Two-stage hybrid flow shop scheduling with preventive maintenance using multi-objective tabu search method

This paper investigates an integrated bi-objective optimisation problem with non-resumable jobs for production scheduling and preventive maintenance in a two-stage hybrid flow shop with one machine on the first stage and m identical parallel machines on the second stage. Sequence-dependent set-up times and preventive maintenance (PM) on the first stage machine are considered. The scheduling objectives are to minimise the unavailability of the first stage machine and to minimise the makespan simultaneously. To solve this integrated problem, three decisions have to be made: determine the processing sequence of jobs on the first stage machine, determine whether or not to perform PM activity just after each job, and specify the processing machine of each job on the second stage. Due to the complexity of the problem, a multi-objective tabu search (MOTS) method is adapted with the implementation details. The method generates non-dominated solutions with several parallel tabu lists and Pareto dominance concept. The performance of the method is compared with that of a well-known multi-objective genetic algorithm, in terms of standard multi-objective metrics. Computational results show that the proposed MOTS yields a better approximation.     

Single CNC machine scheduling with controllable processing times and multiple due dates

In this study, we solve the single CNC machine scheduling problem with controllable processing times. Our objective is to maximize the total profit that is composed of the revenue generated by the set of scheduled jobs minus the sum of total weighted earliness and weighted tardiness, tooling and machining costs. Customers offer multiple due dates to the manufacturer, each coming with a distinct price for the order that is decreasing as the date gets later, and the manufacturer has the flexibility to accept or reject the orders. We propose a number of ranking rules and scheduling algorithms that we employ in a four-stage heuristic algorithm that determines the processing times for each job and a final schedule for the accepted jobs simultaneously, to maximize the overall profit.     

生产调度与维护集成的多目标Lorenz非劣遗传优化

研究了一种单机环境下集成生产和维护的双目标优化调度问题。机床的故障间隔时间和平均维修时间服从指数分布,同时结合加工序列相关准备时间。预防性维护活动不能与作业加工同时进行,但与准备时间不相冲突。调度目标是同时最小化作业总计完成时间和机床不可得性。在问题建模的基础上,构造了一种基于Lorenz非劣关系的分类遗传算法(表示为L-NSGA-Ⅱ),详细设计了算法的核心部分。最后,通过大量计算实验,将L-NSGA-II算法与NSGA-II算法进行了比较分析,说明了L-NSGA-II算法的有效性。     

Single-machine scheduling with deteriorating effects and machine maintenance

In this paper, the single-machine scheduling problems with deteriorating effects and a machine maintenance are studied. In this circumstance, the deterioration rates of the jobs during the machining process are the same which reduces the production efficiency. The actual processing time of the job is a linearly increasing function of the starting time. In this process, the machine only performs a maintenance activity, and the maintenance time is a fixed value. After the maintenance work is completed, the machine will be restored to the initial state, and the deterioration of the job will be start again. The goal is to determine the optimal schedule in order to minimise the maximum completion time (i.e. the makespan) and the sum of job completion times. We prove that both problems are polynomial time solvable, and we also provide the corresponding algorithms.     

SINGLE-MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND EARLINESS,TARDINESS AND COMPLETION TIME PENALTIES

The paper considers the problem of scheduling nindependent and simultaneously available jobs on a single machine, where the job processing times are compressible as a linear cost function. The objective is to find an optimal permutation of the jobs, an optimal due date and the optimal processing times which jointly minimize a cost function consisting of the earliness, tardiness, completion time and compressing costs. It shows that the problem can be solved as an assignment problem.     

同时最优化时间表长与总完工时间的双代理单机序列分批排序问题（英）

本文研究在一台序列分批处理机上同时最优化$A$代理的时间表长和$B$代理的总完工时间的双代理排序问题．在序列分批的背景下，工件被分批加工（但不同代理的工件不能在同一批中加工，且每个代理都希望最小化仅依赖于各自工件完工时间的费用函数）且一批的加工时间等于这一批中所有工件的加工时间和．而且在一个新批开始加工前，机器有一个常数的安装时间．此外，根据批容量，序列分批模型又被分成有界模型和无界模型．在本文中，我们对所研究问题的有界模型和无界模型分别给出了一个多项式时间算法．     

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.     

Scheduling parallel batch processing machines with arbitrary job sizes and incompatible job families

Motivated by a bottleneck operation in an MLCC (multi-layer ceramic capacitor) production line, we study the scheduling problem of parallel batch processing machines in which a number of jobs can be processed simultaneously in a machine as a batch. Volumes of the jobs are different from each other and each job belongs to the family in which all jobs have the same processing time. In this situation, we analyse three kinds of problems whose performance measures are makespan, total completion time, and total weighted completion time, respectively. Since these problems are known to be NP-hard, we propose a number of heuristics and design genetic algorithms for the problems. Through some computational experiments, we evaluate the performances of the heuristic algorithms proposed, including the genetic algorithms for each of three problems.     

