Dual Resource Constrained Job Shop Research Articles

A multi-method approach to scheduling and efficiency analysis in dual-resource constrained job shops with processing time uncertainty

In dual-resource constrained job shop scheduling, jobs have to be assigned to workers and machines. While the problem is notoriously hard in terms of computational complexity, additional practical difficulties arise from data uncertainty and worker efficiency variation. In this paper, we propose a methodological pipeline combining mathematical optimization, simulation, and data analysis to cope with these aspects over time. Accounting for uncertain worker processing times, we employ an iterative two-stage optimization-simulation approach: A first-stage optimization model determines an assignment of workers to jobs; in the second stage, the scheduling of this assignment is evaluated operationally using sampled realizations of worker processing times. Both stages are executed in an alternating fashion until no further improvement is possible in the average realized makespan. At the end of a work day, realized worker efficiencies are then measured in a slacks-based data envelopment analysis on the operations level. Workers learn about their individual efficiency and are prompted to reduce inefficiencies. The resulting overall methodology not only provides robustified schedules for dual-resource constrained job shops under uncertainty, but also reduces the impact of uncertainty over time by motivating workers to operate on the efficient frontier. Computational results are conducted in several settings with both heuristic and exact solution procedures for the second-stage dual-resource constrained job shop scheduling problem. The results demonstrate the versatility of the outline with respect to addressing uncertainty and worker inefficiency.

Threat elimination algorithm for Dual Resource Constrained Flexible Job Shop Scheduling Problems

This paper proposes an expert knowledge based algorithm for solving the Dual Resource Constrained Job Shop Scheduling Problem (DRC-FJSSP), the Biggest Threat First (BTF). The main idea behind this algorithm is that by eliminating your biggest threat, you get much closer to achieving your goal. Moreover, the BTF algorithm considers an encoded representation of the schedule, which combines 2 vectors: the Blacklist and the Deployment. The Blacklist sorts the major threats in descending order, while the Deployment vector allocates a worker-machine pair to tackle each assigned task. Results show that this method utterly outperforms a state-of-the-art metaheuristic, the KGFOA, at makespan minimization problems when applied to the MK1-10 benchmark dataset. Future work may access the algorithm's performance in problems with different performance metrics, such as the weighted tardiness. Moreover, research may be carried to apply the BTF to problems where the processing time of operations varies with the allocated worker-machine pair.

Ageing workforce effects in Dual-Resource Constrained job-shop scheduling

Currently, the ageing population is getting higher attention in production systems due to the increasing percentage of the ageing workforce, which persists longer in the working environment. Older workers are more vulnerable because of a possible decrease in physical capacities but can have a higher experience level. It is important to evaluate these factors during production process decisions and adapt the working environment to such workers. In such a way, production systems performance and workers’ well-being are jointly achieved. In companies aiming to include these aspects, digitalisation and automation can provide tools that can be used at tactical, strategic or operational levels. For example, at the operational level, wearable sensors, smart devices or trackers can be used in analysing the working time, effort and physical fatigue of operators via human-energy expenditure. These measures can be used to assess the required recovery time. However, the most challenging step is to include these measures in the decision-making process to organise the working process for operators according to their profiles and health restrictions. In this paper, we show how fatigue can be incorporated into operational processes such as scheduling in the context of a Dual-Resource Constrained (DRC) job shop. We consider several models to integrate rest allowance into the scheduling process and present a heuristic approach to assign operations to workers and machines. The impact of rest allowance on system performance is measured and managerial insights are provided.

A game theory model based on Gale-Shapley for dual-resource constrained (DRC) flexible job shop scheduling

Most job shops in practice are constrained by both machine and labor availability. Worker assignment in these so-called Dual Resource Constrained (DRC) job shops is typically solved in the literature via the use of meta-heuristics, i.e. “when” and “where” rules, or heuristic assignment rules. While the former does not necessarily lead to optimal results, the latter suffers from high computational time and complexity, especially when there is a large number of workstations. This paper uses game theory to propose a new worker assignment rule for DRC job shops. The Gale-Shapley model (also known as the stable marriage problem) forms a ‘couple’ made up of a worker and machine following a periodic review strategy. Simulation is used to evaluate and compare the proposed model to “when” and “where” rules previously proposed in the literature. Simulation experiments under different conditions demonstrate that the Gale-Shapley model provides better results for worker assignments in complex DRC systems, particularly when the workers have different efficiency levels. The implications of the findings for research and practice are outlined.

