Incompatible Families Research Articles

Metaheuristics for solving a flexible flow‐shop scheduling problem with s‐batching machines

AbstractA scheduling problem for a two‐stage flexible flow shop with s‐batching machines motivated by processes in additive manufacturing is considered. A batch is a group of jobs that are processed together on a single machine. Each job belongs to an incompatible family. Only jobs of the same family can be batched together. A maximum batch size is given. A setup time occurs between different batches. The jobs of a batch are processed in a serial manner, that is, the processing time of a batch is the sum of the processing times of the jobs forming the batch. Batch availability is assumed. A job has a weight, a due date, and a release date. The total weighted tardiness is considered as performance measure. We establish a mixed integer linear programming formulation for this scheduling problem. For large‐sized problem instances, an iterative decomposition approach (IDA) is proposed that uses a grouping genetic algorithm or an iterated local search (ILS) scheme to solve the single‐stage subproblems. Moreover, an alternative ILS scheme based on a disjunctive graph representation of the problem at hand is designed. Results of computational experiments based on randomly generated problem instances demonstrate that the IDA hybridized with ILS outperforms the two other schemes.

Incompatibility as a Resource for Programmable Quantum Instruments

Quantum instruments represent the most general type of quantum measurement, as they incorporate processes with both classical and quantum outputs. In many scenarios, it may be desirable to have some “on-demand” device that is capable of implementing one of many possible instruments whenever the experimenter desires. We refer to such objects as programmable instrument devices (PIDs), and this paper studies PIDs from a resource-theoretic perspective. A physically important class of PIDs are those that do not require quantum memories to implement, and these are naturally “free” in this resource theory. Additionally, these free objects correspond precisely to the class of unsteerable channel assemblages in the study of channel steering. The traditional notion of measurement incompatibility emerges as a resource in this theory since any PID controlling an incompatible family of instruments requires a quantum memory to build. We identify an incompatibility preorder between PIDs based on whether one can be transformed into another using processes that do not require additional quantum memories. Necessary and sufficient conditions are derived for when such transformations are possible based on how well certain guessing games can be played using a given PID. Ultimately our results provide an operational characterization of incompatibility, and they offer semi-device-independent tests for incompatibility in the most general types of quantum instruments. Published by the American Physical Society 2024

A Metaheuristic Framework for Energy-Intensive Industries With Batch Processing Machines

Batch processing machines, which operate multiple jobs at a time, are commonly used in energy-intensive industries. A significant amount of energy can be saved in such industries using production scheduling as an approach to enhance efficiency. This study deals with an energy-aware scheduling problem for parallel batch processing machines with incompatible families and job release times. In such an environment, a machine may need to wait until all the jobs in the next batch become ready. During waiting time, a machine can be switched <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> or kept <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> standby for more energy-efficient scheduling. We first present a mixed-integer linear programming (MILP) model to solve the problem. However, the presented MILP model can only solve small problem instances. We therefore propose an energy-efficient tabu search (ETS) algorithm for solving larger problem instances. The proposed solution framework incorporates multiple neighborhood methods for efficient exploration of the search space. An energy-related heuristic is also integrated into the ETS for minimizing energy consumption during the waiting time. The performance of our proposed ETS algorithm is validated by comparing it with CPLEX for small problem instances and with two other heuristic algorithms for larger problem instances. The contribution of different components in ETS is also established in our experimental studies. The proposed solution framework is expected to bring many benefits in energy-intensive industries both economically and environmentally.

A Hybrid Large Neighborhood Search Method for Minimizing Makespan on Unrelated Parallel Batch Processing Machines with Incompatible Job Families

This paper studies a scheduling problem with non-identical job sizes, arbitrary job ready times, and incompatible family constraints for unrelated parallel batch processing machines, where the batches are limited to the jobs from the same family. The scheduling objective is to minimize the maximum completion time (makespan). The problem is important and has wide applications in the semiconductor manufacturing industries. This study proposes a mixed integer programming (MIP) model, which can be efficiently and optimally solved by commercial solvers for small-scale instances. Since the problem is known to be NP-hard, a hybrid large neighborhood search (HLNS) combined with tabu strategy and local search is proposed to solve large-scale problems, and a lower bound is proposed to evaluate the effectiveness of the proposed algorithm. The proposed algorithm is evaluated on numerous compatible benchmark instances and newly generated incompatible instances. The results of computational experiments indicate that the HLNS outperforms the commercial solver and the lower bound for incompatible problems, while for compatible problems, the HLNS outperforms the existing algorithm. Meanwhile, the comparison results indicate the effectiveness of the tabu and local search strategies.

