Actual Processing Time Research Articles

Scheduling in bicriteria single machine systems with past-sequence-dependent setup times and learning effects

Scheduling with setup times and learning plays a crucial role in today's manufacturing and service environments where scheduling decisions are made with respect to multiple performance criteria rather than a single criterion. In this paper, we address a bicriteria single machine scheduling problem with job-dependent past-sequence-dependent setup times and job-dependent position-based learning effects. The setup time and actual processing time of a job are respectively unique functions of the actual processing times of the already processed jobs and the position of the job in a schedule. The objective is to derive the schedule that minimizes a linear composite function of a pair of performance criteria consisting of the makespan, the total completion time, the total lateness, the total absolute differences in completion times, and the sum of earliness, tardiness, and common due date penalty. We show that the resulting problems cannot be solved in polynomial time; thus, branch-and-bound (B&B) methods are proposed to obtain the optimal schedules. Our computational results demonstrate that the B&B can solve instances of various size problems with attractive times.

Scheduling with Multiple Common Due Windows Assignment and General Position-Dependent and Resource-Dependent Processing Times

In this paper we consider multiple common due windows assignment and single-machine scheduling problems with general position-dependent and resource-dependent processing times simultaneously. Multiple common due windows, an extension of single common due window, allow a job to fit one from multiple common due windows. We assume that the number of common due windows to be assigned to the jobs is given. Two resource allocation models are examined, namely the linear resource consumption model and the convex re-source consumption model. The actual processing time of a job is a function of its scheduled position in a sequence and its resource allocation. We aim to determine jointly the optimal common due window positions and sizes, the set of jobs assigned to each common due window, the optimal resource allocations, and the optimal schedule for minimizing an objective function which includes earliness, tardiness, common due windows assignment, makespan, and resource consumption costs. We provide some properties of the optimal schedule for the problem and propose polynomial time algorithms for all the problems considered.

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.

Parallel machines scheduling with deteriorating jobs and availability constraints

We consider parallel machines scheduling problem in which the actual processing time of the job is a proportional function of its starting time and each machine is not available in a specified time period. We consider the non-resumable case. The objective is to minimize the weighted sum of completion times. We show that the general case of the problem is inapproximable unless P = NP and present a pseudo-polynomial dynamic programming algorithm. We also present a fully polynomial-time approximation scheme for the special case of the problem where only one machine is not available in a specified time period.

Single machine common flow allowance scheduling with deteriorating jobs and a rate-modifying activity

We study a single machine slack due date assignment (usually referred to as SLK) scheduling problem with deteriorating jobs and a rate-modifying activity. The deterioration effect manifest such that the job processing time is a function of its starting time in a sequence. The rate-modifying activity is an activity that changes the processing rate of machine, i.e., the machine performs a rate-modifying activity. Hence the actual processing time of a job is a variable, which depends not only on its starting time in a sequence but also on whether it is scheduled before or after a rate-modifying activity. The goal is to schedule the rate-modifying activity, the optimal common flow allowance and the sequence of jobs to minimize the total earliness, the total tardiness and the common flow allowance cost. We show that the problem remains polynomially solvable under the proposed model.

Scheduling deteriorating jobs with a learning effect on unrelated parallel machines

In this study we consider unrelated parallel machines scheduling problems with learning effect and deteriorating jobs, in which the actual processing time of a job is a function of joint time-dependent deterioration and position-dependent learning. The objective is to determine the jobs assigned to corresponding each machine and the corresponding optimal schedule to minimize a cost function containing total completion (waiting) time, total absolute differences in completion (waiting) times and total machine load. If the number of machines is a given constant, we show that the problems can be solved in polynomial time under the time-dependent deterioration and position-dependent learning model.

Single-machine group scheduling problem considering learning, forgetting effects and preventive maintenance

An integrated single-machine group scheduling model is proposed, which incorporates both learning and forgetting effects and preventive maintenance (PM) planning. The objective is to minimise the expected makespan by optimising job sequence and PM decisions. This model contains sequence-dependent set-up time, actual processing time, planned PM time and expected minimal repair time simultaneously. Based on the properties of group production, three learning functions under different circumstances are proposed to deduce the variable processing time of each part, considering the learning effect when consecutively producing identical or similar parts, together with the forgetting effect when transferring jobs interrupts the production process and makes retrogress in learning. Both run-based maintenance and minimal repair policies are specified to handle the uncertainty of machine breakdowns. The search algorithm for the model is developed, and the numerical example is studied. The computational results and sensitivity analysis show that this improved group scheduling model can well balance the machine resource requirements from different practical manufacturing-related activities.