Reinforcement Learning for Dual-Resource Constrained Scheduling

Abstract This paper proposes using reinforcement learning to solve scheduling problems where two types of resources of limited availability must be allocated. The goal is to minimize the makespan of a dual-resource constrained flexible job shop scheduling problem. Efficient practical implementation is very valuable to industry, yet it is often only solved combining heuristics and expert knowledge. A framework for training a reinforcement learning agent to schedule diverse dual-resource constrained job shops is presented. Comparison with other state-of-the-art approaches is done on both simpler and more complex instances that the ones used for training. Results show the agent produces competitive solutions for small instances that can outperform the implemented heuristic if given enough time. Other extensions are needed before real-world deployment, such as deadlines and constraining resources to work shifts.

Optimization Algorithm Simulation for Dual-Resource Constrained Job-Shop Scheduling

Optimization Algorithm Simulation for Dual-Resource Constrained Job-Shop Scheduling

Dual-Resource Constraints in Classical and Flexible Job Shop Problems: A State-of-the-Art Review

The Job shop Scheduling Problem (JSP) is one of the most known problems in the domain of the production task scheduling. The Dual-Resource Constrained Job shop Scheduling Problem (DRCJSP) and the Dual-Resource Constrained Flexible Job shop Scheduling Problem (DRCFJSP) are two extensions of the classical JSP consisting of three sub-problems: (i) Assigning operations to resources of machines, (ii) Assigning operations to resources of workers; (iii) Sequencing the operations on the machines considering workers in order to optimize the performance measure. In this paper, we make a state-of-the-art review of the different works proposed for the DRCJSP and DRCFJSP, where we present a new classification schema according to six criteria such as the used method, the machine flexibility, the worker flexibility, the optimization criteria, the implemented approaches, and the structure of the approach.

A branch population genetic algorithm for dual-resource constrained job shop scheduling problem

The manufacturing systems constrained by both machines and heterogeneous workers are referred to as Dual Resource Constrained (DRC) systems. DRC scheduling problem has attracted more and more attention in recent years. In order to address the Dual Resource Constrained Job Shop Scheduling Problem (DRCJSP) to minimize the makespan and cost, a meta-heuristic algorithm named Branch Population Genetic Algorithm (BPGA) is proposed in this paper. The proposed algorithm is a genetic algorithm (GA) based scheduling approach, and it introduces the branch population to accumulate and transfer evolutionary experience of parent chromosomes via pheromone. The branch population can strengthen the population diversity and accelerate convergence. Additionally, several mechanisms are applied to optimize the performance of BPGA. The elite evolutionary operator is utilized to optimize search ability by laying particular emphasis on the evolution of the elite population. The roulette selection operator based on sector segmentation is proposed to decrease the computational complexity and avoid the algorithm prematurity. The scheduling strategy based on compressed time window is proposed to improve the global scheduling performance. In our research, BPGA shows convergence to the Pareto front according to the Markov chain theory. Numerical experiments with randomly generated examples and case studies are analyzed to evaluate the performance of the proposed algorithm. Computational experiments show BPGA can provide the promising results for the DRCJSP.

A hybrid discrete particle swarm optimization for dual-resource constrained job shop scheduling with resource flexibility

In this paper, a novel hybrid discrete particle swarm optimization algorithm is proposed to solve the dual-resource constrained job shop scheduling problem with resource flexibility. Particles are represented based on a three-dimension chromosome coding scheme of operation sequence and resources allocation. Firstly, a mixed population initialization method is used for the particles. Then a discrete particle swarm optimization is designed as the global search process by taking the dual-resources feature into account. Moreover, an improved simulated annealing with variable neighborhoods structure is introduced to improve the local searching ability for the proposed algorithm. Finally, experimental results are given to show the effectiveness of the proposed algorithm.

Simulated annealing approach to solve dual resource constrained job shop scheduling problems: layout impact analysis on solution quality

Real-world manufacturing systems are operating subject to a substantial level of resource constraints. One characteristic model that considers the combination of human and machine resource constraints is called dual resource constrained (DRC). In this context a number of machines nmach is managed by a selection of operators nop, with typically nop ≤ nmach.. A real life case study for an Italian manufacturing company is introduced that uses a set of identical parallel machines being operated by a set of operators. Each job is scheduled to one machine with corresponding loading and unloading process times. A simulated annealing approach is proposed to solve the DRC job shop scheduling problem. A sensitivity analysis is conducted for a selection of algorithm-specific parameters used to solve characteristic DRC layouts. Being characteristic for the just-in-time (JIT) production environment, the high variability in job times has also been taken into account. The results show that the selected layout nmach./nop ratio strongly influences the production system performance. The impact of the ratio of constrained resources has been analysed for different layouts, showing that simulated annealing performs better for single resource constrained problems while also demonstrating that this trend is not symmetrical for different layouts, either operator or machine constrained.

