Multi-objective fuzzy parallel machine scheduling problems under fuzzy job deterioration and learning effects

Multi-objective parallel machine scheduling problem with job deterioration and learning effect under fuzzy environment

This chapter presents a mixed integer non-linear programming (MINLP) model for a fuzzy parallel machine scheduling problem under fuzzy job deterioration and learning effects with fuzzy processing times in order to minimize fuzzy makespan. The uncertainty of parameters such as learning/deterioration effects and processing times in a scheduling problem makes the solution of the problem uncertain. Fuzzy sets can be used to encode uncertainty in parameters. In this chapter, possibilistic distributions of fuzzy parameters and possibilistic linear programming approaches are used in order to create a solution method for MINLP model of fuzzy parallel machine scheduling problem.

This chapter considers a dynamic multi-objective machine scheduling problem in response to continuous arrival of new jobs with deterioration effect, under the assumption that jobs can be rejected and job processing time is controllable by allocating extra resources. By deterioration effect, we mean that each job’s processing time may be subject to change due to the capability deterioration with machine’s usage, i.e., the actual processing time of a job becomes longer if the job starts processing later. The operational cost and the disruption cost need to be optimized simultaneously. To solve these dynamic scheduling problems, a directed search strategy (DSS) is introduced into the elitist non-dominated sorting genetic algorithm (NSGA-II) to enhance its capability of tracking changing optimums while maintaining fast convergence. The DSS consists of a population re-initialization mechanism (PRM) to be adopted upon the arrival of new jobs and an offspring generation mechanism (OGM) during evolutionary optimization. PRM re-initializes the population by repairing the non-dominated solutions obtained before the disturbances occur, modifying randomly generated solutions according to the structural properties, as well as randomly generating solutions. OGM generates offspring individuals by fine-tuning a few randomly selected individuals in the parent population, employing intermediate crossover in combination with Gaussian mutations to generate offspring, and using intermediate crossover together with differential evolution based mutation operator. Both PRM and OGM aim to strike a good balance between exploration and exploitation in solving the dynamic multi-objective scheduling problem. Comparative studies are performed on a variety of problem instances of different sizes and with different changing dynamics. Experimental results demonstrate that the proposed DSS is effective in handling the dynamic scheduling problems under investigation.

A multi-population genetic algorithm to solve multi-objective scheduling problems for parallel machines

In this paper, a problem of scheduling jobs with different sizes and fuzzy processing times (FPT) on non-identical parallel batch machines to minimize makespan is investigated. Moreover, the processing time (PT) of each batch is subject to the location-based learning and total-PT-based deterioration effect. Since this is an NP-hard combinatorial optimization problem, an improved intelligent algorithm based on fruit fly optimization algorithm (IFOA) is proposed. To verify the performance of the algorithm, the IFOA is compared with three state-of-the-art algorithms. The comparative results demonstrate that the proposed IFOA outperforms the other compared algorithms.

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

In industries machine maintenance is used in order to avoid untimely machine fails as well as to improve production effectiveness. This research regards a permutation flow shop scheduling problem with aging and learning effects considering maintenance process. In this study, it is assumed that each machine may be subject to at most one maintenance activity during the planning horizon. The objectives aim to minimize the makespan, tardiness of jobs, tardiness cost while maximizing net present value, simultaneously. Due to complexity and Np-hardness of the problem, two Pareto-based multi-objective evolutionary algorithms including non-dominated ranked genetic algorithm (NRGA) and non-dominated sorting genetic algorithm (NSGA-II) are proposed to attain Pareto solutions. In order to demonstrate applicability of the proposed methodology, a real-world application in polymer manufacturing industry is considered.

Integrated process planning and scheduling is a significant research focus in recent years, which could improve the performance of manufacturing system. In real manufacturing environment, multi-objectives should be taken into consideration simultaneously during the machining process. Meanwhile, the processing time for each job is often imprecise in many real applications. Therefore, multi-objective integrated process planning and scheduling (IPPS) problem with fuzzy processing time is addressed in this paper. The processing time is described as triangular fuzzy number. A multi-objective genetic algorithm (MOGA) is designed to search for the Pareto solutions of multi-objective IPPS problem with fuzzy processing time. An instance has been designed to test the performance of proposed algorithm. The experiment result shows that the proposed MOGA could obtain satisfactory Pareto solutions for the multi-objective IPPS problem with fuzzy processing time.

