A methodology for joint optimization for maintenance planning, process quality and production scheduling

Performance of a manufacturing system depends significantly on the shop floor performance. Traditionally, shop floor operational policies concerning maintenance scheduling, quality control and production scheduling have been considered and optimized independently. However, these three aspects of operations planning do have an interaction effect on each other and hence need to be considered jointly for improving the system performance. In this paper, a model is developed for joint optimization of these three aspects in a manufacturing system. First, a model has been developed for integrating maintenance scheduling and process quality control policy decisions. It provided an optimal preventive maintenance interval and control chart parameters that minimize expected cost per unit time. Subsequently, the optimal preventive maintenance interval is integrated with the production schedule in order to determine the optimal batch sequence that will minimize penalty-cost incurred due to schedule delay. An example is presented to illustrate the proposed model. It also compares the system performance employing the proposed integrated approach with that obtained by considering maintenance, quality and production scheduling independently. Substantial economic benefits are seen in the joint optimization.     

Integrated production and preventive maintenance scheduling for a single machine with failure uncertainty

This paper addresses the problem of finding a robust and stable schedule for a single machine with availability constraints. The machine suffers unexpected breakdowns and follows the Weibull failure function. A joint model for integrating run-based preventive maintenance (PM) into the production scheduling problem is proposed, in which the sequence of jobs, the PM times and the planned completion times of jobs are proactively determined simultaneously. Aiming at optimizing the bi-objective of system robustness and stability, a genetic algorithm based on the properties of the optimal schedule is proposed. The experimental results demonstrate that the proposed algorithm is efficient and effective under practical problem sizes. In addition, the impact of degree of uncertainty on the performance and the tradeoff between robustness and stability are explored in detail.     

An optimal production and inspection strategy with preventive maintenance error and rework

This study considers the integrated problem of production, preventive maintenance (PM), inspection, and inventory for an imperfect production process where rework and PM error exist. PM is performed when the process is in a controlled state. The correct implementation of PM results in a lower system failure rate, whereas a PM error results in the system shifting to the out-of-control state with a certain probability. The age of the system after PM is correlated with the level of PM performed. When the process in an out-of-control state produces a certain percentage of non-conforming items, we assume that a certain proportion of the non-conforming items can be reworked into conforming items. In a deteriorating production system, we determine the optimal inspection interval, inspection frequency, and production quantity that will yield the maximal unit expected profit. Numerical analyses are used to investigate the effectiveness of imperfect PM and to explore the effect of rework and PM error on profit.     

Performance evaluation of subsea BOP control systems using dynamic Bayesian networks with imperfect repair and preventive maintenance

The work presents a dynamic Bayesian networks (DBN) modeling of series, parallel and 2-out-of-3 (2oo3) voting systems, taking account of common-cause failure, imperfect coverage, imperfect repair and preventive maintenance. Seven basic events of one, two or three component failure are proposed to model the common-cause failure of the three-components-systems. The imperfect coverage is modeled in the conditional probability table by defining a coverage factor. A multi-state degraded component is used to model the imperfect repair and preventive maintenance. Using the proposed method, a DBN modeling of a subsea blowout preventer (BOP) control system is built, and the reliability and availability are evaluated. The mutual information is researched in order to assess the important degree of basic events. The effects of degradation probability, failure rate and mean time to repair (MTTR) on the performances are studied. The results show that the repairs and maintenance can improve the system performance significantly, whereas the imperfect repair cannot degrade the system performance significantly in comparison with the perfect repair, and the preventive maintenance can improve the system performance slightly in comparison with the imperfect repair. In order to improve the performance of subsea BOP control system, the single surface components and the components with all-common-cause failure should given more attention. The influence of degradation probability on the performance is in the order of PLC, PC and ES. The influence of failure rate and MTTR on the performance is in the order of PLC, ES, PC, DO, DI and AI.     