Novel condensed workflow for recombinant protein purification from E.coli (LB275)

Many scientists require purified proteins for their research applications. To meet this need, a multitude of recombinant expression techniques have been developed. While many expression systems are available, E. coli represents the most optimized and widely used vehicles for the expression of 6x Histidine tagged recombinant proteins. Traditionally, the recombinant protein purification workflow consists of five distinct phases: Harvest, Lysis, Clarification, Purification and Analysis. Lysis typically requires multiple time consuming, hands‐on steps, such as freeze/thaw cycling and sonication, which may be harsh and may negatively impact protein quality and contribute to sample variability. Clarification is typically performed in a centrifuge, which makes automation challenging and is primarily needed to reduce clogging in the downstream purification step. Purification is typically performed using columns packed with agarose beads with specificity for the tag on the recombinant protein. While columns provide an easy approach for manipulation of the affinity media, they are greatly affected by lysate consistency and carry‐over of cell debris, which can lead to clogging and poor protein purification and recovery. To guarantee maximum recovery of protein activity and integrity, we have developed a protocol leveraging gentle enzymatic cell lysis and purification with magnetic beads to condense the traditional His‐tag protein purification workflow. A significantly improved workflow was developed by combining Lysis and Purification and eliminating the need for Clarification, resulting in a greater than two hour time savings over the traditional workflow. In addition, this condensed workflow facilitates automation, resulting in increased sample throughput while further reducing actual hands‐on processing time.

Single-machine scheduling with time-dependent and position-dependent deteriorating jobs

In many real-life scheduling situations, the jobs deteriorate at a certain rate while waiting to be processed. This study introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The objective is to find the optimal schedule such that the makespan or total completion time is minimised. This study first shows that both problems are solvable in O(n log n) time. This study further shows that in both cases there exists an optimal schedule that is the shortest processing time, longest processing time, or V-shaped with respect to the job normal processing times, depending on the relationships between problem parameters.

Unrelated parallel machines scheduling with deteriorating jobs and resource dependent processing times

We consider unrelated parallel machines scheduling problems involving resource dependent (controllable) processing times and deteriorating jobs simultaneously, i.e., the actual processing time of a job is a function of its starting time and its resource allocation. Two generally resource consumption functions, the linear and convex resource, were investigated. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. This paper focus on the objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. If the number of unrelated parallel machines is a given constant, we show that the problems remain polynomially solvable under the proposed model.

Single-machine group scheduling with processing times dependent on position, starting time and allotted resource

This article considers scheduling problems on a single machine with learning effect, deteriorating jobs and resource allocation under group technology (GT) assumption. We assume that the actual processing time of a job depends on the job position, the group position, the starting time and the amount of resource allocated to them concurrently, and the actual setup times of groups depend on the group position and the amount of resource allocated to them concurrently. Two resource allocation functions are examined for minimizing the weighted sum of makespan and total resource cost. We prove that the problems have polynomial solutions under the condition that the number of jobs in each group are the same.

Single machine scheduling with sum-of-logarithm-processing-times based deterioration

In this study we consider the single machine scheduling problems with sum-of-logarithm-processing-times based deterioration, i.e., the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. We show that even with the introduction of the sum-of-logarithm-processing-times based deterioration to job processing times, single machine makespan minimization problem remain polynomially solvable. But for the total completion time minimization problem, we show that the optimal schedule is not always V-shaped with respect to job normal processing times. Heuristic algorithms and computational results are presented for the total completion time minimization problem.

Multi-machine scheduling with general position-based deterioration to minimize total load revisited

In this paper, we investigate multi-machine scheduling problems with general position-dependent effects where the actual processing time functions of jobs are not only associated with the job's position in the sequence but also associated with the machine number and the job number. All the processing time functions of jobs are not restricted to any specific form. The objective is to minimize the total load on machines. Analytical results show that all the considered multi-machine scheduling problems can be optimally solved in polynomial time.

Single-machine batch delivery scheduling and common due-date assignment with a rate-modifying activity

We consider batch delivery scheduling on a single machine, where a common due-date is assigned to all the jobs and a rate-modifying activity on the machine may be scheduled, which can change the processing rate of the machine. Thus the actual processing time of a job is variable depending on whether it is processed before or after the rate-modifying activity. The objective is to determine the optimal job sequence, the optimal partition of the job sequence into batches, the optimal assigned common due-date, and the optimal location of the rate-modifying activity simultaneously to minimize the total cost of earliness, job holding, weighted number of tardy jobs, due-date assignment, and batch delivery. We derive some structural properties of the problem, based on which we design polynomial-time algorithms to solve some special cases of the problem.

Single-machine rescheduling with deterioration and learning effects against the maximum sequence disruption

In this paper, we study the issue of single-machine rescheduling with linear deteriorating jobs and position-based learning effects simultaneously in response to an unexpected arrival of new jobs. The scheduling efficiency is measured in terms of the makespan, while the cost of disruption is measured in terms of the maximum difference in processing orders of the original jobs before and after disruption. By introducing the effects of deterioration and learning, the job actual processing time is defined by an increasing function of its starting time, meanwhile a decreasing function of its position. Two types of problems are considered. For the first one, the makespan is minimised subject to a limit on the maximum sequence disruption; while in the second one, a linear combination of the makespan and the maximum sequence disruption is minimised. For each problem, the polynomial solvability is demonstrated, and an efficient algorithm is then developed. Finally, extensive computational experiments are conducted to show the efficiency and running behaviours of the proposed algorithms.

