Variance Of Job Completion Times Research Articles

A two-phase simulated annealing algorithm to minimise the completion time variance of jobs in flowshops

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

A two-phase simulated annealing algorithm to minimise the completion time variance of jobs in flowshops

A two-phase simulated annealing algorithm to minimise the completion time variance of jobs in flowshops

Simulated annealing algorithms to minimise the completion time variance of jobs in permutation flowshops

In this paper, the permutation flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs is considered, and a simulated annealing algorithm (SA) and two modified SAs (MSA1 and MSA2) are proposed. In the first phase, the proposed algorithms are used to minimise CTV of jobs without any right shifting of completion times of jobs on the last machine (RSCT). As followed in the literature some times, the RSCT (except that of the last job) is attempted in the second phase, and in the third phase, we convert sequences so as to follow the V-shaped property with respect to processing time of jobs on the last machine, followed by RSCT except that of the last job, so that the makespan and the machine utilisation in the shop floor remain the same. We present an extensive computational evaluation of the existing and the proposed heuristic algorithms.

Simulated annealing algorithms to minimise the completion time variance of jobs in permutation flowshops

In this paper, the permutation flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs is considered, and a simulated annealing algorithm (SA) and two modified SAs (MSA1 and MSA2) are proposed. In the first phase, the proposed algorithms are used to minimise CTV of jobs without any right shifting of completion times of jobs on the last machine (RSCT). As followed in the literature some times, the RSCT (except that of the last job) is attempted in the second phase, and in the third phase, we convert sequences so as to follow the V-shaped property with respect to processing time of jobs on the last machine, followed by RSCT except that of the last job, so that the makespan and the machine utilisation in the shop floor remain the same. We present an extensive computational evaluation of the existing and the proposed heuristic algorithms.

A dominance-based heuristic to minimise completion time variance in a single machine system

This paper addresses the problem of minimising the variance of job completion times in a deterministic single-machine scheduling system. Minimising completion time variance is an appropriate objective in scheduling environments where service uniformity is essential. Due to the NP-hard nature of the problem, various heuristics have been presented to obtain a near-optimal solution. In this paper, we introduce a new heuristic based on some powerful precedence (dominance) relation structures, including the concepts of permanent and temporary precedence (dominance) relationships, to determine the positions of adjacent and non-adjacent jobs in a sequence. Our computational experiments demonstrate that the proposed heuristic significantly outperforms the existing ones in deriving the optimal or near-optimal solutions for three well-known sets of benchmark problems and some large randomly generated instances. [Received: 5 August 2018; Revised: 24 December 2018; Accepted: 23 January 2019]

Heuristics to minimize the completion time variance of jobs on a single machine and on identical parallel machines

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

A modified ant-colony optimisation algorithm to minimise the completion time variance of jobs in flowshops

In this work, the flowshop scheduling problem is considered with the objective of minimising the completion-time variance (CTV) of jobs, and an Ant Colony Optimisation (ACO) algorithm is presented. Two implementations of the Modified Ant Colony Optimisation algorithm (MACO-I and MACO-II) are proposed to solve the permutation flowshop scheduling problem. The proposed ant-colony-algorithm implementations have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed MACO implementations are compared with various algorithms and with the best CTV of jobs reported in the literature. The proposed MACO implementations are found to perform very well in minimising the chosen performance measure.

Another well-solvable case of the QAP: Maximizing the job completion time variance

We analyze a special case of the maximum quadratic assignment problem where one matrix is a monotone anti-Monge matrix and the other matrix has a multi-layered structure that is built on top of certain Toeplitz matrices. To demonstrate an application of our main result, we derive a (simple and concise) alternative proof for a recent result on the scheduling problem of maximizing the variance of job completion times.

Minimising variance of job completion times in a single machine

In this paper, we consider a deterministic n-job, single-machine sequencing problem with the objective of minimising the variance of job completion times. Completion time variance (CTV) is relevant in situations where uniformity in service is needed. CTV is a non-regular performance measure that can decrease when one or more completion times increases. It penalises jobs that are completed early as well as late. Minimising CTV in a single machine is a ‘hard’ problem. The objective of this paper is to provide an exact algorithm to solve the single-machine CTV minimisation problem based on implicit enumeration. We develop a lower bound for a given partial sequence and present a branch and bound algorithm to solve the problem. Computational results show that optimal solutions for problems up to 80 jobs can be obtained with less computational time when compared to an existing pseudo-polynomial algorithm.

