Single-machine scheduling with preventive periodic maintenance and resumable jobs in remanufacturing system

A single-machine scheduling with preventive periodic maintenance activities in a remanufacturing system including resumable and non-resumable jobs is studied.The objective is to find a schedule to minimize the makespan and an LPT-LS algorithm is proposed.Non-resumable jobs are first scheduled in a machine by the longest processing time（LPT） rule,and then resumable jobs are scheduled by the list scheduling（LS） rule.And the worst-case ratios of this algorithm in three different cases in terms of the value of the total processing time of the resumable jobs（denoted as S2） are discussed.When S2 is longer than the spare time of the machine after the non-resumable jobs are assigned by the LPT rule,it is equal to 1.When S2 falls in between the spare time of the machine by the LPT rule and the optimal schedule rule,it is less than 2.When S2 is less than the spare time of the machine by the optimal schedule rule,it is less than 2.Finally,numerical examples are presented for verification.

The single-machine scheduling problems with deteriorating jobs and learning effect

In this paper we consider a single-machine scheduling model with deteriorating jobs and simultaneous learning, and we introduce polynomial solutions for single machine makespan minimization, total flow times minimization and maximum lateness minimization corresponding to the first and second special cases of our model under some agreeable conditions. However, corresponding to the third special case of our model, we show that the optimal schedules may be different from those of the classical version for the above objective functions.

Single-machine scheduling of two activities with slack: CPM to minimize the total tardiness

In a CPM network, the longest path problem is one of the most important subjects. According to the intrinsic principle of CPM network, the length of the paths between arbitrary two nodes is presented. Furthermore, the length of the longest path from start node to arbitrary node and from arbitrary node to end node is proposed. In view of a scheduling problem of two activities with float in the CPM scheduling, we put forward Barycenter Theory and prove this theory based on the algorithm of the length of the longest path. By this theory, we know which activity should be done firstly. At last, we show our theory by an example.

An Improved Ant Colony Algorithm for a Single-machine Scheduling Problem with Setup Times

Motivated by industrial applications we study a single-machine scheduling problem in which all the jobs are mutu- ally independent and available at time zero.The machine processes the jobs sequentially and it is not idle if there is any job to be pro- cessed.The operation of each job cannot be interrupted.The machine cannot process more than one job at a time.A setup time is needed if the machine switches from one type of job to another.The objective is to find an optimal schedule with the minimal total jobs’completion time.While the sum of jobs’processing time is always a constant,the objective is to minimize the sum of setup times.Ant colony optimization(ACO)is a meta-heuristic that has recently been applied to scheduling problem.In this paper we propose an improved ACO-Branching Ant Colony with Dynamic Perturbation(DPBAC)algorithm for the single-machine schedul- ing problem.DPBAC improves traditional ACO in following aspects:introducing Branching Method to choose starting points;im- proving state transition rules;introducing Mutation Method to shorten tours;improving pheromone updating rules and introduc- ing Conditional Dynamic Perturbation Strategy.Computational results show that DPBAC algorithm is superior to the traditional ACO algorithm.

Neighborhood Combination Search for Single-Machine Scheduling with Sequence-Dependent Setup Time

In a local search algorithm,one of its most important features is the definition of its neighborhood which is crucial to the algorithm's performance.In this paper,we present an analysis of neighborhood combination search for solv-ing the single-machine scheduling problem with sequence-dependent setup time with the objective of minimizing total weighted tardiness(SMSWT).First,We propose a new neighborhood structure named Block Swap(B1)which can be con-sidered as an extension of the previously widely used Block Move(B2)neighborhood,and a fast incremental evaluation technique to enhance its evaluation efficiency.Second,based on the Block Swap and Block Move neighborhoods,we present two kinds of neighborhood structures:neighborhood union(denoted by B1UB2)and token-ring search(denoted by B1→B2),both of which are combinations of B1 and B2.Third,we incorporate the neighborhood union and token-ring search into two representative metaheuristic algorithms:the Iterated Local Search Algorithm(ILSnew)and the Hybrid Evolutionary Algorithm(HEA_(new))to investigate the performance of the neighborhood union and token-ring search.Exten-sive experiments show the competitiveness of the token-ring search combination mechanism of the two neighborhoods.Tested on the 120 public benchmark instances,our HEA_(new)has a highly competitive performance in solution quality and computational time compared with both the exact algorithms and recent metaheuristics.We have also tested the HEA,new algorithm with the selected neighborhood combination search to deal with the 64 public benchmark instances of the single-machine scheduling problem with sequence-dependent setup time.HEAnew is able to match the optimal or the best known results for all the 64 instances.In particular,the computational time for reaching the best well-known results for five chal-lenging instances is reduced by at least 61.25%.

A branch-and-price algorithm to perform single-machine scheduling for additive manufacturing

Additive manufacturing(AM)has attracted significant attention in recent years based on its wide range of applications and growing demand.AM offers the advantages of production flexibility and design freedom.In this study,we considered a practical variant of the batch-processing-machine(BPM)scheduling problem that arises in AM industries,where an AM machine can process multiple parts simultaneously,as long as the twodimensional rectangular packing constraint is not violated.Based on the set-partitioning formulation of our mixed-integer programming(MIP)model,a branch-and-price(B&P)algorithm was developed by embedding a column-generation technique into a branchand-bound framework.Additionally,a novel labelling algorithm was developed to accelerate the column-generation process.Ours is the first study to provide a B&P algorithm to solve the BPM scheduling problem in the AM industry.We tested the performance of our algorithm using a modern MIP solver(Gurobi)and real data from a 3D printing factory.The results demonstrate that for most instances tested,our algorithm produces results similar or identical to those of Gurobi with reasonable computation time and outperforms Gurobi in terms of solution quality and running time on some large instances.

A dynamic programming algorithm for scheduling problems on earliness award and tardiness penalty with time-dependent processing time

In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total weighted earliness award and tardiness penalty. Our aim is to find an optimal schedule so as to minimize the objective function. As the problem is NP-hard, some properties and polynomial time solvable cases of this problem are given. A dynamic programming algorithm for the general case of the problem is provided.

Control of Neural Network Feedback Linearization Based on Chaotic Particle Swarm Optimization

A new chaotic particle swarm algorithm is proposed in order to avoid the premature convergence of the particle swarm optimization and the shortcomings of the chaotic optimization, such as slow searching speed and low accuracy when used in the multivariable systems or in large search space. The new algorithm combines the particle swarm algorithm and the chaotic optimization, using randomness and ergodicity of chaos to overcome the premature convergence of the particle swarm optimization. At the same time, a new neural network feedback linearization control system is built to control the single-machine infinite-bus system. The network parameters are trained by the chaos particle swarm algorithm, which makes the control achieve optimization and the control law of prime mover output torque obtained. Finally, numerical simulation and practical application validate the effectiveness of the method.