Tardy Jobs Research Articles

A multi-objective production scheduling model and dynamic dispatching rules for unrelated parallel machines with sequence-dependent set-up times

This study presents a production scheduling for unrelated parallel machines with machine and job sequence-dependent setup times. The system performance measures to minimize include makespan, total tardiness, and number of tardy jobs. The aim of the study is to develop a solution methodology that can solve the problem for the large scale. First, the problem is formulated as a mixed-integer linear programming model. The augmented ɛ-constraint method is applied to find Pareto solutions for small problem instances. The purpose is to demonstrate that Pareto solutions, which balance the trade-offs among three measures of performance, can be found for these instances. Dispatching rule-based heuristics is developed to solve large problem instances. The heuristics feature three dispatching rules that are designed to handle the dependent setup time. In addition, these rules are combined into six variants using a time-based rule-switching mechanism. The heuristics are tested with 18 problem instances, containing 244 to 298 jobs, in two demand scenarios derived from the monthly demand data from an industrial user. Under each demand scenario, a set of heuristics that provides the best performance with respect to the three measures is identified. The heuristics include combinations of the shortest completion time and due date-based rules. Finally, a multi-criteria decision-making analysis is performed to determine the conditions specified by the weight given to each measure, with which one heuristic is preferred over the others.

Serial batching to minimize the weighted number of tardy jobs

AbstractThe $$1\vert \text {s-batch}(\infty ),r_j\vert \sum w_jU_j$$ 1 | s-batch ( ∞ ) , r j | ∑ w j U j scheduling problem takes as input a batch setup time $$\Delta $$ Δ and a set of n jobs, each having a processing time, a release date, a weight, and a due date; the task is to find a sequence of batches that minimizes the weighted number of tardy jobs. This problem was introduced by Hochbaum and Landy (Oper Res Lett 16(2):79–86, 1994); as a wide generalization of Knapsack, it is $$\textsf{NP}$$ NP -hard. In this work, we provide a multivariate complexity analysis of the $$1\vert \text {s-batch}(\infty ), r_j\vert \sum w_jU_j$$ 1 | s-batch ( ∞ ) , r j | ∑ w j U j problem with respect to several natural parameters. That is, we establish a classification into fixed-parameter tractable and $$\textsf{W}[1]$$ W [ 1 ] -hard problems, for parameter combinations of (i) $$\#p$$ # p = number of distinct processing times, (ii) $$\#w$$ # w = number of distinct weights, (iii) $$\#d$$ # d = number of distinct due dates, (iv) $$\#r$$ # r = number of distinct release dates. Thereby, we significantly extend the work of Hermelin et al. (Ann Oper Res 298:271–287, 2018) who analyzed the parameterized complexity of the non-batch variant of this problem without release dates. As one of our key results, we prove that $$1\vert \text {s-batch}(\infty ), r_j\vert \sum w_jU_j$$ 1 | s-batch ( ∞ ) , r j | ∑ w j U j is $$\textsf{W}[1]$$ W [ 1 ] -hard parameterized by the number of distinct processing times and distinct due dates. To the best of our knowledge, these are the first parameterized intractability results for scheduling problems with few distinct processing times. Further, we show that $$1\vert \text {s-batch}(\infty ), r_j\vert \sum w_jU_j$$ 1 | s-batch ( ∞ ) , r j | ∑ w j U j is fixed-parameter tractable parameterized by $$\#d + \#p + \#r$$ # d + # p + # r , and parameterized by $$\#d + \#w$$ # d + # w if there is just a single release date. Both results hold even if the number of jobs per batch is limited by some integer b.

Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.