Discrete particle swarm optimisation algorithms for minimising the completion-time variance of jobs in flowshops

In this paper, the problem of scheduling in the permutation flowshop scheduling problem is considered with the objective of minimising the completion-time variance of jobs (CTV). Two particle swarm optimisation algorithms (PSOAs) are proposed and analysed. The first PSOA is inspired from the solution construction procedures that are used in ant colony optimisation algorithms. The second algorithm is a newly developed one. The proposed algorithms are applied to a set of benchmark flowshop scheduling problems, and performances of the algorithms are evaluated by comparing the obtained results with the results published in the literature. The performance analysis demonstrates the effectiveness of the proposed algorithms in solving the permutation flowshop sequencing problem with the CTV objective.

Minimization of Job Waiting Time Variance on Identical Parallel Machines

We consider the problem of scheduling independent jobs on identical parallel machines so as to minimize the waiting time variance of the jobs ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ). We show that the optimal value of( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) is identical to the optimal value of the problem for minimizing the completion time variance of jobs on identical parallel machines( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ). We prove that, given the same job set, any feasible schedule of ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) can be transformed into the feasible solution for ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) with the same job set by applying the polynomial algorithms proposed in this paper. Several other important properties of ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) are also proved. Heuristic algorithms are proposed to solve ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Pm</i> // <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WTV</i> ) problems. We present the testing results of these heuristic algorithms, which are applied to problems with both small and large job sets.

A New Dispatching Rule for the Stochastic Single-Machine Scheduling Problem

In this article, the authors consider the n-job single-machine scheduling problem in which jobs with stochastic processing time requirements arrive to the system at random times. The performance measure combines both mean and variance of job completion times. In this study, a dispatching rule is designed to minimize the performance measure using a simulation model built using AWESIM. Different variations of the rule are tested to select the best implementing policy of the rule. Extensive experimentation is conducted to determine the best parameter values in terms of problem parameters.

A branch and bound algorithm to minimize completion time variance on a single processor

In this paper we discuss a single machine scheduling problem with the objective of minimizing the variance of job completion times. The CTV problem has been proved to be NP hard (Oper. Res. Lett. 14 (1993) 49) and no polynomial time algorithm exists to find an optimal solution for CTV minimization on single machine. Hence enumerative techniques and heuristics are used to get optimal and near optimal solutions, respectively. We present a branch and bound algorithm and extend the same algorithm to generate epsilon optimal solutions for large sized problems (i.e., number of jobs >30). The algorithm has been computationally tested, with randomly generated problems involving up to 100 jobs, using a personal computer (PC) with a 64 MB RAM capacity. The computational time required for generating optimal solutions are in few seconds for problems with jobs between 25 and 30. The performance of the branch and bound algorithm is compared with the pseudo-polynomial algorithm (Oper. Res. 40 (1992) 1148) for small sized problems. For problems with greater number of jobs, the epsilon optimal solutions obtained using branch and bound algorithm are compared with results of simulated annealing (Single machine scheduling with some non-regular objectives, M.S. Thesis, IIT Madras, 1997), tabu search (Proceedings of Operations Management Conference, IIT Madras, 2000) and heuristic proposed by Manna and Prasad (Eur. J. Oper. Res. 114 (1999) 411). Scope and purpose Scheduling jobs in manufacturing systems considering non-regular measures of performance have gained importance in recent years. The objectives of minimizing completion time variance ( CTV problem) and minimizing squares of deviations of job completion times from a given common due-date ( MSD problem) are the two problems that use non-regular measures, and have attracted attention in single machine scheduling and flowshop scheduling when jobs require uniform treatment i.e., each entity spends approximately same time in the system or waits for service as every other entity. This problem is very much relevant when a manufacturing/service system places emphasis on Just-in-Time philosophy. The purpose of this paper is to present an algorithm for minimizing completion time variance for a set of jobs to be processed on a single machine. The proposed algorithm is computationally evaluated with randomly generated problems involving up to 100 jobs and results are reported.