The potential of positron emission tomography for intratreatment dynamic lung tumor tracking: A phantom study

This study aims to evaluate the potential and feasibility of positron emission tomography for dynamic lung tumor tracking during radiation treatment. The authors propose a center of mass (CoM) tumor tracking algorithm using gated-PET images combined with a respiratory monitor and investigate the geometric accuracy of the proposed algorithm. The proposed PET dynamic lung tumor tracking algorithm estimated the target position information through the CoM of the segmented target volume on gated PET images reconstructed from accumulated coincidence events. The information was continuously updated throughout a scan based on the assumption that real-time processing was supported (actual processing time at each frame ≈ 10 s). External respiratory motion and list-mode PET data were acquired from a phantom programmed to move with measured respiratory traces (external respiratory motion and internal target motion) from human subjects, for which the ground truth target position was known as a function of time. The phantom was cylindrical with six hollow sphere targets (10, 13, 17, 22, 28, and 37 mm in diameter). The measured respiratory traces consisted of two sets: (1) 1D-measured motion from ten healthy volunteers and (2) 3D-measured motion from four lung cancer patients. The authors evaluated the geometric accuracy of the proposed algorithm by quantifying estimation errors (Euclidean distance) between the actual motion of targets (1D-motion and 3D-motion traces) and CoM trajectories estimated by the proposed algorithm as a function of time. The time-averaged error of 1D-motion traces over all trajectories of all targets was 1.6 mm. The error trajectories decreased with time as coincidence events were accumulated. The overall error trajectory of 1D-motion traces converged to within 2 mm in approximately 90 s. As expected, more accurate results were obtained for larger targets. For example, for the 37 mm target, the average error over all 1D-motion traces was 1.1 mm; and for the 10 mm target, the average error over all 1D-motion traces was 2.8 mm. The overall time-averaged error of 3D-motion traces was 1.6 mm, which was comparable to that of the 1D-motion traces. There were small variations in the errors between the 3D-motion traces, although the motion trajectories were very different. The accuracy of the estimates was consistent for all targets except for the smallest. The authors developed an algorithm for dynamic lung tumor tracking using list-mode PET data and a respiratory motion signal, and demonstrated proof-of-principle for PET-guided lung tumor tracking. The overall tracking error in phantom studies is less than 2 mm.

Scheduling with deteriorating jobs and setup times on a single machine

This paper addresses several single-machine scheduling problems with deteriorating jobs and setup times to minimise the maximum lateness, the weighted number of tardy jobs and the total weighted completion time. The actual job processing times and setup times are both proportional functions of their starting times. For the maximum lateness problem, we first show that the general problem is -hard, which also resolves an open question on its complexity raised in the literature, and then we show that the problem with a fixed number of families is polynomially solvable. For the weighted number of tardy jobs problem, we first present a pseudo-polynomial-time algorithm when the number of families is fixed, and then we provide an O(n2)-time algorithm for the unweighted problem with uniform family due dates. For the total weighted completion time problem, we present a polynomial-time algorithm when the number of families is fixed.

Some single-machine scheduling problems with learning effects and two competing agents.

This study considers a scheduling environment in which there are two agents and a set of jobs, each of which belongs to one of the two agents and its actual processing time is defined as a decreasing linear function of its starting time. Each of the two agents competes to process its respective jobs on a single machine and has its own scheduling objective to optimize. The objective is to assign the jobs so that the resulting schedule performs well with respect to the objectives of both agents. The objective functions addressed in this study include the maximum cost, the total weighted completion time, and the discounted total weighted completion time. We investigate three problems arising from different combinations of the objectives of the two agents. The computational complexity of the problems is discussed and solution algorithms where possible are presented.

Single-machine due window assignment and scheduling with a common flow allowance and controllable job processing time

In this paper, we consider single-machine due window assignment and scheduling with a common flow allowance and controllable job processing times, subject to unlimited or limited resource availability. Due window assignment with a common flow allowance means that each job has a job-dependent due window, the starting time and completion time of which are equal to its actual processing time plus the job-independent parameters q1 and q2, respectively, which are common to all the jobs. The processing time of each job is either a linear or a convex function of the amount of a common continuously divisible resource allocated to the job. We study five versions of the problem that differ in terms of the objective function and processing time function being used. We provide structural properties of the optimal schedules and polynomial-time solution algorithms for the considered problems.

Scheduling problems with multiple due windows assignment and controllable processing times on a single machine

This paper deals with multiple due windows assignment scheduling problems and controllable processing times on a single machine. We assume that the actual processing time of a job can be controlled by the introduction of additional resource and any due window is not allowed to contain another due window as a proper subset. The objective is to determine the optimal due window positions and sizes, the set of jobs assigned to each due window, the optimal job compressions, and the optimal schedule to minimize a total cost function, which consists of the earliness, the tardiness, the processing time compressions, and the due windows related costs. We show that for the case when the number of jobs assigned to each due window is given in advance, the problem is polynomially solvable in O(n3) time, where n is the total number of jobs; while if the number of jobs assigned to each due window is unknown, the problem can be optimally solved in O(nm+2) time, where m is the number of due windows. Furthermore, we extend the problem by incorporating with the aging effect and prove that it remains polynomially solvable.