Deviation Of Completion Times Research Articles

Rescheduling for new orders on a single machine with rejection

We consider a single machine rescheduling problem where a set of original jobs have been scheduled to minimize the total weighted completion time. However, before formal processing begins, a new set of jobs arrives and creates a disruption. The decision maker can reject a subset of the new jobs by paying certain rejection penalties, and reschedule the original and the remaining new jobs without excessively disrupting the original schedule, which is measured by the maximum completion time deviation for any original jobs between the original and adjusted schedules. The objective is to minimize the sum of total weighted completion time of the original jobs and the accepted new jobs in the adjusted schedule, the weighted maximum completion time deviation and the total rejection cost. We first provide a dynamic programming-based exact algorithm running in pseudo-polynomial time, and then propose a fully polynomial time approximation scheme. Given the NP-hardness for the studied problem, our result is the best possible from the approximation algorithm perspective. In addition, we conduct extensive computational experiments to evaluate the performance of our proposed methods, and provide some managerial insights on their applicability under different situations.

A deep reinforcement learning based approach for dynamic distributed blocking flowshop scheduling with job insertions

The distributed blocking flowshop scheduling problem (DBFSP) with new job insertions is studied. Rescheduling all remaining jobs after a dynamic event like a new job insertion is unreasonable to an actual distributed blocking flowshop production process. A deep reinforcement learning (DRL) algorithm is proposed to optimise the job selection model, and local modifications are made on the basis of the original scheduling plan when new jobs arrive. The objective is to minimise the total completion time deviation of all products so that all jobs can be finished on time to reduce the cost of storage. First, according to the definitions of the dynamic DBFSP problem, a DRL framework based on multi-agent deep deterministic policy gradient (MADDPG) is proposed. In this framework, a full schedule is generated by the variable neighbourhood descent algorithm before a dynamic event occurs. Meanwhile, all newly added jobs are reordered before the agents make decisions to select the one that needs to be scheduled most urgently. This study defines the observations, actions and reward calculation methods and applies centralised training and distributed execution in MADDPG. Finally, a comprehensive computational experiment is carried out to compare the proposed method with the closely related and well-performing methods. The results indicate that the proposed method can solve the dynamic DBFSP effectively and efficiently.

Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection

We consider two-stage no-wait proportionate flow shops with the objective of minimizing service time variation measured by defining the mid-processing point of a job and minimizing the Total Absolute Deviation of mid-processing Points (TADZ). We show that the two-stage no-wait proportionate flow shop with the TADZ objective is solvable in O(nlogn) time. Our findings provide an affirmative answer to an open research question posed by Kovalev et al. (2019) regarding existence of a solvable variant of the two-stage no-wait proportionate flow shop problem with the Total Absolute Deviation of Completion Times (TADC) objective. Moreover, we show when a generic two-stage no-wait proportionate flow shop scheduling problem is solvable in O(nlogn) time. We present practical applications where TADZ is more suitable than TADC as a scheduling objective. We also introduce a new metric defined as the sum of all partial schedule lengths SPSL and show that the two-stage no-wait proportionate flow shop with the SPSL objective is solvable in O(nlogn) time; thus, an additional solvable variant of the two-stage no-wait proportionate flow shop with the SPSL objective is identified and solved. Finally, we consider the option of rejecting a job from the schedule by paying a job-specific penalty for each rejected job and solve the resulting problem with the TADZ objective and the rejection option in O(n3) time by dynamic programming.

Some Scheduling Problems With Job Rejection And A Learning Effect

AbstractIn this paper, we examined single and parallel machine scheduling problems with a learning effect and job rejection simultaneously. In real life, job processing times decrease when there is a learning effect. In some cases, producers cannot process all the jobs and pay the penalty cost for these jobs that they do not process. In our study, learning effect and job rejection are considered at the same time. We examined four different objective functions. Our objectives for single-machine scheduling problems are makespan and rejection cost minimization, total completion time and rejection cost minimization and total absolute deviation of completion times (TADC) and rejection cost minimization. Our objective for parallel machines is makespan and rejection cost minimization. The problems are solved by mathematical models, and four different algorithms are proposed for the problems. From these algorithms, the same results are obtained with single-machine makespan and rejection cost minimization, parallel machine makespan and rejection cost minimization and total completion time and rejection cost minimization. The accuracy for these models is obtained as 100%. The proposed algorithm for TADC and rejection cost minimization yielded close-to-optimal results. Mathematical model and algorithm results for 10 jobs, 20 jobs and 30 jobs are compared and the results are presented. The obtained solutions are obtained in polynomial time.

