based technique, Invasive Weed Optimization, is developed to solve them. A comparative analysis is performed to choose the optimum TRSP model based on two factors which are distance of communities to the main depot and balanced service times during planning horizon. The performance of the models is evaluated through the real-world data obtained from the telecom provider. The results prove that the overnight TRSP model is capable of substantially decreasing travel costs and the number of technicians that are required to perform the same set of services. [ABSTRACT FROM AUTHOR]

This paper concentrates on the divisional seru scheduling and worker assignment joint decision-making problem, and synthetically considers the difference in workers’ skill sets, the diversity of workers’ skill levels, the process sequence constraints, setup time, lot-splitting, etc., and then a nonlinear integer programming model is constructed to minimize the makespan. We show that it is necessary to consider the process sequence constraints, and the optimal makespan of the worker-operation allocation scheme without considering the process sequence constraints is much larger than that of considering the process sequence constraints. Moreover, as the number of workers increases, the advantage of considering sequence constraints becomes more obvious. Considering the multi-decision attributes and intractable computations of the studied problem, we turn it into bi-level programming. Then based on the combination of a hybrid genetic variable neighbourhood search algorithm (HGVNSA) and a greedy heuristic algorithm (GHA), a bi-level nested heuristic algorithm (HGVNSA-GHA) is designed. Finally, numerical experiment results show that the proposed algorithm can achieve better results and higher efficiency for the divisional seru scheduling and worker assignment model. [ABSTRACT FROM AUTHOR]

This paper considers the problem of scheduling independent jobs with release dates and tails on m identical machines to minimize the makespan. The three main bounds are the preemptive bound, the energetic bound and the Jackson Pseudo Preemptive bound. It is known that they are very close in practice. The aim of this paper is to provide worst case instances where the slack between them is maximal and to prove tight bounds on the slack. We show that the slack is smaller than the maximal processing time. [ABSTRACT FROM AUTHOR]

In this paper, we study the construction of a cyclic appointment schedule in an outpatient department. In particular, we determine the capacity distribution between elective and urgent patients and the scheduling of the time slots reserved for these patients such that the operational waiting times of elective and urgent patients are minimised. The proposed solution methodology devises a Pareto set of cyclic appointment schedules based on these waiting times with different capacity allocations for urgent patients. An approximation of the Pareto set of non-dominated schedules is obtained using a multi-objective archived simulated annealing heuristic. To accurately validate the cyclic appointment schedules, we incorporate operational decision-making via scheduling individual patients. To this end, we simulate operational variability, i.e., patient arrivals, no-show behaviour, punctuality and scan durations, based on real-life input data. The patients are assigned one-by-one using an online scheduling rule. Computational experiments are conducted with a real-life case study. We compare different appointment scheduling rules and discuss the impact of the capacity distribution between elective and urgent patients and the timing of urgent slots in the cyclic appointment schedules. The results show that the distribution of capacity between patient types, the timing of urgent slots and appointment rules all have significant impacts on patient waiting times. Appointment waiting times improve when urgent slots are spread equally over and throughout the days considered and when the Bailey–Welch rule is used to schedule patients. Trade-offs between elective and urgent waiting times resulting from different capacity distributions or slot timing are exemplified via a Pareto front. The proposed method outperforms relevant single-pass methodologies, and we demonstrate that its performance is strengthened thanks to the integrated optimisation of strategic, tactical and operational decisions. [ABSTRACT FROM AUTHOR]

The objective of the Patrol Boat Scheduling Problem with Complete Coverage (PBSPCC) is to find a minimum size patrol boat fleet to provide continuous coverage at a set of maritime patrol regions, ensuring that there is at least one vessel on station in each patrol region at any given time. The requirement for continuous patrol coverage is complicated by the need for vessels to be replenished on a regular basis. This combinatorial optimization problem contains both routing and scheduling components and is known to be NP-hard. In this paper, we show how recent theoretical insights can be used in conjunction with specially tailored heuristics to accelerate a column generation solution approach over a resource-space-time network construct. We show how the column generation approach can be used within a branch-and-price framework and combined with various reduction techniques to find cyclic and long-term scheduling solutions on a range of test problems. [ABSTRACT FROM AUTHOR]