A Production Plan Considering Parallel Machines and Deteriorating Effects: Minimizing the Makespan in the Section of Steel Box Girder Processing

With the popularization of energy conservation and emission reduction, amounts of industrial production has taken energy conservation as a goal to achieve. The paper considers an online parallel-batch scheduling problem with deteriorating and incompatible families on identical machines to minimize the makespan, which minimizes the maximum energy consumption of machines. Specifically, the processing time of job [Formula: see text] is defined by an increasing function of its starting time [Formula: see text], i.e., [Formula: see text], where [Formula: see text] is the deterioration rate of job [Formula: see text]. For the problem, we propose an online algorithm with a competitive ratio of [Formula: see text], where [Formula: see text] is the largest deterioration rate in an instance. Furthermore, the paper presents a concise computational study of the numerical experiment to show that our algorithm performs very well in practice of this model.

Parallel batching with multi-size jobs and incompatible job families

Parallel batch scheduling has many applications in the industrial sector, like in material and chemical treatments, mold manufacturing and so on. The number of jobs that can be processed on a machine mostly depends on the shape and size of the jobs and of the machine. This work investigates the problem of batching jobs with multiple sizes and multiple incompatible families. A flow formulation of the problem is exploited to solve it through two column generation-based heuristics. First, the column generation finds the optimal solution of the continuous relaxation, then two heuristics are proposed to move from the continuous to the integer solution of the problem: one is based on the price-and-branch heuristic, the other on a variable rounding procedure. Experiments with several combinations of parameters are provided to show the impact of the number of sizes and families on computation times and quality of solutions.

Scheduling identical parallel batch processing machines involving incompatible families with different job sizes and capacity constraints

This paper investigates the problem of scheduling jobs on parallel batch processing machines with incompatible job families, non-identical job sizes, arbitrary job release times, and machine capacity constraints. A mixed-integer linear programming (MILP) model is established to minimize makespan. A lower bound is proposed to test the solution quality obtained from heuristic and metaheuristic algorithms. Since the problem is strongly NP-hard, we propose five constructive and polynomially bounded heuristic algorithms. To improve the solutions obtained by these constructive algorithms, we describe a job family constraint-guided artificial immune system (CGAIS) based algorithm. In the proposed CGAIS algorithm, only jobs in the same family can be executed by the secondary immune response. The longest batch processing time rule is used to form the batches. The effectiveness of the proposed constructive and the CGAIS algorithms is empirically tested on the randomly generated problem instances. These computational results show that the proposed CGAIS algorithm can obtain better near-optimal solutions than the existing algorithms.

The family traveling salesman problem with incompatibility constraints

AbstractIn this article, we propose a new variant of the family traveling salesman problem (FTSP). The FTSP is an NP‐hard problem that generalizes the traveling salesman problem. In the FTSP, the set of cities is partitioned into several families and one wants to find the minimum cost route that visits a given number of cities in each family. A new variant arises by introducing incompatibilities between families, that is, cities from incompatible families cannot be visited in the same route, and it is called the FTSP with incompatibility constraints (FTSP‐IC). We propose compact and non‐compact mixed integer linear programming models for the FTSP‐IC where the incompatibility constraints are modeled by defining paths in a compatibility graph for each family. Additionally, we present a set of valid inequalities motivated by the incompatible families. The non‐compact models and the valid inequalities were tested using a branch‐and‐cut framework. To evaluate the models we generated incompatibility matrices for benchmark instances of the FTSP, which are available in the website http://familytsp.rd.ciencias.ulisboa.pt/. With the branch‐and‐cut algorithm, we were able to obtain the optimal value of instances with up to 127 nodes. We also developed an ant colony optimization (ACO) algorithm and an iterated local search algorithm (ILS) to address the largest sized instances. Both metaheuristics are able to provide solutions for instances that the branch‐and‐cut algorithm cannot address and to improve the majority of the upper bounds obtained by the branch‐and‐cut algorithm in less computational time.

Online Scheduling of Incompatible Family Jobs with Equal Length on an Unbounded Parallel-Batch Machine with Job Delivery

In this paper, we consider the online scheduling of incompatible family jobs with equal length on an unbounded parallel-batch machine with job delivery. The jobs arrive online over time and belong to [Formula: see text] incompatible job families, where [Formula: see text] is known in advance. The jobs are first processed in batches on an unbounded parallel-batch machine and then the completed jobs are delivered in batches by a vehicle with infinite capacity to their customers. The jobs from distinct families cannot be processed and delivered in the same batch. The objective is to minimize the maximum delivery completion time of the jobs. For this problem, we present an online algorithm with the best competitive ratio of [Formula: see text].