An effective neighborhood search for scheduling in dual-resource constrained interval job shop with environmental objective

In this study, scheduling problem in dual-resource constrained (DRC) job shop with interval processing time and heterogeneous resources is investigated. A lexicographical method is applied to minimize interval carbon footprint and makespan. A dynamical neighborhood search (DNS) is proposed, which is composed of two phases. Two-string representation is used and its chromosome consists of the operation-based string and the resource string. Several initial solutions are produced and improved in the first phase and only one solution is applied in the second phase. Four neighborhood structures and their dynamical transition mechanism are utilized to produce new solutions. DNS is tested on a number of instances and compared with other algorithms. Computational experiments show DNS can provide the promising results for the problem.

A practical method for evaluating worker allocations in large-scale dual resource constrained job shops

In two recent articles, Lobo et al. present algorithms for allocating workers to machine groups in a Dual Resource Constrained (DRC) job shop so as to minimize Lmax , the maximum job lateness. Procedure LBSA delivers an effective lower bound on Lmax , while the heuristic delivers an allocation whose associated schedule has a (usually) near-optimal Lmax value. To evaluate an HSP-based allocation’s quality in a given DRC job shop, the authors first compute the gap between HSP’s associated Lmax value and ’s lower bound. Next they refer this gap to the distribution of a “quasi-optimality” gap that is generated as follows: (i) independent simulation replications of the given job shop are obtained by randomly sampling each job’s characteristics; and (ii) for each replication, the associated quasi-optimality gap is computed by enumerating all feasible allocations. Because step (ii) is computationally intractable in large-scale problems, this follow-up article formulates a revised step (ii) wherein each simulation invokes , an improved version of , to yield an approximation to the quasi-optimality gap. Based on comprehensive experimentation, it is concluded that the -based distribution did not differ significantly from its enumeration-based counterpart; and the revised evaluation method was computationally tractable in practice. Two examples illustrate the use of the revised method.

Dual Resource Constrained Job Shop Dynamic Scheduling with Local Time Window

To solve the Dual Resource Constrained Job Shop Dynamic Scheduling Problem with heterogeneous workers (DRCJDSP-HW),a three-tier dynamic scheduling system including dynamic disturbance analysis, dynamic disturbance evaluation and dynamic scheduling method was constructed based on the idea of scheduling with local time window. To minimize the revision of old scheduling scheme in DRCJDSP-HW, a hybrid dynamic scheduling algorithm was proposed based on the chromosome reduction mechanism and the scheduling optimization of local job in stages. The outstanding application effect of the dynamic scheduling system and the hybrid dynamic scheduling algorithm were validated reducing the influence of dynamic disturbances effectively by simulation experiment at last.

Dual Resource Constrained Job Shop Scheduling Based on Compressed Time Window

To solve the double-objective Dual Resource Constrained Job-Shop Scheduling Problem with heterogeneous workers (DRCJSP-HW), a scheduling strategy based on compressed time window is proposed which compress and move up task time window to optimize global scheduling performance index at the expense of sacrificing scheduling performance of partial tasks. Against the limited ability of searching global optimum solution of Ant Colony algorithm and the slow convergence of genetic algorithm when solving double objective scheduling problem, the PBGA which inherit evolution experience of parent chromosome population with pheromone is designed. At last, simulation results demonstrate not only the satisfying optimization result of the scheduling strategy based on compressed time window but also the validity of the PBGA used for solving DRCJSP-HW.

An effective lower bound on [formula omitted] in a worker-constrained job shop

A common industrial operation is a dual resource constrained job shop where: (a) the objective is to minimize Lmax, the maximum job lateness; (b) machines are organized into groups; and (c) each worker is assigned to a specific machine group. Because this problem is NP-hard, finding optimal solutions by enumeration is impractical. This paper details a procedure to compute a lower bound on Lmax that will be used in follow-up work to effectively evaluate the absolute performance of heuristic solutions. Given an allocation of workers to machine groups, a lower bound on Lmax is first computed for each machine group using a network-flow formulation. The lower bound on Lmax for the job shop is the largest of the lower bounds for the machine groups. A search algorithm then finds a worker allocation yielding the smallest such lower bound on Lmax for the job shop; and the latter quantity is our proposed lower bound on Lmax. Given a worker allocation, we use the Virtual Factory (a heuristic scheduler developed by Hodgson et al. in 1998) to generate a schedule. Experiments with a wide variety of job shops indicated that the proposed lower bound on Lmax could often be achieved by a Virtual Factory schedule based on the worker allocation yielding this lower bound. However, there were problem instances for which other worker allocations enabled the Virtual Factory to generate better schedules. Follow-up work provides optimality criteria, and heuristics to find improved allocations if these criteria are not satisfied.

