A fuzzy multi-objective programming for scheduling of weighted jobs on a single machine

This paper concerns sensitivity analysis of a class of complex job shop scheduling problems which are characterized by: (1) a large number of jobs and machines, (2) uncertain jobs processing times, and (3) multiple measures of schedule performance including average weighted tardiness, the number of tardy jobs, the total setup times, the total idle time of machines, and the total flow times of jobs. The base schedule is generated by applying a new fuzzy multiobjective genetic algorithm which takes into consideration batching of the jobs of a similar type, jobs’ lots sizing and load balancing of the machines. The aim of the proposed sensitivity analysis of a generated schedule is to investigate the consequences of prolongations of job processing times on the measures of schedule performance. The processing times are described by triangular fuzzy numbers and their prolongation is done by expanding the supports of fuzzy numbers. The sensitivity analysis is performed through a series of numerical experiments. The effects of prolongations of job processing times on the measures of performance of a generated schedule are recorded and analysed. It is shown that the sensitivity analysis is among the primaries in evaluating the quality of a generated schedule. The sensitivity analysis is used in identifying the critical jobs and the critical machines which have the properties that the prolongations of their processing times produce the largest deteriorations of the performance measures and the overall quality of a generated schedule.

This paper deals with unrelated parallel machines scheduling problem with sequence dependent setup times under fully fuzzy environment to minimize total weighted fuzzy earliness and tardiness penalties, which belongs to NP-hard class. Due to inherent uncertainty in Processing times, setup times and due dates of jobs, they are considered here with triangular and trapezoidal fuzzy numbers in order to take into account the unpredictability of parameters in practical settings. Although this study is not the first one to study on fuzzy parallel machines scheduling problem, it advances this area of research in three fields: (1) it selects a fuzzy environment to cover the whole area of the considered problem not just part of it, and also, it chooses an appropriate fuzzy method based on an in-depth investigation of the effect of spread of fuzziness on the variables; (2) It introduces a mathematical programming model for the addressed problem as an exact method; and (3) due to NP-hardness of the problem, it develops an existing algorithm in the literature for the considered problem through extensive simulated experiments and statistical tests on the same benchmark problem test by proposing a genetic algorithm (GA) and a modified simulated annealing (SA) methods to solve this hard combinatorial optimization problem. The result shows the superiority of our modified SA.

Just-in-time JIT (Just In Time) is an important procedure in scheduling problems which aims at minimizing minimising both earliness and tardiness at the same time. In this case, the problem is a multi-objective scheduling problem. A candidate solution method for this type of problem is finding the Pareto-optima. The present research investigates the single single machine scheduling problem in which the three objects: number of tardy job, maximum earliness, and maximum tardiness must be minimized minimised

Scheduling unit processing time jobs on a single machine with multiple criteria

Solving TSP by Considering Processing Time: Meta-Heuristics and Fuzzy Approaches

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

In this paper, we consider some scheduling problems on a single machine, where weighted or unweighted total tardiness has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. For the total weighted tardiness maximization problem, we present an NP-hardness proof and a pseudo-polynomial solution algorithm. For the unweighted total tardiness maximization problem with release dates, NP-hardness is proven. Complexity results for some other classical objective functions (e.g., the number of tardy jobs, total completion time) and various additional constraints (e.g., deadlines, weights and/or release dates of jobs may be given) are presented as well.

This paper considers the problem of assigning a common due-date to a set of simultaneously available jobs and sequencing them on a single machine. The objective is to determine the optimal combination of the common due-date and job sequence that minimizes a cost function based on the assigned due-date, job earliness values, and number of tardy jobs. It is shown that the optimal due-date coincides with one of the job completion times. Conditions are derived to determine the optimal number of nontardy jobs. It is also shown that the optimal job sequence is one in which the nontardy jobs are arranged in nonincreasing order of processing times. An efficient algorithm of O(n logn) time complexity to find the optimal solution is presented and an illustrative example is provided. Finally, several extensions of the model are discussed.

This study extends the best hybrid ant colony optimization variant developed by Liao et al. (2014) for crisp unrelated parallel machine scheduling problems to solve fuzzy unrelated parallel machine scheduling problems in consideration of trapezoidal fuzzy processing times, trapezoidal fuzzy sequencing dependent setup times and trapezoidal fuzzy release times. The objective is to find the best schedule taking minimum fuzzy makespan in completing all jobs. In this study, fuzzy arithmetic is used to determine fuzzy completion times of jobs and defuzzification function is used to convert fuzzy numbers back to crisp numbers for ranking. Eight fuzzy ranking methods are tested to find the most feasible one to be employed in this study. The fuzzy arithmetic testing includes four different cases and each case with the following operations separately, i.e., addition, subtraction, multiplication and division, to investigate the spread of fuzziness as fuzzy numbers are subject to more and more number of operations. The effect of fuzzy ranking methods on hybrid ant colony optimization (hACO) is investigated. To prove the correctness of our methodology and coding, unrelated parallel machine scheduling with fuzzy numbers and crisp numbers are compared based on scheduling problems up to 15 machines and 200 jobs. Relative percentage deviation (RPD) is used to evaluate the performance of hACO in solving fuzzy unrelated parallel machine scheduling problems. A numerical study on large-scale scheduling problems up to 20 machines and 200 jobs is conducted to assess the performance of the hACO algorithm. For comparison, a discrete particle swarm optimization (dPSO) algorithm is implemented for fuzzy unrelated parallel machine scheduling problem as well. The results show that the hACO has better performance than dPSO not only in solution quality in terms of RPD value, but also in computational time.

In this paper we address the scheduling problem of unit processing time jobs on a single machine considering number of tardy jobs and a measure of earliness. We consider total absolute lateness, total earliness and maximum earliness, as earliness measures.

Characterizations of endograph metric and Γ-convergence on fuzzy sets

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers.

Multi-objective scheduling in labor-intensive manufacturing systems

A composite heuristic for the single machine early/tardy job scheduling problem

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the sizes of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. Here, the processing time of job j on machine i is governed by random variable P_{ij} , and its realization becomes known only upon job completion. With w_j being the given weight of job j, we study the objective to minimize the expected total weighted completion time E[Sum w_j.C_j] , where C_j is the completion time of job j. By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee (3+D)/2+e. Here, e>0 is arbitrarily small, and D is an upper bound on the squared coefficient of variation of the processing times. When jobs also have individual release dates r_{ij}, our bound is (2+D)+e. We also show that the dependence of the performance guarantees on D is tight. Via D=0, currently best known bounds for deterministic scheduling on unrelated machines are contained as special case.