Constraint Programming Approach for Scheduling Jobs With Release Times, Non-Identical Sizes, and Incompatible Families on Parallel Batching Machines

We study a parallel batch-scheduling problem that involves the constraints of different job release times, non-identical job sizes, and incompatible job families, is addressed. Mixed integer programming and constraint programming (CP) models are proposed and tested on a set of common problem instances from a paper in the literature. Then, we compare the performance of the models with that of a variable neighborhood search (VNS) heuristic from the same paper. Computational results show that CP outperforms VNS with respect to solution quality and run time by 3.4%–6.8% and 47%–91%, respectively. When compared to optimal solutions, the results demonstrate CP is capable of generating a near optimal solution in a short amount of time.

Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities

We consider the problem of scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities to minimize makespan. A job can only be assigned to a machine whose capacity is not less than the size of the job. A machine can process a group of jobs as a batch simultaneously, as long as the total size of the jobs in this batch does not exceed the capacity of the machine. The processing time of a batch is equal to the longest processing time of all the jobs in the batch. For the case of equal release times, we obtain a fast 5-approximation algorithm, as well as an algorithm with approximation ratio arbitrarily close to 2. For the case of unequal release times and a fixed number of different batch capacities, we obtain an algorithm with approximation ratio arbitrarily close to 2. We also study the problem of scheduling jobs with equal release times, arbitrary sizes, inclusive processing set restrictions and incompatible families on batch machines with identical capacities to minimize makespan. We obtain a 8/3-approximation algorithm, as well as an algorithm with approximation ratio arbitrarily close to 2. If only a single family is considered, a 2-approximation algorithm is presented. It is likely that these results cannot be too substantially improved upon, since all of the problems studied cannot be approximated to within a ratio smaller than 2 unless P=NP.

Online batch scheduling with kind release times and incompatible families to minimize makespan

This paper studies online scheduling of jobs with incompatible families on a single unbounded batch machine under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when the machine is busy. The goal is to determine a feasible schedule to minimize the makespan. We provide a best online algorithm with a competitive ratio of $$1+\frac{\sqrt{f^{2}-f+1}-1}{f}$$ , where f is the number of job families.

Full-batch-oriented scheduling algorithm on batch processing workstation of β1→β2 type with re-entrant flow

This paper focuses on the scheduling problem of batch processing workstation (BPW) of β1→β2 type in semiconductor wafer fabrication (SWF). The constraints consist of incompatible families, limited waiting time, and re-entrant flow. BPW is a bottleneck in SWF. In order to ensure BPW that can process full-batch continuously, a new pull-based scheduling algorithm is proposed. According to collaborative strategy, the pull-based scheduling algorithm consists of three sub-algorithms. They are one-to-one forming batch sub-algorithm, two-to-one forming batch sub-algorithm, and pulling preceding jobs sub-algorithm. The experiments are implemented on a scheduling simulation platform of SWF. In the whole scheduling horizon, the three sub-algorithms are executed circularly. The results show that the proposed approach obtains better solutions.

A hybrid tabu search for batching and sequencing decisions in a single machine environment

This paper proposes a hybrid tabu search (HTS) to minimise the total weighted tardiness (TWT) for the batching and sequencing of jobs originating from incompatible families in which sequence dependent family setup times exist on single machine. The developed HTS includes distinguished features such as the strict arc based tabu classification along with dynamic tabu tenures, hybrid neighbourhood structures and iterative phases which consist of job and batch sequencing phases. The authors developed a testing methodology to determine the quality of the HTS solution. A mixed integer linear programing (MILP) model was developed to evaluate the optimality of the solution of the HTS for a small-size instance that consists of 640 problems. In addition, three dispatching rule heuristic combinations (EDD–EDD, EDD–BATCS and ATC–BATCS) were developed to test the HTS for large-size instances that deals with 1440 problems. The HTS provided comparable results with the MILP for small-size instances and outperformed the developed dispatching heuristics.

Improved online algorithms for the batch scheduling of equal-length jobs with incompatible families to maximize the weighted number of early jobs

We consider the online scheduling of equal-length jobs with incompatible families on \(m\) identical batch machines. Each job has a release time, a deadline and a weight. Each batch machine can process up to \(b\) jobs (which come from the same family) simultaneously as a batch, where \(b\) is called the capacity of the machines. Our goal is to determine a preemption-restart schedule which maximizes the weighted number of early jobs. For this problem, Li et al. (Inf Process Lett 112:503–508, 2012) provided an online algorithm of competitive ratio \(3+2\sqrt{2}\) for both \(b=\infty \) and \(b<\infty \). In this paper, we study two special cases of this problem. For the case that \(m=2\), we first present a lower bound 2, and then provide an online algorithm with a competitive ratio of 3 for both \(b=\infty \) and \(b<\infty \). For the case in which \(m=3\), \(b=\infty \) and all jobs come from a common family, we present an online algorithm with a competitive ratio of \((8+2\sqrt{15})/3\approx 5.249\).