An Approximation Scheme for Minimizing Agreeably Weighted Variance on a Single Machine

We consider the problem of minimizing the weighted variance of job completion times on a single machine with job-dependent, agreeable weights. In 1995, Cai derived a fully polynomial time approximation scheme for the special case where the weights of the jobs are polynomially bounded in the number n of jobs. In this article, we completely settle the approximability status of this scheduling problem. We construct a fully polynomial time approximation scheme for the general case, without putting any restrictions on the weights of the jobs.

Bounds for the position of the smallest job in completion time variance minimization

The problem of scheduling jobs on a single machine so as to minimize the variance of job completion times is considered. We develop bounds on the position of the smallest job in an optimal sequence, which is vital due to the fact that an optimal sequence is necessarily a V-shaped sequence. Results of numerical experimentation indicate that the bounds are very effective if the job processing times are homogeneous. Using these bounds, we develop a new heuristic method to solve the problem. Based on numerical investigation, it is shown that performance of this heuristic compares favorably with existing but older heuristics.

Minimization of expected variance of completion times on single machine for stochastic jobs

This article deals with the problem of scheduling jobs with random processing times on single machine in order to minimize the expected variance of job completion times. Sufficient conditions for the existence of V-shaped optimal sequences are derived separately for general and ordered job processing times. It is shown that when coefficient of variation of random processing times are bounded by a certain value, an optimal sequence is V-shaped. © 1997 John Wiley & Sons, Inc.

Sequencing jobs with random processing times to minimize weighted completion time variance

We examine the problem of sequencing a set of jobs on a single machine, where each job has a random processing time and is associated with a known, job-dependent weight. The objective is to minimize the expectation of the weighted variance of job completion times. We establish the NP-completeness of this problem, and further show that the problem under some compatible conditions is NP-complete in the ordinary sense. We introduce the concept of a W-shaped solution for the problem and find that an optimal W-shaped sequence exists under the compatible conditions. We propose an exact algorithm, based on this W-shaped property, which can generate an optimal solution in pseudopolynomial time.

V-shape property for job sequences that minimize the expected completion time variance

We consider the problem of sequencing n jobs with random processing time on a single machine so as to minimize the expected variance of job completion times. Our main result is a new sufficient condition for an optimal sequence to be V-shaped in terms of the mean processing times when n ⩾ 3. We show that this condition is satisfied by a wide variety of problem instances, including those in which the processing times follow different patterns of distributions. This result relaxes a condition proposed before.

Note: ?Simultaneous optimization of efficiency and performance balance measures in single-machine scheduling problems?

n independent jobs are to be scheduled nonpreemptively on a single machine so as to minimize some performance measure. Federgruen and Mosheiov [2] show that a large class of such scheduling problems can be optimized by solving either a single instance or a finite sequence of instances of the so-called SQC problem, in which all the jobs have a fixed or controllable common due date and the sum of general quasiconvex functions of the job completion times is to be minimized. In this note we point out that this is not always true. In particular, we show that the algorithm proposed in [2] does not always find a global optimal schedule to the problem of minimizing the weighted sum of the mean and variance of job completion times.

New results on the completion time variance minimization

A single machine scheduling problem where the objective is to minimize the variance of job completion times is considered. The model is applicable to many environments where it is desirable to provide jobs, customers or computer files, with approximately the same service. It is shown that the problem can be formulated as a problem of maximizing a zero-one quadratic function which is a submodular function with a special cost structure. It immediately follows from the cost structure that value of the function for a sequence that minimizes total absolute deviation about a common unrestrictive due date is at most 100% smaller than the one for an optimal sequence for the completion time variance problem. The Monge property holds for the costs. Other simple properties of the function are also presented. A pair of dynamic programs for maximizing the function is proposed. The worst case time complexity of the best of the pair is O( n 2spt), where spt is the mean flow time of an SPT-schedule for all jobs except the longest one.