Forecasting and maintenance problem under subcontracting constraint with transportation delay

In this paper, a forecasting production/maintenance optimization problem has been proposed with a random demand and single machine M₁ on a finite horizon. The function rate of the machine M₁ is depending on the production rate for each period of the forecasting horizon. In order to satisfy the customer, a subcontracting assures the rest of the production through machine M₂ with transportation delay. An analytic formulation of the problem has been proposed using a sequential computation of the optimal production plan for which an optimal preventive maintenance policy has been calculated based on minimal repair. Firstly, we find, the optimal production plans of principal and subcontracting machines, which minimises the total production and inventory cost for the cases without and with returned products under service level and subcontracting transportation delay. Secondly, we determine a joint effective maintenance policy with the optimal production plan, which integrates the various constraints for the production rates, the transportation delay and the returned production deadline. Numerical results are presented to highlight the application of the developed approach and sensitivity analysis shows the robustness of the model.     

Improved preventive maintenance in the framework of forecasting problem under subcontractor constraint

The paper presents a new improved preventive maintenance strategy for a forecasting problem of production and maintenance optimisation under subcontractor constraint. In order to satisfy the customer, the manufacturing system consists of a principal machine M₁ and called upon subcontractor machine M_s. Knowing that both machines are subjected to random failures, failure rate of main machine increases with time and according to production rates. An improved preventive maintenance strategy is used for control of the machine M₁, whereas subcontractor machine M_s is uncontrollable from preventive maintenance point of view. An analytic formulation of problem has been proposed in order to determine the economical production plans for M₁ and M_s. An improved maintenance strategy (IMS) is developed in order to minimise the total production loss, when the subcontractor machine is unavailable. It consists of determining the best time to perform preventive maintenance actions taking into account production rates, history of M₁ and the state of subcontractor machine M_s. Numerical results and sensitivity analysis are presented to highlight the performance measure and the usefulness of the IMS.     

Integrated production,statistical process control,and maintenance policy for unreliable manufacturing systems

The objective of this paper is to develop an integrated approach for the joint control of production, maintenance and quality for batch manufacturing systems. We consider such systems that are subject to degradation which is at the origin of the production of defective units. The quality control of lots produced is performed using an ‘x-bar’ control chart. This graphical tool will allow estimating the quality of the batch being produced and possibly undertake perfect preventive or corrective maintenance actions on the production system. A buffer stock is built to maintain continuity of supply during maintenance actions. The incurred total cost includes setup cost, inventory costs, the cost of unused products, maintenance costs and quality costs. Decision variables include the buffer stock size, the sample size, the sampling interval, the surveillance and the control limits of the control chart. Numerical experiments and sensitivity analyses are provided to evaluate the effectiveness of the proposed control policy and the robustness of the solving approach.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

A methodology for simultaneous optimisation of design parameters for the preventive maintenance and quality policy incorporating Taguchi loss function

The performance of a production system depends on the breakdown-free operation of equipment and processes. Maintenance and quality control play an important role in achieving this goal. In addition to deteriorating with time, equipment may experience a quality shift (i.e. process moves to out-of-control state), which is characterised by a higher rejection rate and a higher tendency to fail. This paper develops an integrated model for joint optimisation of preventive maintenance interval and control parameters incorporating the Taguchi loss function. We consider two types of maintenance policies: minimal corrective maintenance that maintains the state of the equipment without affecting the age and imperfect preventive maintenance that upgrades the equipment in between ‘as good as new’ and ‘as bad as old’ condition. The proposed model enables the determination of the optimal value of each of the four decision variables, i.e. sample size (n), sample frequency (h), control limit coefficient (k), and preventive maintenance interval (t _PM) that minimises the expected total cost of the integration per unit time. A numerical example is presented to demonstrate the effect of the cost parameters on the joint economic design of preventive maintenance and process quality control policy. The sensitivity of the various parameters is also examined.     

Preventive maintenance of manufacturing systems under environmental constraints

The paper describes a new preventive maintenance approach for manufacturing systems under environment constraints. The manufacturing system under consideration consists of a machine M₁ that produces a single product in a Just-in-Time context. To satisfy a constant demand d, the system called upon another machine M₂ (the subcontractor), comprising the so-called environment, which produces at a certain rate the same type of product as M₁. Both machines are subjected to random failures. Whereas machine M₂ is uncontrollable from the maintenance point of view, an age-limit policy is used for preventive maintenance of machine M₁. It is proved that the best age to perform preventive maintenance depends on the history of machine M₁ and the state of M₂. A numerical example is used to illustrate the proposed approach.     