Control of a batch-processing machine: A computational approach

Batch processing machines, where a number of jobs are processed simultaneously as a batch, occur frequently in semiconductor manufacturing environments, particularly at diffusion in wafer fabrication and at burn-in in final test. In this paper we consider a batch-processing machine subject to uncertain (Poisson) job arrivals. Two different cases are studied: (1) the processing times of batches are independent and identically distributed (IID), corresponding to a diffusion tube; and (2) the processing time of each batch is the maximum of the processing times of its constituent jobs, where the processing times of jobs are IID, modelling a burn-in oven. We develop computational procedures to minimize the expected long-run-average number of jobs in the system under a particular family of control policies. The control policies considered are threshold policies, where processing of a batch is initiated once a certain number of jobs have accumulated in the system. We present numerical examples of our methods and verify their accuracy using simulation.     

Machining conditions-based preventive maintenance

In this study we propose an operating conditions-based preventive maintenance (PM) approach for computer numerical control (CNC) turning machines. A CNC machine wears according to how much it is used and the conditions under which it is used. Higher power or production rates result in more wear and higher failure rates. This relationship between the operating conditions and maintenance requirements is usually overlooked in the literature. On CNC turning machines we can control the machining conditions such as cutting speed and feed rate, which in turn affect the PM requirements of the CNC machine. We provide a new model to link the PM decisions to the machining conditions selection decisions, so that these two decision-making problems can be solved together by considering their impact on each other. We establish that our proposed geometric programming model captures the related cost terms along with the technological restrictions of CNC machines. The proposed preventive maintenance index function can be used to provide an intelligent CNC machine degradation assessment.     

Rescheduling with controllable processing times for number of disrupted jobs and manufacturing cost objectives

We consider a machine rescheduling problem that arises when a disruption such as machine breakdown occurs to a given schedule. Machine unavailability due to a breakdown requires repairing the schedule as the original schedule becomes infeasible. When repairing a disrupted schedule a desirable goal is to complete each disrupted job on time, i.e. not later than the planned completion time in the original schedule. We consider the case where processing times of jobs are controllable and compressing the processing time of a job requires extra processing cost. Usually, there exists a nonlinear relation between the processing time and manufacturing cost. We solve a bicriteria rescheduling problem that trades off the number of on-time jobs and manufacturing cost objectives. We give a mixed-integer second-order cone programming formulation for the problem. We develop a heuristic search algorithm to generate efficient solutions for the problem. Heuristic algorithm searches solution space by moving and swapping jobs among machines. We develop cost change estimates for job moves and swaps so that the heuristic implements only promising moves and hence generates a set of efficient solutions in reasonably short CPU times.     

Parallel-machine scheduling with controllable processing times and rate-modifying activities to minimise total cost involving total completion time and job compressions

In this paper, we consider unrelated parallel-machine scheduling involving controllable processing times and rate-modifying activities simultaneously. We assume that the actual processing time of a job can be compressed by allocating a greater amount of a common resource to process the job. We further assume that each machine may require a rate-modifying activity during the scheduling horizon. The objective is to determine the optimal job compressions, the optimal positions of the rate-modifying activities and the optimal schedule to minimise a total cost function that depends on the total completion time and total job compressions. If the number of machines is a given constant, we propose an efficient polynomial time algorithm to solve the problem.     

Bi-objective optimisation for integrated scheduling of single machine with setup times and preventive maintenance planning

This paper deals with an integrated bi-objective optimisation problem for production scheduling and preventive maintenance in a single-machine context with sequence-dependent setup times. To model its increasing failure rate, the time to failure of the machine is subject to Weibull distribution. The two objectives are to minimise the total expected completion time of jobs and to minimise the maximum of expected times of failure of the machine at the same time. During the setup times, preventive maintenance activities are supposed to be performed simultaneously. Due to the assumption of non-preemptive job processing, three resolution policies are adapted to deal with the conflicts arising between job processing and maintenance activities. Two decisions are to be taken at the same time: find the permutation of jobs and determine when to perform the preventive maintenance. To solve this integrated problem, two well-known evolutionary genetic algorithms are compared to find an approximation of the Pareto-optimal front, in terms of standard multi-objective metrics. The results of extensive computational experiments show the promising performance of the adapted algorithms.     

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.     

Bicriteria scheduling problems involving job rejection,controllable processing times and rate-modifying activity

This paper addresses the bicriteria scheduling problems with simultaneous consideration of job rejection, controllable processing times and rate-modifying activity on a single machine. A job is either rejected, in which case a rejection penalty will be incurred, or accepted and processed on the machine. The rate-modifying activity is an activity on the machine that changes the processing times of the jobs scheduled after the activity. The processing time of a job scheduled after the rate-modifying activity decreases with a job-dependent factor. The processing time of each job can also be controlled by allocating extra resource which is either a linear or a convex function of the amount of a common continuously divisible resource allocated to the job. The objective is to determine the rejected job set, the accepted job sequence, the time (location) of the rate-modifying activity and the resource allocation that jointly find the trade-off between two criteria, where the first criterion is measured as the sum of total completion time and resource consumption cost while the second criterion is the total rejection cost. We consider four different models for treating the two criteria. The computational complexity status and solution procedures are provided for the problems under consideration.     