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.

This paper presents a multi-objective mathematical model for a flexible job shop scheduling problem (FJSSP) with fuzzy processing times, which is solved by a hybrid intelligent algorithm (HIA). This problem contains a combination of a classical job shop problem with parallel machines (JSPM) to provide flexibility in the production route. Despite the previous studies, the number of parallel machines is not pre-specified in this paper. This constraint with other ones (e.g., sequence-dependent setup times, reentrant workflows, and fuzzy variables) makes the given problem more complex. To solve such a multi-objective JSPM, Pareto-based optimization algorithms based on multi-objective meta-heuristics and multi-criteria decision making (MCDM) methods are utilized. Then, different comparison metrics (e.g., quality, mean ideal distance, and rate of achievement simultaneously) are used. Also, this paper includes two major phases to provide a new model of the FJSSP and introduce a new proposed HIA for solving the presented model, respectively. This algorithm is a hybrid genetic algorithm with the SAW/TOPSIS method, namely HGASAW/HGATOPSIS. The comparative results indicate that HGASAW and HGATOPSIS outperform the non-dominated sorting genetic algorithm (NSGA-II) to tackle the fuzzy multi-objective JSPM.

Some scheduling problems with deteriorating jobs and learning effects

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.21

PurposeThe purpose of this paper is to describe the introduction of simple assembly line balancing problems (SALBPs) under four joint combinations of two learning effects and two deterioration effects.Design/methodology/approachIn this paper, effects of learning and deterioration are considered simultaneously. By the effects of learning and deterioration, it is meant that the task time of a task is defined by increasing function of its execution start time and position in the sequence.FindingsIt was shown that polynomial solutions can be obtained for SALBP under four joint combinations of two learning effects and two deterioration effects. Furthermore, this paper also discusses the adaptations of the proposed models by using known ALB problem.Originality/valueIn this paper, SALBPs were introduced under four joint combinations of two learning effects and two deterioration effects. Position dependent learning effect and time dependent learning effect were considered for learning effect when linear deterioration effect and non‐linear deterioration effect were taken up.

There are many uncertain factors in job shop scheduling problems. However, those uncertainties are critical for the scheduling procedures. The imprecise processing times are modeled as triangular fuzzy numbers (TFNs) and the due dates are modeled as trapezium fuzzy numbers in this paper. A multi-objective genetic algorithm is proposed to solve fuzzy job shop scheduling problems, in which the objective functions are conflicting. Agreement index (AI) is used to show the satisfaction of client which is defined as value of the area of processing time membership function intersection divided by the area of the due date membership function. The multi-objective function is composed of maximize both the minimum agreement and maximize the average agreement index. Two benchmark problems were used to show the effectiveness of the proposed approach. Experimental results demonstrate that the multi-objective genetic algorithm does not get stuck at a local optimum easily, and it can solve job-shop scheduling problems with fuzzy processing time and fuzzy due date effectively.

This paper introduces the parallel machine scheduling problems with work related musculoskeletal disorder (WMSD) risk considerations. By the WMSD consideration, we mean that job processing times are an increasing function of occupational repetitive technical actions (OCRA) risk factor. The OCRA index was recruited for risk assessment of occupational repetitive technical actions. WMSD risks were modeled with cumulative mean value of OCRA index. Due to NP-Hard structure of parallel machine scheduling problems with WMSD considerations and learning rate, the solution cannot be found always. However, problem can be solved by transforming assignment problem. In spite of the fact that the computational effort remains O (n 4 ), problem is solved within more efficient time. In this study, a model that includes learning effect and WMSD risk was proposed. WMSD risk was considered as cumulative mean of risk value throughout shift. In order to the balance between productivity and WMSD risk, jobs’ foreseeable cycle time (FCT) value was changed. It is aimed to decrease mean of risk along schedule without increasing total basic process time. The value of sacrifice from the FCT was compensating from job which have optimal, acceptable, borderline or slight risk level. Process time and risk values were recalculated by using new FCT value. Thus, balanced process times and risk values obtained. Proposed model was solved with Lingo software and sequence of jobs was obtained. Total flow time and mean of risk were compared for balanced and none balanced schedules. Total flow time and mean of risk belong to balanced schedule is smaller than none balanced schedule. It was shown that handled problem is solvable at the polynomial time and total flow time can be improved by bringing balance between WMSD risks and productivity.