Analysis of on-line maintenance strategies for -out-of- standby safety systems

The objective of this paper is to compare the performance of three on-line test and maintenance strategies (corrective maintenance, preventive maintenance and predictive maintenance) for standby k-out-of-n safety systems. Each channel of the k-out-of-n system is modelled by an age-dependent unavailability model to reflect the effect of maintenance on the aging process. The system unavailability, the probability of spurious operation and the overall cost under the above maintenance strategies are analyzed and compared to obtain the optimal maintenance strategy. Sensitivity analyses are performed to reveal the effect of different model parameters on the system performance. A standby safety system in Canadian Deuterium–Uranium (CANDU) Nuclear Power Plants (NPPs), the Shutdown System Number One (SDS1), is used to illustrate the proposed analysis and the procedure. It is concluded that maintenance should neither be performed too frequently nor too rarely. When the system deteriorates very slowly, the corrective maintenance is more preferable than the preventive and predictive maintenance. When the failure rate of the system is high, the preventive maintenance results in the best system performance.     

A tabu search approach for buffer allocation in production lines with unreliable machines

The optimal allocation of buffers is an important research issue in designing production lines. In this study, a tabu search (TS) algorithm is proposed to find near-optimal buffer allocation plans for a serial production line with unreliable machines. The main objective is to maximize the production rate, i.e. throughput, of the line. The efficiency of the proposed method is also tested to solve buffer allocation problems with the objective of total buffer size minimization. To estimate the throughput of the line with a given specific buffer allocation, an analytical decomposition approximation method is used. The performance of the tabu search algorithm is demonstrated on existing benchmark problems. The results obtained by the TS algorithm are clearly encouraging, as the TS algorithm is much better than the other algorithms for all considered benchmark problems.     

Effect of maintenance policies on the just-in-time production system

Using simulation, experimental design, and regression analysis, mathematical models are developed here to describe the effect that maintenance policy, machine unreliability, processing time variability, ratio of preventive maintenance time to processing time, ratio of minimal repair time to preventive maintenance time, and production line size have on various measures of performance, namely total production line output and production line variability of the just-in-time production system. The analysis of the data shows that under different situations, different maintenance policies do not have the same effect on the production line performance. The following conclusions were obtained; when the number of production machines is low (five machines or less), and/or when the ratio of minimal repair time to preventive maintenance time is high, maintenance policy III leads to a higher performance than maintenance policy II. Otherwise maintenance policy II, which is more sensitive to the change of the ratio of minimal repair time to preventive maintenance time, leads to a higher performance. The results of the study can be utilized in choosing a maintenance policy as a function of the production process parameters. Once a policy is chosen, the practitioner can select the most important factors to control under that policy in order to minimize the machine idle time, maximize the production process reliability, improve productivity, and therefore increase the production line performance.     

Simultaneous determination of preventive maintenance and replacement policies in a queue-like production system with minimal repair

This paper addresses the joint effects of preventive maintenance and replacement policies on a queue-like production system with minimal repair at failures. We consider a policy which calls for a preventive maintenance operation whenever N parts have been processed. If a failure occurs and at least K preventive maintenance operations have been carried out, the system is replaced by a new one. Otherwise, a failure is handled by minimal repair. An analytical model is developed and the argument of renewal–reward theory is used to provide long-run expected profit per unit time for a given maintenance and replacement policy. Numerical examples are given to provide some managerial insights.     

Joint optimization of maintenance,buffers and machines in manufacturing lines

This article considers a series manufacturing line composed of several machines separated by intermediate buffers of finite capacity. The goal is to find the optimal number of preventive maintenance actions performed on each machine, the optimal selection of machines and the optimal buffer allocation plan that minimize the total system cost, while providing the desired system throughput level. The mean times between failures of all machines are assumed to increase when applying periodic preventive maintenance. To estimate the production line throughput, a decomposition method is used. The decision variables in the formulated optimal design problem are buffer levels, types of machines and times between preventive maintenance actions. Three heuristic approaches are developed to solve the formulated combinatorial optimization problem. The first heuristic consists of a genetic algorithm, the second is based on the nonlinear threshold accepting metaheuristic and the third is an ant colony system. The proposed heuristics are compared and their efficiency is shown through several numerical examples. It is found that the nonlinear threshold accepting algorithm outperforms the genetic algorithm and ant colony system, while the genetic algorithm provides better results than the ant colony system for longer manufacturing lines.     

Buffers and backup machines in automatic transfer lines

Buffer storage of the work-in-process inventory, decouples successive stages of automatic transfer production lines, assuring partial operability under machine failure. Certain special features such as secondary (standby) machines, special maintenance and diagnostic systems can lengtben the uptime or shorten the downtime of individual stages. When special features for K stages and spaces for M buffers are available, it is of great interest to system designers to know which stages should have the special features and where the buffer spaces should be inserted to maximize the line output rate. This paper addresses itself to such design problems. A bivariate dynamic programming procedure is developed which provides a layout for the buffers and an allocation of special features, maximizing the line output rate as defined by Buzacott (1967, 1968). The Buzacott formula is based on a heuristic argument which provides, in general, an upper bound on the true system output rate.     

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.     

