Note on Scheduling with the Exponential Learning and Simple Linear Deterioration

A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems

Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration

The paper deals with some single-machine scheduling problems with setup time considerations where the processing time of a job is given as a function of its starting times and position in a sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (\( \delta \geqslant 0 \)) power of job completion times, the total weighted completion time, the maximum lateness and the number of tardy jobs. We show that the makespan minimization problem, the total completion time minimization problem, and the sum of the δth power of job completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.

ABSTRACTThis article addresses permutation flowshop scheduling problems with simple linear deterioration. The objectives are to minimize logarithm of the makespan, total logarithm of the completion time, total weighted logarithm of the completion time, and the sum of the quadratic job logarithms of the completion times. Approximation algorithms and their worst-case bounds are presented and analysed. Branch-and-bound algorithms are also proposed to solve the problems optimally. Computational experiments are performed to illustrate the algorithms.

In simple flow shop problems, each machine operation center includes just one machine. If at least one machine center includes more than one machine, the scheduling problem becomes a flexible flow shop problem (FFSP). Flexible flow shops are thus generalization of simple flow shops. Flexible flow shop scheduling problems have a special structure combining some elements of both the flow shop and the parallel machine scheduling problems. FFSP can be stated as finding a schedule for a general task graph to execute on a multiprocessor system so that the schedule length can be minimized. FFSP is known to be NP-hard. In this study, we present a particle swarm optimization (PSO) algorithm to solve FFSP. PSO is an effective algorithm which gives quality solutions in a reasonable computational time and consists of less numbers parameters as compared to the other evolutionary metaheuristics. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast towards near-optimal solution and hence reduce computational efforts further. The performance of schedules is evaluated in terms of total completion time or makespan (Cmax). The results are presented in terms of percentage deviation (PD) of the solution from the lower bound. The results are compared with different versions of genetic algorithm (GA) used for the purpose from open literature. The results indicate that the proposed PSO algorithm is quite effective in reducing makespan because average PD is observed as 2.961, whereas GA results in average percentage deviation of 3.559. Finally, influence of various PSO parameters on solution quality has been investigated.

On three-machine flow shop scheduling with deteriorating jobs

In order to solve the flow shop problem efficiently, an immune algorithm is proposed to solve the flow shop scheduling problem. The algorithm is designed according to the immune system mechanism of human or other higher animals, takes the scheduling objectives and constraints as the antigen, takes the solution of the problem as the antibody, encodes the antibody with natural numbers according to the workpiece processing order, and takes the reciprocal of the maximum process time as the fitness function. Through the introduction of isolation niche and other technologies, the adaptability of the immune algorithm is improved, the diversity of the population is ensured, and the premature convergence is overcome, The convergence speed is improved. The benchmark test of flow shop problem shows that the algorithm not only has good scalability in the scale of solving the problem, but also is lower than tabu search algorithm and simulated annealing algorithm in operation time, which verifies the effectiveness of the algorithm.

Single-machine scheduling with effects of exponential learning and general deterioration

In this paper, a network based formulation of a permutation flow shop problem is presented. Two nuances of flow shop problems with different levels of complexity are solved using different approaches to the linear programming formulation. Key flow shop parameters inclosing makespan of the flow shop problems were obtained without recourse to the traditional approach of using Gantt charts. The linear programming models of the flow shop problems considered were solved using LINGO 7.0. The present technique has been shown to be very effective and efficient.http://dx.doi.org/10.4314/njt.v34i2.11

Flexible flow shop scheduling with uniform parallel machines

In this paper we consider the flow shop scheduling problems with the effects of learning and deterioration. In this model the processing times of a job is defined as a function of its starting time and position in a sequence. The scheduling objective functions are makespan and total completion time. We prove that even with the introduction of learning effect and deteriorating jobs to job processing times, some special flow shop scheduling problems remain polynomially solvable.

Flow shop scheduling problems much studied by several researchers. One problem with scheduling is the tardiness. Total tardiness is the performance to minimize tardiness jobs. it is the right performance if there is a due date. This study proposes the Cross-Entropy Genetic Algorithm (CEGA) method to minimize the mean tardiness in the flow shop problem. In some literature, the CEGA algorithm is used in the case of minimizing the makespan. However, CEGA not used in the case of minimizing total tardiness. CEGA algorithm is a combination of the Cross-Entropy Algorithm which has a function to provide optimal sampling distribution and Genetic Algorithms that have functions to get new solutions. In some numeric experiments, the proposed algorithm provides better performance than some algorithms. For computing time, it is affected by the number of iterations. The higher the iteration, computing requires high time.

A two-stage flexible flow shop problem with unit-execution-time jobs and batching

In this paper, a parallel machine scheduling problem was considered, where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.

On the complexity and some properties of multi-stage scheduling problems with earliness and tardiness penalties