Non-regular Performance Measure Research Articles

Minimization of completion time variance in flowshops using genetic algorithms

The majority of the flowshop scheduling literature focuses on regular performance measures like makespan, flowtime etc. In this paper a flowshop scheduling problem is addressed where the objective is to minimize completion time variance (CTV). CTV is a non-regular performance measure that is closely related to just-in-time philosophy. A Microsoft Excel spreadsheet-based genetic algorithm (GA) is proposed to solve the problem. The proposed GA methodology is domain-independent and general purpose. The flowshop model is developed in the spreadsheet environment using the built-in formulae and function. Addition of jobs and machines can be catered for without the change in the basic GA routine and minimal change to the spreadsheet model. The proposed methodology offers an easy-to-handle framework whereby the practitioners can implement a heuristic-based optimization tool with the need for advanced programming tools. The performance of the proposed methodology is compared to previous studies for benchmark problems taken from the literature. Simulation experiments demonstrate that the proposed methodology solves the benchmark problems efficiently and effectively with a reasonable accuracy. The solutions are comparable to previous studies both in terms of computational time and solution quality.

Triple‐chromosome genetic algorithm for unrelated parallel machine scheduling under time‐of‐use tariffs

Energy demand is increasing as the population and economy grow. Many countries have implemented time‐of‐use (TOU) tariffs to meet such demand so that the demand during peak periods could be reduced by shifting its usage from peak periods to off‐peak periods. This paper addresses the unrelated parallel machine scheduling under TOU to minimize the sum of weighted makespan and electricity cost. Because the problem has nonregular performance measure, delaying the starting time of the job can produce a better solution. Hence, not only do we determine the job sequencing and the job assignment, but also we determine the starting time of the job. We propose a triple‐chromosome genetic algorithm that represents the job sequencing, the job assignment and the optimal starting time of the job simultaneously. A self‐adaptive algorithm is developed to determine the value of the third chromosome after crossover and mutation process. Numerical experiment and statistical analysis are conducted to show the appropriateness and efficacy of the proposed approach. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Single-machine common due date total earliness/tardiness scheduling with machine unavailability

Research on non-regular performance measures is at best scarce in the deterministic machine scheduling literature with machine unavailability constraints. Moreover, almost all existing works in this area assume either that processing on jobs interrupted by an interval of machine unavailability may be resumed without any additional setup/processing or that all prior processing is lost. In this work, we intend to partially fill these gaps by studying the problem of scheduling a single machine so as to minimize the total deviation of the job completion times from an unrestrictive common due date when one or several fixed intervals of unavailability are present in the planning horizon. We also put serious effort into investigating models with semi-resumable jobs so that processing on a job interrupted by an interval of machine unavailability may later be resumed at the expense of some extra processing time. The conventional assumptions regarding resumability are also taken into account. Several interesting cases are identified and explored, depending on the resumability scheme and the location of the interval of machine unavailability with respect to the common due date. The focus of analysis is on structural properties and drawing the boundary between polynomially solvable and $$\mathcal {NP}$$ -complete cases. Pseudo-polynomial dynamic programming algorithms are devised for $$\mathcal {NP}$$ -complete variants in the ordinary sense.

Completion time variance minimisation on two identical parallel processors

The problem of scheduling jobs to minimise completion time variance (CTV) is a well-known problem in scheduling research. CTV is categorized as a non-regular performance measure and its value may decrease by increasing the job completion times. This objective is relevant in situations where providing uniform service to customers is important, and is in-line with just-in-time philosophy. The problem concerned in this paper is to schedule n jobs on two identical parallel machines to minimise CTV. We consider the unrestricted version of the problem. The problem is said to be restricted when a machine is not allowed to remain idle when jobs are available for processing. It may be necessary to delay the start of job processing on a machine in order to reduce the completion time deviations. This gives rise to the unrestricted version of the problem. We discuss several properties of an optimal schedule to the problem. In this paper, we develop a lower bound on CTV for a known partial schedule and propose a branch and bound algorithm to solve the problem. Optimal solutions are obtained and results are reported.

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.

Minimising mean squared deviation of job completion times about a common due date in multimachine systems

In this paper we consider the problem of scheduling n jobs on two identical parallel machines in order to minimise the mean squared deviation (MSD) of job completion times about a given common due date. When due dates are small and large deviations of job completion times from the due dates are undesirable, it becomes necessary to consider parallel machines. MSD comes under the category of non-regular performance measures, which penalises jobs that are early as well as late. In this paper we develop a lower bound on MSD for a given partial schedule and present a branch and bound algorithm to solve the problem. Optimal solutions for problem instances up to 35 jobs have been obtained for different values of due dates and the results of computational testing are presented. Based on our experiments we observe that when the due date exceeds a certain value the second machine becomes undesirable. We also propose a heuristic to provide quick solutions for problems of larger size.

Minimizing flow-time variance in a single-machine system using genetic algorithms

This paper addresses an n-job, single-machine scheduling problem with an objective to minimize flow-time variance, a non-regular performance measure. A spreadsheet-based genetic algorithm (GA) approach is presented to solve the problem. A domain-independent general-purpose GA is used, which is an add-in to the spreadsheet software. The paper demonstrates an adaptation of the proprietary GA software to the problem of variance minimization. To test the performance of the proposed approach, test problems are taken from already published literature. The proposed approach is found to perform better than the previous GA, simulated annealing (SA) and Tabu search (TS) approaches for variance minimization in that it produces an optimal solution for all the test problems. Empirical analysis was carried out to study the effect of GA parameters, namely, the crossover rate, mutation rate, and population size.