Lockout/tagout and optimal production control policies in failure-prone non-homogenous transfer lines with passive redundancy

This paper considers a production problem for a transfer line subject to random failures and repairs, and differs from other studies on transfer lines. It considers a manufacturing system consisting of three machines (two machines with passive redundancy, and one in series with the previous ones) producing one part type. The control problem is subject to non-negative constraints on work-in-process (WIP). The decision variables are the production rates of two main machines and a standby machine, and influence the WIP levels, the inventory levels and the system's capacity, which is assumed to be described by a finite-state Markov chain. The objective of this paper is to minimise WIP and finished goods inventory costs; it also aims to respect the essential space–time during intervention on machine down, in order to minimise the possibility of the circumvention of protection devices or of the retraction of lockout/tagout procedures through a passive redundancy system. This paper therefore verifies the effect of passive redundancy on optimal stock levels. Given that an analytical or even a numerical solution of the problem is very difficult to find, and that we want to have a more realistic model for industries, we present a combined approach, which is presented based on a combination of analytical formalism, simulation modelling, design of experiments, and response surface methodology to optimise a transfer line with passive redundancy, producing one part type. The usefulness of the proposed approach is illustrated through a numerical example and a sensitivity analysis.     

A combinatorial approach to a class of parallel-machine,continuous-time scheduling problems

The paper analyzes a manufacturing system with N non-identical, parallel machines continuously producing one product type in response to its demand. Inventory and backlog costs are incurred when tracking the demand results in inventory surpluses and shortages respectively. In addition, the production cost of a machine is incurred when the machine is not idle. The objective is to determine machine production rates so that the inventory, backlog, and production costs are minimized. For problems with demand defined as an arbitrary function of time, numerical methods are suggested to approximate an optimal solution. The complexity of the approximation methods is polynomial, while finding an exact optimal solution requires exponential time. In a case when production is to cope with a special form of a single-mode, K-level piece-wise constant demand, we prove, with the aid of the maximum principle, that the exact optimal solution can be found as a combination of analytical and combinatorial tools in O(KN ²( max {K,2N})²) time.     

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.     

Scheduling manufacturing systems with work-in-process inventory control: Reentrant systems

In this paper, we propose a procedure for production flow control in reentrant manufacturing systems. The system under study consists ofN machines and producesM product types simultaneously. Each part goes through the system following a predefined process and may visit a machine many times. All machines are subject to random failures and need random repair times. The scheduling objectives are to keep the production close to demand and to keep the WIP inventory level and cycle times at low values. The model is motivated by semiconductor fabrication production. A three-level hierarchical controller is constructed to regulate the production. At the top level of this hierarchy, we perform capacity planning by selecting the desirable buffer sizes and the target production level for each operation. A production flow rate controller is at the middle level which recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. Comparison with alternative control is made through simulation and it shows that the control policy performs well.     

Optimal maintenance plan for two-level assembly system and risk study of machine failure

This paper deals with the optimisation of two-levels assembly system planning. This system is composed of a single machine, inventories at levels 1 and 2 for stock keeping components to assembly and final assembled product. It assumed that the machine processes all assembly operations and is subject to random failure. A mathematical model is developed to incorporate a supply planning for two-level assembly systems under stochastic lead times and breakdowns machine. A preventive maintenance plan is carried out to reduce the frequency of the corrective maintenance actions. This work has double goals. The first one is to find the optimal order release dates for the different components at level 2 and the optimal preventive maintenance plan. The second one is to quantify the risk due to machine failures which have an impact on the lead-time of the finished product. To consider the maintenance actions, preventive maintenance actions are perfectly performed to restore the machine to state “as good as new”, minimal repair is considered at failure. The model minimises the total cost, which is the sum of inventory holding cost for components at levels 1 and 2, backlogging and inventory holding cost for the finished products and maintenance costs. To illustrate the effectiveness of the proposed model, different meta-heuristics are applied; the genetic algorithm shows the most suited to our analytical model, the optimal release date founded by this algorithm allows finding the optimal preventive maintenance plan. The obtained optimal maintenance planning is used in the risk assessment in order to find the threshold repair period that avoids lost profit.     

Optimal production control: analytical solution for the limit cycles

The paper analyzes a manufacturing system with tandem machines producing one part type. The system is periodically stopped for maintenance. The objective is to determine machine production rates so that the inventory and backlog-related expenses could be minimized. We show only a few so-called restricting machines need to be considered. A numerical example is used to demonstrate the solution approach proposed in the paper.     

Performance evaluation of production lines with finite buffer capacity producing two different products

This paper presents an approximate analytical method for the performance evaluation of a production line with finite buffer capacity, multiple failure modes and multiple part types. This paper presents a solution to a class of problems where flexible machines take different parts to process from distinct dedicated input buffers and deposit produced parts into distinct dedicated output buffers with finite capacity. This paper considers the case of two part types processed on the line, but the method can be extended to the case of n part types. Also, the solution is developed for deterministic processing times of the machines which are all identical and are assumed to be scaled to unity. The approach however is amenable of extension to the case of inhomogeneous deterministic processing times. The proposed method is based on the approximate evaluation of the performance of the k-machine line by the evaluation of 2(k-1) two-machine lines. An algorithm inspired by the DDX algorithm has been developed and the validation of the method has been carried out by means of testing and comparison with simulation. Correspondence to: T. Tolio