Minimizing the Total Weighted Waiting Times and Instability in a Rescheduling Problem with Dynamic Jobs Weight

Thanks to smart technological tools, customers can at any moment create or modify their commands. This reality forced many production firms to become sensitive in rescheduling processes. In the literature, most of rescheduling problems consider classical efficiency measures. However, some existing works also consider stability as a measure for limiting the deviation from initial schedule. In this work, we aim to bridge the gap in existing works on rescheduling by investigating a new approach to measure simultaneously efficiency by the total weighted waiting times and stability by the total weighted completion time deviation. This combination of criteria is very significant in industrial and hospital environments. In this paper, a single machine rescheduling problem with jobs arriving over time is considered. A mixed integer linear programming (MILP) model is designed for this problem and an iterative predictive-reactive strategy for dealing with the online part. Numerical results show that, at each time the jobs are rescheduled, the low weight ones move forward. Consequently, a new concept consisting in increasing the jobs weight as function of time is established. The effect of this new conception is evaluated by the variation of the average flowtime. Eventually, the computing time of the MILP resolution is studied to explore its limitations.

Predictive-reactive strategy for identical parallel machine rescheduling

Through new technologies development, customers can make or cancel an order at any time, which disrupts the established production schedule. This reality forced many companies to become sensitive in dealing with this situation through rescheduling processes. While efficiency criteria are used to assess the performance of a scheduling system, in dynamic environments, stability criteria measure the impact of job deviation. Differently from previous works, this paper investigates a new performance measure to simultaneously assess schedule efficiency by the total weighted waiting times, and schedule stability by the weighted completion time deviation. This mix could be a very helpful and significant criterion in industrial and health care environments. The studied problem considers an identical parallel machine rescheduling with jobs arriving over time. Based on a predictive-reactive strategy, a Mixed Integer Linear Programming model (MILP) is developed, as well as an iterative methodology for dealing with the online part. At last, numerical results are presented, discussing the impact of the efficiency-stability coefficient on the system performance, as well as the computing time to solve the described problem.

Single-machine slack due-window assignment scheduling with multiple maintenance activities and position-and-resource-dependent processing times

This paper studies the slack due-window assignment method for single-machine scheduling problems with position-and resource-dependent processing times, for which the actual processing time is a continuous bivariate non-increasing convex function involving position and resource allocation. Only the slack due-window assignment method will be used. Two linear combination problems concerning position-dependent effects and resource allocation will be studied, in which the machine requires multiple maintenance activities. We present the optimal properties or design optimal algorithms to minimise the combination of the makespan, the total completion time and the total absolute deviation of completion time and to minimise the combination of the total costs of tardiness, the slack due date, the earliness cost, and the resource amount. Finally, we also consider the bi-criteria scheduling problem with nonmaintenance activities to minimise the combination of the total resource allocation cost, the weighted number of tardy jobs, and slack due-window assignment costs. A pseudo-polynomial time algorithm is designed to solve the bi-criteria scheduling problem.

Predictive-reactive Strategy for Flowshop Rescheduling Problem: Minimizing the Total Weighted Waiting Times and Instability

Due to the fourth revolution experiencing, referred to as Industry 4.0, many production firms are devoted to integrating new technological tools to their manufacturing process. One of them, is rescheduling the tasks on the machines responding to disruptions. While, for static scheduling, the efficiency criteria measure the performance of scheduling systems, in dynamic environments, the stability criteria are also used to assess the impact of jobs deviation. In this paper, a new performance measure is investigated for a flowshop rescheduling problem. This one considers simultaneously the total weighted waiting time as the efficiency criterion, and the total weighted completion time deviation as the stability criterion. This fusion could be a very helpful and significant measure for real life industrial systems. Two disruption types are considered: jobs arrival and jobs cancellation. Thus, a Mixed Integer Linear Programming (MILP) model is developed, as well as an iterative predictive-reactive strategy for dealing with the online part. At last, two heuristic methods are proposed and discussed, in terms of solution quality and computing time.