It has been proposed that if replacement time is planned too early prior to failure, a waste of operation cost, i.e., excess costs, would incur because the system might run for an additional period of time to complete critical operations, and if replacement time is too late after failure, a great failure cost, i.e., shortage cost, is incurred due to the delay in time of the carelessly scheduled replacement. In order to make the preventive replacement policies perform in a more general way, the above two variable types of costs are taken into considerations for periodic replacement policies in this paper. We firstly take up a standard model in which the unit is replaced preventively at periodic times. Secondly, the modeling approaches of whichever occurs first and last are applied into periodic and random models, and replacement first and last policies are discussed to find optimum periodic replacement times for a random working time. Furthermore, optimum working numbers are obtained for the extended models. We give analytical discussions of the above replacement policies, and finally, numerical examples are illustrated. [ABSTRACT FROM AUTHOR]

Multi-position refining furnaces are a critical strategy for energy-intensive industries to meet its demands of fast-paced production. In most literature, however, they serve only as a buffer, holding up to at most two ladles to maintain the proper temperature of ladles. These studies do not take full advantage of them, nor do they study the production scheduling of energy-intensive enterprises with multi-position refining furnaces under time-of-use (TOU) tariffs. Therefore, this paper presents a steelmaking-continuous casting (SCC) scheduling problem with multi-position refining furnaces under TOU tariffs. We firstly develop a mixed integer nonlinear programming (MINLP) model with the goals of minimizing jobs completion time, machines idle time, and total electricity costs, which subjects to the double-position characteristics and other process constraints. Owing to the complexity between the time-slots of TOU tariffs and the processing cycles of jobs, we design an intermediate function to calculate objectives efficiently. Furthermore, a Lagrangian relaxation (LR) algorithm based on a subgradient algorithm is utilized to solve the proposed model, and an interior point algorithm is adopted to solve sub-problems obtained by job-level and batch-level decomposition, whose solution approximates optimality comparing to GUROBI solver. The computational results demonstrate that the solution of job-level decomposition algorithm approximates the optimal scheduling scheme in an acceptable time and is superior to that of GUROBI solver. In addition, double-position instance can find a better scheduling scheme than nondouble-position one. [ABSTRACT FROM AUTHOR]

In a recent study, Sun et al. (AOR 292:113–131, 2020) studied due-window proportionate flow shop scheduling problems with position-dependent weights. For common due-window (denoted by CONW) and slack due-window (denoted by SLKW) assignment methods, they proved that these two problems can be solved in O (n 2 log n) time respectively, where n is the number of jobs. In this paper, we consider the same problems, and our contribution is that the CONW problem can be optimally solved by a lower-order algorithm, which runs in O (n log n) time, implying an improvement of a factor of n. [ABSTRACT FROM AUTHOR]

Mixed-criticality scheduling addresses the problem of sharing common resources among jobs of different degrees of criticality and uncertain processing times. The processing time of jobs is observed during the online execution of the schedule with the prolongations of critical jobs being compensated by the rejection of less critical ones. One of the central questions in the field of mixed-criticality scheduling is ensuring the high reliability of the system with as few resources as possible. In this paper, we study the computation of the execution probability of jobs with uncertain processing times in a static mixed-criticality schedule. The aim is to compute the execution probability of jobs (i.e., the objective function of a schedule), which is a problem solvable by a closed-form formula when the jobs are not replicated. We introduce the job replication, i.e., scheduling a single job multiple times, as a new mechanism for increasing the execution probability of jobs. We show that the general problem with job replication becomes # P -hard, which is proven by the reduction from the counting variant of 3-sat problem. To compute the execution probability, we propose an algorithm utilizing the framework of Bayesian networks. Furthermore, we show that cases of practical interest admit a polynomial-time algorithm and are efficiently solvable. The proposed methodology demonstrates an interesting connection between schedules with uncertain execution and probabilistic graphical models and opens a new approach to the analysis of mixed-criticality schedules. [ABSTRACT FROM AUTHOR]

This paper addresses the class of permutation flow shop scheduling where jobs, after their completion, must be grouped in batches. This is a common scheme in industrial environments, where products undergo multiple process steps in different shops and, when completed, must be transported to customers or the next production step. A new optimisation criterion is used, the inter-exit time, i.e., the difference between the completion times of two jobs. An upper bound is proposed and demonstrated for a general permutation flow shop with m machines. [ABSTRACT FROM AUTHOR]