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

In this paper, the complexity and some other properties of several multi-stage problems with a non-regular performance measure are investigated. Mainly, we deal with two-machine problems. The problems are extensions of a one-machine problem with a common due date and a non-regular optimization criterion, where the sum of absolute deviations of the completion times from the due date is to be minimized. There are two reasonable generalizations: Either, the objective function is kept the same as in the one-machine problem, where the completion time is now the completion time of the last operation of the job, or a second penalty is added to this term which takes into account the storage costs of the intermediate. For both types of problems, we study the flow shop, the job shop, and the open shop environment. In the case of intermediate storage costs, we distinguish the cases of a due date d=0 (which leads to a regular optimization criterion) and a non-restrictive due date. We obtain the following results. The two-machine flow shop problem with intermediate storage costs defined in this paper is NP-hard in the strong sense for d=0 as well as for a non-restrictive due date. We prove the similar results for the two-machine open shop problem. In absence of intermediate storage costs, the open shop and the job shop problem are polynomially solvable for a non-restrictive due date. Scope and purpose The just-in-time production philosophy has lead to a growing interest in scheduling problems considering both earliness and tardiness penalties. Most publications considering these so-called non-regular objective functions are devoted to single-stage problems. This paper describes the two main approaches to extend the objective function to multi-stage environments and investigates the computational complexity of the problems obtained. The investigations in this paper may serve as a starting point for the development of appropriate algorithms for the type of problem considered.

Optimal idle time insertion in early-tardy parallel machines scheduling with precedence constraints

Consider a set of n jobs to be processed on a set of w unrelated parallel machines subject to precedence constraints, where the objective is to minimize the sum of earliness and tardiness penalties. In minimizing this non-regular performance measure, it is necessary to assign jobs to machines, determine the sequence on each machine and possibly insert intentional idle times between jobs. Here, this third aspect is considered assuming that the assignment of jobs to machines and the sequence on each machine are known. This idle time insertion problem, though polynomially solvable, is not a trivial task, since it requires the consideration of all machines simultaneously when precedence constraints among jobs are present. It can also be seen as the problem of optimally timing a partially ordered set of tasks with respect to the above non-regular performance measure. An exact procedure is proposed based on repeated solutions of maximum cardinality matching problems on a bipartite graph with O ( mn ) complexity where m < w · n is the total number of non-redundant arcs of the digraph induced by the precedence relationships. Computational results are provided.

Tabu search for a class of single-machine scheduling problems

In this paper we develop a tabu search-based solution procedure designed specifically for a certain class of single-machine scheduling problems with a non-regular performance measure. The performance of the developed algorithm is tested for solving the variance minimization problem. Problems from the literature are used to test the performance of the algorithm. This algorithm can be used for solving other problems such as minimizing completion time deviation from a common due date. Scope and purpose Scheduling problems with non-regular performance measures has gained a great importance in modern manufacturing systems. These problems are found to be hard to solve and analyze. The purpose of this paper is to present a tabu search approach for solving a certain class of single-machine scheduling problems with non-regular performance measure. Minimizing the variance of completion times and the total deviation from a common due date are two examples of such problems. The proposed approach is found to perform better than the simulated annealing approach for the variance minimization problem.

One-machine rescheduling heuristics with efficiency and stability as criteria

Heuristics for the problem of rescheduling a machine on occurrence of an unforeseen disruption are developed. The criteria include minimization of the makespan (schedule efficiency) and the impact of the schedule change (schedule stability). The impact of schedule change is a non-regular performance measure defined in two ways: (1) the starting time deviations between the new schedule and the original schedule, and (2) a measure of the sequence difference between the two schedules. Three local search procedures are developed for the bicriterion problem and a set of experiments are conducted to test the efficacy of the heuristics. The heuristic solutions are shown to be effective in that the schedule stability can be increased significantly with little or no sacrifice in makespan.

A greedy heuristic for bicriterion single machine scheduling problems

This paper presents a greedy heuristic for solving a bicriterion single machine scheduling problem. The job to be scheduled on the machine has an available time, a1, a processing time p1, a system time, q1 and a due date, d1. With the makespan as a performance measure, Schrage has presented at heuristic approach by choosing the ready job with the largest tail to solve the problem. Moreover, Carlier has further improved this heuristic and provided an efficient branch and bound procedure with successful runs of thousand jobs reported. In this research, we introduce the total absolute deviation as another criterion to be considered for the cell coordination purpose. As a result, a bicriterion single machine scheduling problem is formed and the bicriterion includes the minimization of the makespan and the total absolute deviation. The absolute deviation of each job is a non-regular performance measure and is defined as the absolute difference between the job's system completion time (i.e. including q1) and its due date. We have assumed a linear combination of these two objectives and present a greedy heuristic which uses the control parameter α to manipulate a1 and q1 of each job to generate a set of nondominant schedules for satisfying these two performance measures. According to this set of schedules, shop floor managers can make a decision based on their application purposes.