Minimizing the number of tardy jobs with generalized due-dates and position-dependent processing times

Minimizing the number of tardy jobs with generalized due-dates and position-dependent processing times

A clustering-aided multi-agent deep reinforcement learning for multi-objective parallel batch processing machines scheduling in semiconductor manufacturing

Batch processing machines are often the bottleneck in semiconductor manufacturing and their scheduling plays a key role in production management. Pioneer researches on multi-objective batch machines scheduling mainly focus on evolutionary algorithms, failing to meet the online scheduling demand. To deal with the challenges confronted by incompatible job families, dynamic job arrivals, capacitated machines and multiple objectives, we propose a clustering-aided multi-agent deep reinforcement learning approach (CA-MADRL) for the scheduling problem. Specifically, to achieve diverse nondominated solutions, an offline multi-objective scheduling algorithm named Multi-Subpopulation fast elitist Non-Dominated Sorting Genetic Algorithm (MS-NSGA-II) is firstly developed to obtain the Pareto Fronts, and a clustering algorithm based on cosine distance is employed to analyze the distribution of Pareto frontier solution, which would be used to guide reward functions design in multi-agent deep reinforcement learning. To realize multi-objective optimization, several reinforcement learning base models are trained for different optimization directions, each of which composed of batch forming agent and batch scheduling agent. To alleviate time complexity of model training, a parameter sharing strategy is introduced between different reinforcement learning base model. By validating the proposed approach with 16 instances designed based on actual production data from a semiconductor manufacturing company, it has been demonstrated that the approach not only meets the high-frequency scheduling requirements of manufacturing systems for parallel batch processing machines but also effectively reduces the total job tardiness and machine energy consumption.

Scheduling in a Simple Assembly Robotics Cell to Minimize Earliness and Tardiness

Background: Robotics Assembly Cells (RAC) have been designed to meet the flexibility requirements demanded by today's globalized market. The objective is to manufacture a vast variety of products at a low cost, which requires equipment with a high level of flexibility, such as robots. The need to schedule a great variety of jobs in an RAC is a very relevant issue, as efficiency and productivity depend on the sequence in which jobs are scheduled. Studies around this matter have developed models with analytical and heuristic approaches, as well as simulation methods and genetic algorithms, seeking to improve performance measures based mainly on time, utilization, and costs. Method: The purpose of this article is to formulate an exact mathematical model using mixed-integer linear programming (MILP) to optimize small scheduling problems. The objective is to minimize the measure of performance related to the tardiness and earliness of jobs. This optimization aims to mitigate the effects of delays in product deliveries, queue times, and work-in-process inventory in subsequent processes. Doing so facilitates adherence to agreed-upon delivery deadlines and prevents bottlenecks in the assembly cell. Results: The proposed mathematical model generates optimal solutions to the job scheduling problem in the assembly cell, which serves as a case study. This addresses the need to minimize tardiness to meet delivery deadlines or minimize earliness while avoiding an increase in work-in-process inventories. The model ensures that optimal scheduling decisions are made to optimize both delivery performance and inventory levels. Conclusions: Due to the NP-hard complexity of the scheduling problem under study, the proposed mathematical model demonstrates computational efficiency in solving scheduling problems with fewer than 20 jobs. The model is designed to handle such smaller-scale problems within a reasonable computational time frame, considering the inherent complexity of the scheduling problem.

A distributionally robust approach for the parallel machine scheduling problem with optional machines and job tardiness

This paper investigates a parallel machine scheduling problem with uncertain job processing time, where the job tardiness and optional machines are considered. To address the factor of energy saving, only a subset of all available machines are turned on, which is referred to as not-all-machine (NAM). To depict the uncertain processing time, a mean–mean absolute deviation (MAD) ambiguity set is utilized, and the cost of job tardiness is minimized under the worst-case distribution scenario over the ambiguity set. After building a distributionally robust optimization (DRO) model, theoretical bounds of the optimal number of machines are obtained. Since the model is not computationally scalable, an upper bound on its inner minimization problem is employed, and a mixed integer linear programming (MILP) approximation is obtained based on McCormick inequalities. For the DRO model, tailored speedup techniques are employed, significantly enhancing the computational performance. To evaluate the validity of the proposed DRO model, we compare it with its stochastic programming (SP) counterpart under various parameter settings. Numerical experiments demonstrate that the DRO model exhibits strong performance in the worst-case scenarios. As the problem size increases, the DRO model casts clear advantages over the SP model in terms of computational efficiency and reliability. It is observed that the performance of the DRO model is more stable than that of the nominal sequence, especially with loose due dates. Furthermore, the out-of-sample performance under various decision making preferences shed new lights into the trade-off between energy saving and production efficiency.