New efficiency-stability criterion for flow shop rescheduling problem with mixed blocking constraints

Abstract New jobs arrival, jobs cancelation or machine breakdowns, are unexpected events that may occur during production run in real environments, thus disrupting the established schedule. Hence, rescheduling process is necessary for efficiently revising the initial schedule, preferably with little movements. In the literature, many scheduling problems consider unlimited buffer spaces between successive machines in flow shop environments. However, in real life systems, the capacity between machines may be limited or no-store existing. To fill the void, this paper considers a flow shop rescheduling problem with mixed blocking constraints, under disruptions caused by new jobs arrival. A new performance measure is investigated, considering simultaneously the schedule efficiency measured by the total weighted waiting time, and the schedule stability evaluated by the total weighted completion time deviation. This combination could be very helpful for real life industrial systems. A mixed integer linear programming model (MILP) is designed, as well as an iterative methodology based on the predictive reactive rescheduling strategy. At last, two heuristic methods are implemented and discussed, in terms of solution quality and computing time.

Minimizing Earliness/Tardiness costs on multiple machines with an application to surgery scheduling

Early or tardy surgeries are frustrating for both patients and personnel, and cause inefficient use of resources at the operating rooms. The stochastic Earliness/Tardiness (E/T) scheduling problem addresses this by minimizing the total expected deviation of the surgery completion times from the planned completion times. We introduce the concept of E/T-concavity as a property of a probability distribution if the E/T costs are concave as a function of the standard deviation of the completion time, whenever the optimal planned completion times are selected. We use this concept to generate an optimal schedule for the multiple machine variant of the E/T problem. The optimal schedule is not unique and therefore allows us to consider several optimization objectives in addition to the E/T objective. We demonstrate the usefulness of our results in practice by proving E/T-concavity for several probability distributions and by showing that, under the assumption of E/T-concavity, a simple Shortest Variance First (SVF) rule is optimal. We conclude by providing a numerical example of surgery scheduling where we demonstrate the benefits of the SVF rule compared to several commonly used scheduling rules.

A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection

We study a scheduling problem with the objective of minimizing total absolute deviation of completion times (TADC). TADC is considered here in the most general form studied so far: the machine setting is that of parallel unrelated, job processing time are assumed to be position-dependent with no restrictions on the functional form, and the option of processing only a subset of the jobs (i.e., job-rejection) is allowed. We show that minimizing TADC in this very general form remains polynomially solvable in the number of jobs.

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.

Resource-dependent scheduling with deteriorating jobs and learning effects on unrelated parallel machine

The focus of this paper is to analyze unrelated parallel-machine resource allocation scheduling problem with learning effect and deteriorating jobs. The goal is to find the optimal sequence of jobs and the optimal resource allocation separately for minimizing the cost function including the total load, the total completion time, the total absolute deviation of completion time and the total resource cost. We show that the problem is polynomial time solvable if the number of machines is a given constant.

Integrated rescheduling and preventive maintenance for arrival of new jobs through evolutionary multi-objective optimization

In this paper, we study a rescheduling problem in response to arrival of new jobs in single machine layout, where preventive maintenance should be determined. Preventive maintenance together with controllable processing time could alleviate the inherent deteriorating effect in manufacturing system. Processing sequence of original and new jobs, compression of each job, and position of maintenance should be optimized simultaneously with regards to total operational cost (job's total completion times, maintenance cost and compression cost) and total completion time deviation. An improved elitist non-dominated sorting genetic algorithm (NSGA-II) has been proposed to solve the rescheduling problem. To address the key problem of balancing between exploration and exploitation, we hybridize differential evolution mutation operation with NSGA-II to enhance diversity, constitute high-quality initial solution based on assignment model for exploitation, and incorporate analytic property of non-dominated solutions for exploration. Finally computational study is designed by randomly generating various instances with regards to the problem size from given distributions. By use of existing performance indicators for convergence and diversity of Pareto fronts, we illustrate the effectiveness of the hybrid algorithm and the incorporation of domain knowledge into evolutionary optimization in rescheduling.