Optimal production scheduling for hybrid manufacturing–remanufacturing systems with setups

Hybrid systems that use both raw materials (manufacturing mode) and returned products (remanufacturing mode) in their production process are considered. The system consists of one facility and necessitates setup for switching from one production mode to another. Since the flow rate of returned products is limited (fixed percentage of the demand rate is considered), switching from one mode to another is unavoidable, and so production and setup scheduling becomes critical for meeting customer demand and manufacturing cost optimization. Analytical solutions for production and setup strategies are obtained, feasibility conditions are derived, and the sensitivity of obtained results over system parameters is investigated. It is demonstrated that there exist two types of systems: mainly manufacturing systems with a relatively low rate of return, and mainly remanufacturing systems with a relatively low use of raw materials. Quantitative criteria distinguishing these two types of systems are developed, and it is shown that systems of different types obey different feasibility conditions and exhibit different optimal behavior.     

An effective heuristic for flexible job-shop scheduling problem with maintenance activities

Most production scheduling problems, including the standard flexible job-shop scheduling problem (FJSP), assume that machines are continuously available. However, in most realistic situations, machines may become unavailable during certain periods due to preventive maintenance (PM). In this paper, a flexible job-shop scheduling problem with machine availability constraints is considered. Each machine is subject to preventive maintenance during the planning period and the starting times of maintenance activities are either flexible in a time window or fixed beforehand. Moreover, two cases of maintenance resource constraint are considered: sufficient maintenance resource available or only one maintenance resource available. To deal with this variant FJSP problem with maintenance activities, a filtered beam search (FBS) based heuristic algorithm is proposed. With a modified branching scheme, the machine availability constraint and maintenance resource constraint can be easily incorporated into the proposed algorithm. Simulation experiments are conducted on some representative problems. The results demonstrate that the proposed filtered beam search based heuristic algorithm is a viable and effective approach for the FJSP with maintenance activities.     

Production planning and worker training in dynamic manufacturing systems

Production planning is a vital activity in any manufacturing system, and naturally implies assigning the available resources to the required operations. This paper develops and analyzes a comprehensive mathematical model for dynamic manufacturing systems. The proposed model integrates production planning and worker training considering machine and worker time availability, operation sequence and multi-period planning horizon. The objective is to minimize machine maintenance and overhead, system reconfiguration, backorder and inventory holding, training and salary of worker costs. Computational results are presented to verify the proposed model.     

Preventive maintenance and replacement scheduling for repairable and maintainable systems using dynamic programming

This paper presents mathematical models and a solution approach to determine the optimal preventive maintenance schedules for a repairable and maintainable series system of components with an increasing rate of occurrence of failure (ROCOF). The maintenance planning horizon has been divided into discrete and equally-sized periods and in each period, three possible actions for each component (maintain it, replace it, or do nothing) have been considered. The optimal decisions for each component in each period are investigated such that the objectives and the requirements of the system can be achieved. In particular, the cases of minimizing total cost subject to a constraint on system reliability, and maximizing system reliability subject to a budgetary constraint on overall cost have been modeled. As the optimization methodology, dynamic programming combined with branch-and-bound method is utilized and the effectiveness of the approach is presented through the use of a numerical example. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

基于柔性维护的堕化单机系统调度研究

针对单机系统,在假设生产系统为堕化系统,且生产过程中作业的加工不可中断的情况下,对考虑柔性时间窗口[[u,v]]下进行长度为[w]的周期预防性维护的调度问题进行了研究。建立了综合考虑生产调度和设备维护的混合整数规划模型,并设计了一套基于贪婪的启发式算法对所研究问题进行优化求解。通过Cplex和启发式算法求解结果的对比证明了算法可以快速、有效地解决此类问题。     

Distributed joint dynamic maintenance and production scheduling in manufacturing systems: Framework based on model predictive control and Benders decomposition

