Sameer Sharma

Fuzzy bi-criteria scheduling on parallel machines involving weighted flow time and maximum tardiness

Abstract This paper considers a bi-criteria scheduling on parallel machines in fuzzy environment which optimizes the weighted flow time and maximum tardiness. The fuzziness, vagueness or uncertainty in processing time of jobs is represented by triangular fuzzy membership function. The bi-criteria problem with weighted flow time and maximum tardiness as primary and secondary criteria, respectively, for any number of parallel machines is NP-hard. So, a heuristic algorithm is proposed to find the optimal sequence of jobs processing on parallel machines so as to minimize the secondary criterion of maximum tardiness without violating the primary criterion of weighted flow time. A numerical illustration is also given in support of the algorithm proposed.

Bi-Objective Scheduling on Parallel Machines in Fuzzy Environment

The present chapter pertains to a bi-objective scheduling on parallel machines involving total tardiness and number of tardy jobs (NT). The processing time of jobs are uncertain in nature and are represented by triangular fuzzy membership function. The objective of the chapter is to find the optimal sequence of jobs processing on parallel identical machines so as to minimize the secondary criteria of NT with the condition that the primary criteria of total tardiness remains optimized. The bi-objective problem with total tardiness and NT as primary and secondary criteria, respectively, for any number of parallel machines is NP-hard. Following the theoretical treatment, a numerical illustration has also been given to demonstrate the potential efficiency of the proposed algorithm as a valuable analytical tool for the researchers.

Bi-criteria parallel machine scheduling using nature-inspired hybrid flower pollination algorithm

Parallel machine scheduling and its complex combinatorial optimisation problems are widely studied. A lot of research has been carried out in this area to determine how to effectively schedule parallel execution of different jobs to be carried out using different machines in order to achieve the optimisation criteria. In this paper, the formulations of multi-objective flower pollination algorithm obtained by the combination of weighted objectives or secondary storage for managing possible solutions along with their hybrids with genetic algorithm have been developed and applied to the problem of scheduling jobs on machines running in parallel in order to optimise bi-criteria, namely, maximum tardiness and weighted flow time. It has been empirically verified that multi-objective flower pollination algorithm using secondary storage and hybridised with genetic algorithm leads to better results as compared to the existing algorithms. The results obtained have been verified by numerical illustrations and statistical tests.

Meta-Heuristic Algorithms to Solve Bi-Criteria Parallel Machines Scheduling Problem

Parallel machine scheduling problems are classified as NP-hard problems. The direct solutions for these problems are not available and meta-heuristic algorithms are required to be used to find near-optimal solutions. In this paper, the formulations of multi-objective Artificial Bee Colony algorithm by using combination of weighted objectives, secondary storage for managing possible solutions and Genetic algorithm have been developed and applied to schedule jobs on parallel machines optimizing bi-criteria namely maximum tardiness and weighted flow time. The results obtained indicate that proposed algorithm outperforms other multi-objective algorithms in optimizing bi-criteria scheduling problems on parallel machines. Further, the sequential optimization of bi-criteria using Early Due Date EDD followed by Genetic Algorithm GA has also been investigated. The efficiencies of the proposed algorithms have been verified by numerical illustrations and statistical tests.

A Heuristic for Permutation Flowshop Scheduling to Minimize Makespan

As the problem related to minimizing makespan as objective is NP-hard for more than two machines in flowshop scheduling, therefore need for heuristics have been felt to yield optimal or near optimal solutions in polynomial time. In the present paper, we propose an alternative heuristic algorithm which is compared with the benchmark Palmer’s, CDS and NEH algorithm for the processing of n-jobs through m-machines. The proposed heuristic gives solution for solving n-job and m-machine flowshop scheduling problem with minimizing makespan as criteria. Comparisons have been made for tested instances.

Analysis of network of biserial queues linked with a common server

This paper is an attempt to study the steady state analysis of a complex network of queues in which a common server is linked in series with each of two parallel biserial servers. The arrival and service pattern follows Poisson law. The generating function technique, law of calculus and statistical tools have been used to find the various queue characteristics. The model finds its application in decision making, in process industry, in banking system, in communication networking, in supermarkets, in healthcare centre and in many administrative setups. An algorithm is proposed to find the mean queue length of customers/jobs, variance of queues and average waiting time of customers/jobs. The performance of algorithm is assessed by a numerical illustration.

Minimizing makespan in flow shop under no-wait restriction on jobs

No-wait flow shop scheduling refers to a continuous flow of jobs through machines. The job once started should have continuous processing through the machines without a wait. This situation occurs when there is a lack of intermediate storage between the handling of jobs on two consecutive machines, or the manufacturing system does so. The problem of no-wait with the objective of minimizing makespan in flow shop scheduling is NP-hard; therefore, the heuristic algorithms are the key to solving the problem with the optimal solution or to approach nearer to the optimal solution in a straightforward manner. The paper describes an algorithm using a heuristic technique for sequencing n-jobs through m-machines in a flow shop under no-wait constraint with the objective of minimizing makespan. The problems found in the literature are solved using the proposed heuristic algorithm, and the comparisons of results are done with the corresponding methods. To explain the computational process of proposed algorithm, numerical illustrations are also given in the paper.

Network Analysis of Biserial Queues Linked with a Flowshop Scheduling System

This paper is an attempt to establish a linkage between networks of queues consisting of two parallel biserial servers connected with a common server in series and a multistage flowshop scheduling system having m machines. In the queue network, both the arrival and service patterns follow Poisson law. The objective of this paper is to develop an algorithm minimizing the total elapsed time with minimum completion time, average waiting time, and minimum queue length for the proposed queuing–scheduling linkage model. The efficiency of the proposed algorithm is tested by a numerical illustration.

Job Block Scheduling with Dual Criteria and Sequence-Dependent Setup Time Involving Transportation Times

A two-machine flowshop scheduling with sequence-dependent setup time (SDST), job block, and transportation time is considered with the objective of minimizing makespan and the rental cost of machines taken on rent under a specified rental policy. The processing time of attributes on these machines is associated with probabilities. To find the optimal or near-optimal solution for these objectives, a heuristic algorithm is developed. To test the efficiency of the proposed heuristic algorithm, a numerical illustration is given.