Cross-docking center is suitable for distributing new products with short shelf life in the supply chain network. Vehicle scheduling and routing are essential decisions at cross-docking centers that must be made for companies at the level of logistics decisions. This decision will be more difficult in real matters under uncertainty in green supply chain networks. This paper proposes a new multi-objective vehicle routing scheduling model at a cross-docking center in the green supply chain under uncertainty to mitigate CO2 emissions of vehicles as a mixed integer non-linear multi-objective problem. The focuses of this paper are minimizing all delivery costs and conducting to minimize total CO2 emissions to pay attention to the green impacts. Then, two numerical studies are given to show the application of the proposed model and to explore its exhibitions. To solve the proposed model, the NSGA-II algorithm is developed and the Taguchi design method is used to set proper values of NSGA-II parameters to improve its efficiency. The effectiveness of the proposed meta-heuristic approach is illustrated by comparing its results with GAMS. The study can potentially guide industry managers in successfully implementing logistics decisions in the GSCN to achieve the sustainable development goals (SDGs) mainly SDG 13. [ABSTRACT FROM AUTHOR]

This paper introduces the d-distance matching problem, in which we are given a bipartite graph G = (S , T ; E) with S = { s 1 , ⋯ , s n } , a weight function on the edges and an integer d ∈ Z + . The goal is to find a maximum-weight subset M ⊆ E of the edges satisfying the following two conditions: (i) the degree of every node of S is at most one in M, (ii) if s i t , s j t ∈ M , then | j - i | ≥ d . This question arises naturally, for example, in various scheduling problems. We show that the problem is NP-complete in general and admits a simple 3-approximation. We give an FPT algorithm parameterized by d and also show that the case when the size of T is constant can be solved in polynomial time. From an approximability point of view, we show that the integrality gap of the natural integer programming model is at most 2 - 1 2 d - 1 , and give an LP-based approximation algorithm for the weighted case with the same guarantee. A combinatorial (2 - 1 d) -approximation algorithm is also presented. Several greedy approaches are considered, and a local search algorithm is described that achieves an approximation ratio of 3 / 2 + ϵ for any constant ϵ > 0 in the unweighted case. The novel approaches used in the analysis of the integrality gap and the approximation ratio of locally optimal solutions might be of independent combinatorial interest. [ABSTRACT FROM AUTHOR]

In this paper we introduce a complex scheduling problem that arises in a real-world industrial test laboratory, where a large number of activities has to be performed using qualified personnel and specialized equipment, subject to time windows and several other constraints. The problem is an extension of the well-known Resource-Constrained Project Scheduling Problem and features multiple heterogeneous resources with very general availability restrictions, as well as a grouping phase, where the jobs have to be assembled from smaller units. We describe an instance generator for this problem and publicly available instance sets, both randomly generated and real-world data. Finally, we present and evaluate different metaheuristic approaches to solve the scheduling subproblem, where the assembled jobs are already provided. Our results show that Simulated Annealing can be used to achieve very good results, in particular for large instances, where it is able to consistently find better solutions than a state-of-the-art constraint programming solver within reasonable time. [ABSTRACT FROM AUTHOR]

Pre-runtime scheduling of avionic systems is used to ensure that the systems provide the desired functionality at the correct time. This paper considers scheduling of an integrated modular avionic system which from a more general perspective can be seen as a multiprocessor scheduling problem that includes a communication network. The addressed system is practically relevant and the computational evaluations are made on large-scale instances developed together with the industrial partner Saab. A subset of the instances is made publicly available. Our contribution is a matheuristic for solving these large-scale instances and it is obtained by improving the model formulations used in a previously suggested constraint generation procedure and by including an adaptive large neighbourhood search to extend it into a matheuristic. Characteristics of our adaptive large neighbourhood search are that it is made over both discrete and continuous variables and that it needs to balance the search for feasibility and profitable objective value. The repair operation is to apply a mixed-integer programming solver on a model where most of the constraints are treated as soft and a violation of them is instead penalised in the objective function. The largest solved instance, with respect to the number of tasks, has 54,731 tasks and 2530 communication messages. [ABSTRACT FROM AUTHOR]

This paper addresses a multi-skill resource-constrained multi-project scheduling problem (MSRCMPSP) with different types of resources and complex industrial constraints, which originates from SNCF heavy maintenance factories. Two objective functions, that have been rarely addressed in the literature, are independently considered: (i) Minimization of the sum of the weighted tardiness of the projects and (ii) Minimization of the sum of the weighted duration of the projects. A time-indexed mixed-integer linear programming model is presented with both resource assignment and capacity constraints. To solve large instances with several thousand activities, a new memetic algorithm combining a novel hybrid simulated genetic algorithm with a simulated annealing is implemented. The memetic algorithm is compared with popular solution approaches. Computational experiments conducted on real instances and benchmark instances validate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]