Scheduling the maintenance based on the condition, respectively the degradation level of the system leads to improved system's reliability while minimizing the maintenance cost. Since the degradation level changes dynamically during the system's operation, we face a dynamic maintenance scheduling problem. In this paper, we address the dynamic maintenance scheduling of manufacturing systems based on their degradation level. The manufacturing system consists of several units with a defined capacity and an individual dynamic degradation model, seeking to optimize their reward. The units sell their production capacity, while maintaining the systems based on the degradation state to prevent failures. The manufacturing units are jointly responsible for fulfilling the demand of the system. This induces a coupling constraint among the agents. Hence, we face a large-scale mixed-integer dynamic maintenance scheduling problem. In order to handle the dynamic model of the system and large-scale optimization, we propose a distributed algorithm using model predictive control (MPC) and Benders decomposition method. In the proposed algorithm, first, the master problem obtains the maintenance scheduling for all the agents, and then based on this data, the agents obtain their optimal production using the distributed MPC method which employs the dual decomposition approach to tackle the coupling constraints among the agents. The effectiveness of the proposed method is investigated on two case studies.     

Use of (max, +) algebra for scheduling and optimization of HVLV systems subject to preventive maintenance

High-Variety, Low-Volume (HVLV) manufacturing systems are built to produce parts of several types in small quantities and under multiple production objectives. They relate to job-shop systems well known by researchers. One of the most studied assumptions of HVLV systems scheduling is considering that machines may be periodically unavailable during the production scheduling. This article deals with an analytical integrating method using (max, +) algebra to model HVLV scheduling problems subject to preventive maintenance (PM) while considering machines availability constraints. Each machine is subject to PM while maintaining flexibility for the start time of the maintenance activities during the planning period. The proposed model controls the placement of maintenance activities along the production operations. Indeed, the sequencing of maintenance activities on the machines depends on the criteria to minimize and may be different for each criteria value. For preventive maintenance, the proposed model aims to generate the best sequencing between activities while respecting the planning program that satisfy the optimal criteria values. In order to illustrate the performance of the proposed methodology, a simulation example is given.     

Bi-objective optimization algorithms for joint production and maintenance scheduling: application to the parallel machine problem

This paper deals with the joint production and maintenance scheduling problem according to a new bi-objective approach. This method allows the decision maker to find compromise solutions between the production objectives and maintenance ones. Reliability models are used to take into account the maintenance aspect of the problem. The aim is to simultaneously optimize two criteria: the minimization of the makespan for the production part and the minimization of the system unavailability for the maintenance side. Two decisions are taken at the same time: finding the best assignment of n jobs to m machines in order to minimize the makespan and deciding when to carry out the preventive maintenance actions in order to minimize the system unavailability. The maintenance actions numbers as well as the maintenance intervals are not fixed in advance. Two evolutionary genetic algorithms are compared to find an approximation of the Pareto-optimal front in the parallel machine case. On a large number of test instances (more than 5000), the obtained results are promising.     

Two-machine flow shop scheduling integrated with preventive maintenance planning

This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.     

Maintenance scheduling and production control of multiple-machine manufacturing systems

This paper deals with the production and preventive maintenance control problem for a multiple-machine manufacturing system. The objective of such a problem is to find the production and preventive maintenance rates for the machines so as to minimize the total cost of inventory/backlog, repair and preventive maintenance. A two-level hierarchical control model is presented, and the structure of the control policy for both identical and non-identical manufacturing systems is described using parameters, referred to here as input factors. By combining analytical formalism with simulation-based statistical tools such as experimental design and response surface methodology, an approximation of the optimal control policies and values of input factors are determined. The results obtained extend those available in existing literature to cover non-identical machine manufacturing systems. A numerical example and a sensitivity analysis are presented in order to illustrate the robustness of the proposed approach. The extension of the proposed production and preventive maintenance policies to cover large systems (multiple machines, multiple products) is discussed.     

A hierarchic approach to production planning and scheduling of a flexible manufacturing system

The paper deals with the problem of improving the machine utilization of a flexible manufacturing cell. Limited tool magazine space of the machines turns out to be a relevant bottleneck. A hierarchic approach for this problem is proposed. At the upper level, sets of parts that can be concurrently processed (batches) are determined. At the lower levels, batches are sequenced, linked, and scheduled. Methods taken from the literature are used for the solution of the latter subproblems, and an original mixed integer programming model is formulated to determine batches. The proposed methods are discussed on the basis of computational experience carried out on real instances.     