Scheduling a no-wait flow shop containing unbounded batching machines

We study the problem of scheduling n jobs in a no-wait flow shop consisting of m batching machines. Each job has to be processed by all the machines. All jobs visit the machines in the same order. A job completed on an upstream machine should be immediately transferred to the downstream machine. Batching machines can process several jobs simultaneously in a batch so that all jobs of the same batch start and complete together. The processing time of a batch is equal to the maximum processing time of the jobs in this batch. We assume that the capacity of any batch is unbounded. The problem is to find an optimal batch schedule such that the maximum job completion time, that is the makespan, is minimized. For m = 2, we prove that there exists an optimal schedule with at most two batches and construct such a schedule in O(n log n) time. For m = 3, we prove that the number of batches can be limited to nine and give an example where all optimal schedules have seven batches. Furthermore, we prove that the best schedules with at most one, two and three batches are 3-, 2- and 3/2-approximate solutions, respectively. The first two bounds are tight for corresponding schedules. Finally, we suggest an assignment method that solves the problem with m machines and at most r batches in O(n^{m(r-2)+1+[m/r]}) time, if m and r are fixed. The method can be generalized to minimize an arbitrary maximum cost or total cost objective function.     

An ordered flow-shop sequencing problem with mean completion time criterion†

This paper investigates a subcategory of the classical n job m machine problem in which the processing times of different jobs are ' ordered '. An extremely simple algorithm is presented which obtains a sequence minimizing the mean completion time of all jobs. The proof of optimality is presented in the Appendix. The problem illustratos that although no efficient procedure exists to solve the classical flow-shop problem with the mean completion time criterion, it is possible to develop such a procedure for a specially structured problem.     

Probabilistic asymptotic analysis of stochastic online scheduling problems

In the stochastic online scheduling environment, jobs with unknown release times and weights arrive over time. Upon arrival, the information on the weight of the job is revealed but the processing requirement remains unknown until the job is finished. In this paper we consider the objective of minimizing the total weighted completion time. With the assumptions that job weights are bounded, machine capacity is adequate, and processing requirements are bounded and identical and independently distributed across the machines and jobs, we show that any nondelay algorithm is asymptotically optimal for the stochastic online single machine problem, flow shop problem, and uniform parallel machine problem. Our simulation studies of these stochastic online scheduling problems show that two generic nondelay algorithms perform very well as long as the number of jobs is larger than 100.     

Inventory-based dispatching of automated guided vehicles on container terminals

This paper deals with automated guided vehicles (AGVs) which transport containers between the quay and the stack on automated container terminals. The focus is on the assignment of transportation jobs to AGVs within a terminal control system operating in real time. First, we describe a rather common problem formulation based on due times for the jobs and solve this problem both with a greedy priority rule based heuristic and with an exact algorithm. Subsequently, we present an alternative formulation of the assignment problem, which does not include due times. This formulation is based on a rough analogy to inventory management and is solved using an exact algorithm. The idea behind this alternative formulation is to avoid estimates of driving times, completion times, due times, and tardiness because such estimates are often highly unreliable in practice and do not allow for accurate planning. By means of simulation, we then analyze the different approaches. We show that the inventory-based model leads to better productivity on the terminal than the due-time-based formulation.     

Scheduling with non-decreasing deterioration jobs and variable maintenance activities on a single machine

There is a situation found in many manufacturing systems, such as steel rolling mills, fire fighting or single-server cycle-queues, where a job that is processed later consumes more time than that same job when processed earlier. The research finds that machine maintenance can improve the worsening of processing conditions. After maintenance activity, the machine will be restored. The maintenance duration is a positive and non-decreasing differentiable convex function of the total processing times of the jobs between maintenance activities. Motivated by this observation, the makespan and the total completion time minimization problems in the scheduling of jobs with non-decreasing rates of job processing time on a single machine are considered in this article. It is shown that both the makespan and the total completion time minimization problems are NP-hard in the strong sense when the number of maintenance activities is arbitrary, while the makespan minimization problem is NP-hard in the ordinary sense when the number of maintenance activities is fixed. If the deterioration rates of the jobs are identical and the maintenance duration is a linear function of the total processing times of the jobs between maintenance activities, then this article shows that the group balance principle is satisfied for the makespan minimization problem. Furthermore, two polynomial-time algorithms are presented for solving the makespan problem and the total completion time problem under identical deterioration rates, respectively.