Minimizing Conditional Mean Tardiness and Mean Earliness on a Single Machine with the due Windows Approach

A Multicriteria scheduling problem that involves four due date-based performance measures; the total tardiness, proportion of tardy jobs, total earliness as well as the proportion of early jobs was reduced to an equivalent bicriteria problem of minimizing conditional mean Tardiness and conditional mean earliness. A schedule that optimizes these measures tend towards an ideal Just-In-Time (JIT) schedule. Two solution methods named GOA 1 and GOA 2 were proposed to solve the equivalent reduced problem. A single machine and due window approach was explored. The ideal JIT schedule with zero tardiness and zero earliness was set as the optimal and used for benchmarking the proposed solution as well as other methods found in the literature. The results show that the proposed heuristics yielded results that are not significantly different from the optimal in some instances.

Improving production and maintenance planning with meta-learning-based failure prediction

Digital manufacturing systems allow for dynamic production and maintenance planning adaptation based on internal and external evolving changes. In this context, data-driven predictive techniques can improve maintenance planning. However, dynamic production environments require the development of novel methods capable of efficiently managing the extensive data generated by manufacturing systems and processes while providing valuable insights for decision-making. Thus, this research proposes an integrated production and maintenance planning (IPMP) approach for digital manufacturing systems featuring a dynamic simulation-based optimization and a meta-learning-based failure prediction, which selects the best prognostic method to predict machine failures in real-time. The proposed model was applied to the Minifab case, in the semiconductor industry, providing a reduction of 20.9 % in lead time and 25.9 % in tardy jobs compared to setups with static dispatching rules and single-prognostic-method failure prediction. Such findings support the pertinence of the proposed novel approach in the area of production planning and control, contributing to the improvement of business performance, reliability, and competitiveness.

Scheduling with jobs at fixed positions

In this paper, we study classical single machine scheduling problems with the additional constraint that a set of special jobs must be scheduled at certain positions in the job sequence. In other words, a special job must start when a certain number of jobs have finished on the machine. We analyze several classical objective functions for this more general setting with the additional constraint of fixed positioned jobs. We show that for some of them they are still polynomially solvable. Then, we focus on the objective of minimizing the number of tardy jobs. Considering the case of just one special job, this allows for a polynomial-time algorithm.

Energy, cost and job-tardiness-minimized scheduling of energy-intensive and high-cost industrial production systems

Energy consumption, production cost, and efficiency are highly concerned by decision makers of energy-intensive and high-cost industrial production systems. Intelligent production scheduling is a necessary means to achieve their optimization. This work delves into a novel multi-objective production scheduling problem arising from a steel hot-rolling process, which is a representative energy-intensive and high-cost industrial process. The challenge of the problem involves scheduling customized production jobs subject to intricate process constraints with the goal to minimize three objective functions, i.e., energy consumption, setup cost, and the number of tardy jobs. A mixed integer linear programming model is formulated for the problem. In order to solve it, an improved multi-objective evolutionary algorithm based on decomposition is presented. The algorithm incorporates problem-specific encoding and model-based decoding mechanisms, rendering it well-suited for addressing the concerned multi-constrained multi-objective optimization problem. The introduced modified Tchebycheff approach mitigates the impact of objective functions with varying value ranges on the algorithm’s convergence. Additionally, a Metropolis acceptance criterion is integrated to facilitate the escape from local optimal solutions, enhancing the algorithm’s global optimization capability. Numerous experiments are conducted to verify the effectiveness of the improvements and to compare the performance of the presented algorithm against its competitive peers. The results demonstrate its high performance, suggesting its significant potential for its application to steel hot-rolling systems.