Scheduling of parallel machines with sequence-dependent batches and product incompatibilities in an automotive glass facility

This application is motivated by a complex real-world scheduling problem found in the bottleneck workstation of the production line of an automotive safety glass manufacturing facility. The scheduling problem consists of scheduling jobs (glass parts) on a number of parallel batch processing machines (furnaces), assigning each job to a batch, and sequencing the batches on each machine. The two main objectives are to maximize the utilization of the parallel machines and to minimize the delay in the completion date of each job in relation to a required due date (specific for each job). Aside from the main objectives, the output batches should also produce a balanced workload on the parallel machines, balanced job due dates within each batch, and minimal capacity loss in the batches. The scheduling problem also considers a batch capacity constraint, sequence-dependent processing times, incompatible product families, additional resources, and machine capability. We propose a two-phase heuristic approach that combines exact methods with search heuristics. The first phase comprises a four-stage mixed-integer linear program for building the batches; the second phase is based on a Greedy Randomized Adaptive Search Procedure for sequencing the batches assigned to each machine. We conducted experiments on instances with up to 100 jobs built with real data from the manufacturing facility. The results are encouraging both in terms of computing time--5 min in average--and quality of the solutions--less than 10 % relative gap from the optimal solution in the first phase and less than 5 % in the second phase. Additional experiments were conducted on randomly generated instances of small, medium, and large size.

Code Switching in Sons and Lovers

Lawrence’s writing is heavily influenced by his social background. He is in an incompatible family, for his parents come from different social classes. His sensitiveness to class distinctions brought about by his family background is deeply rooted in his writings. Novel Sons and Lovers is this typical work. One of the distinctive features of the novel is the use of two language varieties which expresses the bilingual situation of the Morels’ family in Sons and Lovers. The writer Lawrence alternatively uses two language varieties in dialogues to reveal the psychology of the characters and the most characteristic of his theme: class conflict. This study researches into the use of language varieties of three major characters (Mr. Mo-rel, Mrs. Morel and their son Paul) in Sons and Loversfrom the viewpoint of code switching to discover how class conflict is presented by alternative use of language varieties. To appreciate and deeply understand the novel, it is necessary to know the application of code switching in this work.

Online scheduling of equal-length jobs with incompatible families on multiple batch machines to maximize the weighted number of early jobs

This paper studies the online scheduling of equal-length jobs with incompatible families on multiple batch machines which can process the jobs from a common family in batches, where each batch has a capacity b with b=∞ in the unbounded batching and b<∞ in the bounded batching. Each job J has an equal-length integral processing time p>0, an integral release time r(J)⩾0, an integral deadline d(J)⩾0 and a real weight w(J)⩾0. The goal is to determine a preemptive schedule with restart which maximizes the weighted number of early jobs. When p=1, we show that a simple greedy online algorithm has a competitive ratio 2, and establish the lower bound 2−1/b. This means that the greedy algorithm is of the best possible for b=∞. When p is any positive integer, we provide an online algorithm of competitive ratio 3+22 for both b=∞ and b<∞. This is the first online algorithm for the problem with a constant competitive ratio.

Metaheuristics for scheduling jobs with incompatible families on parallel batching machines

In this paper, we discuss the scheduling of jobs with incompatible families on parallel batching machines. The performance measure is total weighted tardiness. This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication where the machines can be modelled as parallel batch processors. Given that this scheduling problem is NP-hard, we suggest an ant colony optimization (ACO) and a variable neighbourhood search (VNS) approach. Both metaheuristics are hybridized with a decomposition heuristic and a local search scheme. We compare the performance of the two algorithms with that of a genetic algorithm (GA) based on extensive computational experiments. The VNS approach outperforms the ACO and GA approach with respect to time and solution quality.

Weighted nested partitions based on differential evolution (WNPDE) algorithm-based scheduling of parallel batching processing machines (BPM) with incompatible families and dynamic lot arrival

The scheduling problem of parallel batching processing machines (BPM) with incompatible families and dynamic lot arrivals in the diffusion and oxidation of semiconductor production line is studied. Given that the batch scheduling problem is NP-hard, it is decomposed into three sub-problems: batch forming, machine assignment and batch sequencing. A novel algorithm named weighted nested partitions based on differential evolution (WNPDE) is proposed for the most critical sub-problem: machine assignment sub-problem. The WNPDE retains the global perspective of nested partitions algorithm and the local search capabilities of differential evolution (DE) algorithm. Experimental results indicate that the proposed WNPDE algorithm has high efficiency to minimise the total weighted tardiness (TWT).