A New Hybrid Optimization Algorithm and its Application in Job Shop Scheduling

In this paper, a dual-resource constrained job shop scheduling problem was studied by designing a hybrid genetic algorithm based on Genetic Algorithm (GA) and Simulated Annealing (SA). GA is used to search for a group of better solutions to the problem of minimizing production cost and then SA is applied to searching them for the best one. The combination of GA and SA utilizes the advantages of the two algorithms and overcomes their disadvantages. The operation-based encoding and an active schedule decoding method were employed. This hybrid genetic algorithm reasonably assigns the resources of machines and workers to jobs and achieves optimum on some performance. The results of numerical simulations, which are compared with those of other well-known algorithms, show better performance of the proposed algorithm.

Adaptive Hybrid ant colony optimization for solving Dual Resource Constrained Job Shop Scheduling Problem

This paper presents a scheduling approach, based on Ant Colony Optimization (ACO), developed to address the scheduling problem in manufacturing systems constrained by both machines and heterogeneous workers called as Dual Resource Constrained Job Shop Scheduling Problem with Heterogeneous Workers. This hybrid algorithm utilizes the combination of ACO and Simulated Annealing (SA) algorithm and proposes a n adaptive control mechanism based on ant flow of route choice to improve the global search ability. Two adaptive adjusting schemes of parameter s based on iteration times and quality of solutions respectively are imposed to actualize the performance optimization by stages. Then the performances of different optimization methods with different resource allocation strategies are compared according to simulation experiments on both concrete instance and random benchmarks while related discussion are represented at last.

Research on Dual Resource Constrained Job Shop Scheduling Based on Time Window

An inherited genetic algorithm based on time window scheduling is proposed to solve the dual resource constrained job shop scheduling problem with complex manufacturing environment.This algorithm makes full use of the time window of workers during the process of numerical control machines based on the intersection of time windows to actualize positive scheduling.Then the evolutionary experience of parent chromosomes is inherited with pheromone as carrier and the branch population is generated with improved pseudo-random probability transfer rule and adaptive adjusting parameters based on cloud theory.The King crossover operator is proposed on the basis of imitating animal population organization mode and some resource evolutionary operators are introduced in response to the features of dual resource constrained.At last,an efficient roulette selection operator with sector partition is used to select Pareto-optimal solutions and better chromosomes.After the theoretical analysis of the global convergence via Markov chain,the statistical analysis on the simulation results of random benchmarks shows that this algorithm has strong search ability and good convergence performance.

Algorithm for Dual Resource Constrained Job Shop Scheduling

A hybrid ant colony algorithm is proposed to solve the dual resource constrained job shop scheduling problem with heterogeneous workers.Based on technological constraints and tabu search ideas,a candidate aggregate of result is built for every ant to contract the search space and improve the search efficiency.Some heuristic policies for resource allocation are imposed to actualize the best collocating of the machines and the worker forces during the ant routing process.Meanwhile,the simulated annealing algorithm is taken as a local search mechanism to improve the global convergence ability of the algorithm.After the theoretical analysis of the global convergence via Markov chain,according to the experiments and statistical analysis,the optimal combination of parameters and the optimal resource allocation policy are chosen.The hybrid ant colony algorithm has strong search ability and good robustness for this problem based on the result of comparing experiment on random benchmarks.

Worker flexibility in a parallel dual resource constrained job shop

In this paper we investigate cross-training policies in a dual resource constraint (DRC) parallel job shop where new part types are frequently introduced into the system. Each new part type introduction induces the need for workers to go through a learning curve. A cross-training policy relates to the level of multi-functionality, the pattern of skill overlaps, and the distribution of skills among workers. Our results show that the frequency of new part type introduction needs to be considered when selecting a cross-training policy. The frequency of new part type introduction has impact on the optimal level of cross-training, the relative advantage of skill overlaps, and the extent to which a cross-training policy should incorporate differences between workers. These findings are important for many DRC job shops, especially for manufacturing cells in which all changes, associated with a part type introduction, are concentrated in one cell.