Improved genetic algorithm for solving the total weight tardiness job shop scheduling problem

An improved genetic algorithm is proposed for the Job Shop Scheduling Problem with Minimum Total Weight Tardiness (JSSP/TWT). In the proposed improved genetic algorithm, a decoding method based on the Minimum Local Tardiness (MLT) rule of the job is proposed by using the commonly used chromosome coding method of job numbering, and a chromosome recombination operator based on the decoding of the MLT rule is added to the basic genetic algorithm flow. As a way to enhance the quality of the initialized population, a non-delay scheduling combined with heuristic rules for population initialization. and a PiMX (Precedence in Machine crossover) crossover operator based on the priority of processing on the machine is designed. Comparison experiments of simulation scheduling under different algorithm configurations are conducted for randomly generated larger scale JSSP/TWT. Statistical analysis of the experimental evidence indicates that the genetic algorithm based on the above three improvements exhibits significantly superior performance for JSSP/TWT solving: faster convergence and better scheduling solutions can be obtained.

No-Idle Flow Shop Scheduling with Deteriorating Jobs and Common Due Date Under Dominating Machines

The phenomenon of deterioration effects can reduce production efficiency caused by extended start time or other factors. Based on it, this paper considers the scheduling situations of the common due date assignment in a no-idle flow shop scheduling environment. Under the given four dominating relationships (i.e., increasing, decreasing, increasing-decreasing and decreasing-increasing dominating machines, correspondingly expressed as idm, ddm, idm–ddm and ddm–idm) between machines, the objective functions are, respectively, to minimize (1) the weighted sum of common due date and total earliness; and (2) the weighted sum of common due date, total earliness and total penalty factors of tardy jobs. It is verified that these problems can be solved in polynomial time under four dominating relationships.

A genetic algorithm for fuzzy identical parallel machine scheduling of minimising total weighted tardiness under resource constraint

Due to the severity of resource consumption and uncertainty in orders, new challenges have arisen for production scheduling in enterprises. This paper studies the scheduling problem of minimising the total weighted tardiness for jobs with fuzzy processing times and due dates on identical parallel machines with resource constraint. To address this research problem, we first propose methods to calculate the upper bound of resource consumption and the maximum number of machines that can be used, effectively reducing the search space and improving the algorithm's efficiency. Secondly, a local search algorithm based on job swapping is proposed to enhance the algorithm's performance. Then, repair algorithms based on job removal and job swapping are designed to repair infeasible solutions. Finally, we propose a fuzzy genetic algorithm (FGALS) to solve the problem based on the above elements. Through extensive simulation experiments, the effectiveness and efficiency of the FGALS algorithm are verified by comparing it with commercial solver Gurobi and several meta-heuristic algorithms.

Quantum annealing-driven branch and bound for the single machine total weighted number of tardy jobs scheduling problem

In the paper we present a new approach to solving NP-hard problems of discrete optimization adapted to the architecture of quantum processors (QPU, Quantum Processor Unit) implementing hardware quantum annealing. This approach is based on the use of the quantum annealing metaheuristic in the exact branch and bound algorithm to compute the lower and upper bounds of the objective function. To determine the lower bound, a new method of defining the Lagrange function for the dual problem (the generalized discrete knapsack problem) was used, the value of which is calculated on the QPU of a quantum machine. In turn, to determine the upper bound, we formulate an appropriate task in the form of binary quadratic programming with constraints.Despite the fact that the results generated by the quantum machine are probabilistic, the hybrid method of algorithm construction proposed in the paper, using alternately a CPU and QPU, guarantees the optimal solution. As a case study we consider the NP-hard single machine scheduling problem with minimizing the weighted number of tardy jobs. The performed computational experiments showed that optimal solutions were already obtained in the root of the solution tree, and the values of the lower and upper bounds differ by only a few percent.