Scheduling problems with effects of deterioration and truncated job-dependent learning

We study the scheduling problems with effects of deterioration and truncated job-dependent learning effect on a single machine, where the actual processing time of a job is a function of the job-dependent learning effect, its starting time, and a control parameter. The objective functions are to minimize the makespan, the total completion time, the total waiting time, the total absolute deviation of completion time, the total absolute deviation of waiting time, the earliness, tardiness and common (CON) (slack (SLK), unrestricted (DIF)) due date penalty, respectively. For the general case, by reducing them to a linear assignment problem, we solve them in polynomial time \(O(n^3)\). For the special case where all the jobs have a common learning rate, we present an \(O(n \log n)\) algorithm to obtain the optimal solution.

Two-phase branch and bound algorithm for robotic cells rescheduling considering limited disturbance

This paper addresses a robotic cell rescheduling problem and focuses on trade-off between the total completion time of all jobs and the disturbance of a reschedule. We first define and measure the disturbance of a reschedule as the deviation of completion time of the jobs already scheduled between the reschedule and the initial schedule. To guarantee the steady performance of the system, we consider a special case that the processing sequence of the jobs already scheduled cannot be changed. The addressed rescheduling problem is transformed into a series of deterministic local scheduling problems with the objective of minimizing the total completion time of all jobs provided that the disturbance is within a given limit. A two-phase branch and bound algorithm is developed to efficiently solve the local scheduling problems. To improve the efficiency of the search procedure, a dynamic enumeration mechanism is applied to eliminate redundant constraints. Furthermore, two search strategies are proposed to direct the search procedure toward finding an optimal solution and a near-optimal solution. Finally, computational results demonstrate the efficiency of our algorithm.

Single Machine Predictive Scheduling Using Inserted Idle Times

A single machine predictive scheduling problem is considered. The primary objective is to minimize the total completion times. The predictability of the schedule is measured by the completion time deviations between the predictive schedule and realized schedule. The surrogate measure of predictability is chosen to evaluate the completion time deviations. Both of the primary objective and predictability are optimized. In order to absorb the effects of disruptions, the predictive schedule is generated by inserting idle times. Right-shift rescheduling method is used as the rescheduling strategy. Three methods are designed to construct predictive schedules. The computational experiments show that these algorithms provide high predictability with minor sacrifices in shop performance.

Unrelated Parallel-Machine Scheduling with Controllable Processing Time

This paper explores an unrelated parallel-machine resource allocation scheduling problem with controllable processing time. The objective is to minimize the cost function containing the weighted of total load, total completion time, total absolute deviation of completion time, and total compression cost. We show that the proposed problem is polynomial time solvable. We also discuss a special case of the problem and show that it can be optimally solved by lower order algorithm.

Unrelated Parallel-Machine Scheduling with Deteriorating Jobs and Rejection

This paper aimed to investigate the unrelated parallel-machine scheduling with deteriorating jobs and rejection. The objective is to find the rejected jobs, the non-rejected jobs, and the optimal non-rejected job sequence so that the cost function that includes the weighted of total load, total completion time, and total absolute deviation of completion time plus the total penalty of the rejected jobs would be minimized. Results showed that the problem is polynomial time solvable when the number of machine is fixed.

Unrelated parallel-machine scheduling with position-dependent deteriorating jobs and resource-dependent processing time

This paper is to analyze unrelated parallel-machine scheduling resource allocation problems with position-dependent deteriorating jobs. Two general resource consumption functions, the linear and convex resource, are investigated. The objectives are to minimize the cost function that includes the weights of total load, total completion time, total absolute deviation of completion time, and total resource cost. Moreover, we try to minimize the cost function that includes the weights of total load, total waiting time, total absolute deviation of waiting time, and total resource cost. Although each job processing time can be compressed through incurring an additional cost, we show that the problems are polynomial time solvable when the number of machines is fixed.