Hierarchical production planning for complex manufacturing systems

A hierarchical approach to production planning for complex manufacturing systems is presented. A single facility comprising a number of work-centers that produce multiple part types is considered. The planning horizon includes a sequence of time periods, and the demand for all part types is assumed known. The production planning problem consists of minimizing the holding costs for all part types, as well as the work-in-process and the backlogging costs for the end items. We present a two-level hierarchy that is based on aggregating parts to part families, work-centers to manufacturing cells and time periods to aggregate time periods. The solution at the aggregate level is imposed as a constraint to the detailed level problems which are formulated for each manufacturing cell separately. This architecture uses a rolling horizon strategy to perform the production management function. We have employed perturbation analysis techniques to adjust certain parameters of the optimization problems at the detailed level to reach a near-optimal detailed production plan. Numerical results for several realistic example problems are presented and the solutions obtained from the hierarchical and monolithic approaches are compared. The results indicate that the hierarchical approach offers major advantages in computational efficiency, while the loss of optimality is acceptable.     

On the importance of sequencing decisions in production planning and scheduling

We discuss the traditional hierarchical approach to production planning and scheduling, emphasizing the fact that scheduling constraints are often either ignored or considered in a very crude way. In particular, we underline that the way scheduling is carried out is crucial for the capacity constraints on the lot sizes. Usual methods to handle capacity in theory or in practice are reviewed. Finally, we present an approach that tries to overcome these drawbacks by capturing the shop–floor capacity through scheduling considerations.     

A modified genetic algorithm approach for scheduling of perfect maintenance in distributed production scheduling

Distributed Scheduling (DS) problems have attracted attention by researchers in recent years. DS problems in multi-factory production are much more complicated than classical scheduling problems because they involve not only the scheduling problems in a single factory, but also the problems in the higher level, which is: how to allocate the jobs to suitable factories. It mainly focuses on solving two issues simultaneously: (i) allocation of jobs to suitable factories and (ii) determination of the corresponding production schedules in each factory. Its objective is to maximize system efficiency by finding an optimal plan for a better collaboration among various processes. However, in many papers, machine maintenance has usually been ignored during the production scheduling. In reality, every machine requires maintenance, which will directly influence the machine's availability, and consequently the planned production schedule. The objective of this paper is to propose a modified genetic algorithm approach to deal with those DS models with maintenance consideration, aiming to minimize the makespan of the jobs. Its optimization performance has been compared with other existing approaches to demonstrate its reliability. This paper also tests the influence of the relationship between the maintenance repairing time and the machine age to the performance of scheduling of maintenance during DS in the studied models.     

Expert systems in production planning and scheduling: A state-of-the-art survey

Intelligent solutions, based on expert systems, to solve problems in the field of production planning and scheduling are becoming more and more widespread nowadays. Especially the last decade has witnessed a growing number of manufacturing companies, including glass, oil, aerospace, computers, electronics, metal and chemical industries—to name just a few—interested in the applications of expert systems (ESs) in manufacturing. This paper is a state-of-the-art review of the use of ESs in the field of production planning and scheduling. The paper presents famous expert systems known in the literature and current applications, analyzes the relative benefits and concludes by sharing thoughts and estimations on ESs future prospects in this area.     

Project-driven planning and scheduling support for virtual manufacturing

The paper addresses the issue of decision-making support for small and medium-size enterprises operating within a virtual project-driven enterprise environment. The problem considered here can be defined in terms of finding a feasible schedule that satisfies the constraints imposed by the work-order duration, the price, and the time-constrained resource availability. The problem belongs to the class of multi-mode case problems of project scheduling, where finding a feasible solution is NP-hard. A heuristic method for process planning and scheduling is proposed. The method is based on a critical path approach and the branch and bound search scheme. It has been implemented in a web-enabled interactive software package, and is illustrated using the example of a virtual construction enterprise. Received: February 2005 / Accepted: January 2006