Multitasking scheduling with job switching allowed between alternate periods

This paper explores the multitasking scheduling problem via alternate periods, which is common in manufacturing and service industries. The shift pattern comprises regular shifts interspersed with breaks, allowing job switching. We focus on two alternate periods consisting of odd periods and even periods. Each job is not only processed completely within odd periods or completely within even periods, but job switching is also allowed between alternate periods with additional overhead. For this problem, we propose two job switching models. The first model is alternate periods multitasking scheduling with switching time, where a fixed switching time is incurred whenever a job is switched from one period to its adjacent period. The second model is alternate periods multitasking scheduling with diverse speeds, where an urgent switching cost is produced if a job is processed through the alternate periods with different speeds. For the two models, we study three scheduling objectives including minimising the total completion time, minimising the maximum lateness, and minimising the number of tardy jobs, respectively. For each of the problems under consideration, we investigate the structural properties of the optimal schedule and develop the corresponding pseudo-polynomial time dynamic programming algorithm. Furthermore, we give examples to effectively illustrate the proposed algorithms.

Using Local Search Methods for Solving Two Multi-Criteria Machine Scheduling Problems

In this paper, we have improved solutions for two of the Multi-Criteria Machine Scheduling Problems (MCMSP). These problems are to maximize early jobs time and range of lateness jobs times (1//(E_max,R_L ), and the second problem is maximum tardy jobs time and range of lateness jobs times (1//(T_max,R_L ) in a single machine with Multi-Objective Machine Scheduling Problems (MOMSP) 1//(E_max+R_L ) and 1//(T_max+R_L ) which are derived from the main problems respectively. The Local Search Methods (LSMs), Bees Algorithm (BA), and a Simulated Annealing (SA) are applied to solve all suggested problems. Finally, the experimental results of the LSMs are compared with the results of the Branch and Bound (BAB) method for a reasonable time. These results are ensuring the efficiency of LSMs.

Minimizing the Weighted Number of Tardy Jobs via (max,+)-Convolutions

In this paper we consider the fundamental scheduling problem of minimizing the weighted number of tardy jobs on a single machine. We present a simple pseudo polynomial-time algorithm for this problem that improves upon the classical Lawler and Moore algorithm from the late 60’s under certain scenarios and parameter settings. Our algorithm uses (max,+)-convolutions as its main tool, exploiting recent improved algorithms for computing such convolutions, and obtains several different running times depending on the specific improvement used. We also provide a related lower bound for the problem under a variant of the well-known Strong Exponential Time Hypothesis (SETH). History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported by the Israel Science Foundation [Grant 1070/20].

Single machine adversarial bilevel scheduling problems

We consider single machine scheduling problems in the context of adversarial bilevel optimization where two agents, the leader and the follower, take decisions on the same jobset and the leader acts first with the aim of inducing the worst possible solution for the follower. Thus, the follower schedules the jobs in order to optimize a given criterion. The considered criteria are the total completion time, the total weighted completion time, the maximum lateness and the number of tardy jobs. We focus on adversarial bilevel scheduling with job selection and data modification. In the case with job selection, the leader selects a fixed cardinality subset of the jobs that the follower schedules next. In the case with data modification, the leader can modify some of the data (processing times, due dates, weights), given a limited budget Q. Thus, the follower schedules the set of jobs with modified data. For all the considered criteria either we provide polynomial-time algorithms or show that they can be solved in the worst-case in pseudo-polynomial time.

Integrated maintenance and production scheduling for unrelated parallel machines with setup times

This paper considers jointly scheduling the production and resource-constrained maintenance activities in a manufacturing setting with unrelated parallel machines. In particular, a single maintenance activity needs to be scheduled on each machine in one of its available time windows, and the maintenance activities require a scarce resource, thereby limiting the number of maintenance activities that can be scheduled simultaneously on different machines. In addition, machine- and sequence-dependent setup times, machine eligibility constraints and job-specific release and due dates are considered. A mixed-integer linear program is formulated with objectives including the makespan and, motivated from practice, a weighted sum of total production completion times at machines and total job tardiness. Additionally, a hybrid genetic algorithm with a novel solution representation is proposed for solving industry-scale large instances. A case study is performed with real-world data from a semiconductor manufacturer, where production and maintenance are scheduled separately. The benefit of simultaneously scheduling production and maintenance is investigated. Tests with real-world data show that the proposed model results in schedules that substantially improve the current factory practice.