Optimal integrated maintenance/production policy for randomly failing systems with variable failure rate

This article deals with the combined production and maintenance plans for a manufacturing system satisfying a random demand. We first establish an optimal production plan which minimises the average total inventory and production cost. Second, using this optimal production plan, and taking into account the deterioration of the machine according to its production rate, we derive an optimal maintenance schedule which minimises the maintenance cost. A numerical example illustrates the proposed approach, this analytical approach, based on a stochastic optimisation model and using the operational age concept, reveals the significant influence of the production rate on the deterioration of the manufacturing system and consequently on the integrated production/maintenance policy.     

An integrated preventive maintenance and production planning model with sequence‐dependent setup costs and times

This paper considers the integration of preventive maintenance and tactical production planning in a multiproduct production system, where setup costs and times are sequence dependent. A set of products needs to be produced in lots during a finite planning horizon, where preventive maintenance is conducted periodically at the end of some production periods and corrective maintenance is always performed when there is a failure. The system downtime—as caused by maintenance and setup—affects the system's available production capacity. We use a sequence‐oriented method to search for the optimal setup sequence and develop some steps to prune the searching tree. Our objective is to find the optimal preventive maintenance interval, production lot size, and production sequence in every period, by minimizing the sum of maintenance, production, inventory, and setup costs within the planning horizon. Numerical examples are presented to illustrate our model.     

Integrating occupational health and safety in facility layout planning,part I: methodology

An influential factor affecting the efficiency of a manufacturing facility is its layout. In a production facility, measure for efficiency can be based on the total cost of transporting the items between different departments and throughout the facility. However, other factors may influence efficiency of the manufacturing facility too. As such are: supporting the organisation's vision through improved material handling, material flow and control; effectively assigning people, equipment, space and energy; minimising capital investment; adaptability and ease of maintenance; as well as providing for employee safety and job satisfaction. By incorporating health and safety measures in the initial design of a facility layout, the organisation may avoid money and manpower loss resulting from industrial accidents. This paper proposes a facility layout planning methodology which integrates the occupational health and safety (OHS) features in the early design of a facility layout. The model considers transportation cost in the facility as well as safety concerns. By this means, the OHS issues are reflected prior to the construction of a facility.     

Maintenance policies for a production system with constrained production rate and buffer capacity

This paper considers the maintenance policies for a production system constrained by its production rate and buffer capacity to cope with unexpected failures and to deal with the variability of demand and production lead times. Using a system dynamics model, we characterize, simulate and compare results obtained by applying several maintenance policies--corrective, age-based maintenance, age and buffer-based maintenance, and modified age and buffer-based maintenance--to the system. This comparison is performed assuming that optimal values of the model parameters involved in the design of each maintenance policy have already been found by using the modified Powell method. We compare and discuss the benefits of different optimization criteria in the maintenance decision making process for a production system with constrained production rate and buffer capacity.     

Optimally maintaining an M/G/1-type production system

The concept of more maintenance effort (or training) implying higher system reliability (or efficiency) is well accepted. In this paper we study an optimal maintenance (training) program based on this concept for a simple production system using the M/G/l vacation queue model. We discuss how to determine the optimal maintenance (training) time to minimize the average time spent by a job in the system.     

Two-critical-number control policy for a stochastic production inventory system with partial backlogging

This paper deals with a production–inventory control model with partial backlogging, in which a reflected Brownian motion governs the inventory level variation. We consider a single storage facility with infinite capacity and assume that shortages are allowed and the total amount of stock-out is a mixture of backordering and lost sales. In addition, the production facility is controlled by a two-parameter (m, M) policy, which switches the production rate when the inventory level reaches the threshold values. The aim is to determine the optimal control parameters m and M by minimising the long-run total expected cost of the system. Some results are illustrated using numerical examples. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

Evaluation of maintenance policies for equipment subject to quality shifts and failures

We develop an economic model for the optimization of maintenance procedures in a production process with two quality states. In addition to deteriorating with age, the equipment may experience a jump to an out-of-control state (quality shift), which is characterized by lower production revenues and higher tendency to failure. The times to quality shift and failure are allowed to be generally distributed random variables. We consider two types of maintenance: minimal maintenance (MM) that upgrades the quality state of the equipment without affecting its age and perfect preventive maintenance (PM) that fully upgrades the equipment to the as-good-as-new condition. We derive the expression for the expected profit per time unit and we investigate, through a large number of numerical examples, the type of the optimal solution. It is concluded that in practically every case the optimal maintenance policy is an extreme one: it either calls for immediate MM as soon as a quality shift occurs (active policy) or it allows operation in the out-of-control state until the time of a scheduled PM action (passive policy).     

Analysis of investments in autonomous maintenance activities

In this paper, we model the situation where operator maintenance activities improve the failure process of equipment. We analyze the business decision to reduce both the mean and variance of the production cycle time and the overall inventory level through an investment in planned autonomous maintenance. We answer: (i) when do optimal autonomous maintenance decisions most improve inventory levels?; and (ii) how do capacity restrictions, equipment characteristics the maintenance response function, and product characteristics impact the autonomous maintenance investment decision? Extensive numerical analyses are performed to develop an approximation to the optimal response for both inventory and autonomous maintenance investments over a wide range of problem parameters. Our solutions provide guidelines on how much time should be invested in autonomous maintenance activities and describe when companies can most benefit from autonomous maintenance programs that increase equipment reliability. We determine the investment in autonomous maintenance activities as a function of available capacity, equipment reliability and demand characteristics.     

Optimal preventive maintenance in a production inventory system

We consider a production inventory system that produces a single product type, and inventory is maintained according to an (S, s) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing. It is assumed that the demand arrival process is Poisson. Also, the unit production time, the time between failures, and the repair and maintenance times are assumed to have general probability distributions. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increase in the system performance. We develop a mathematical model of the system, and derive expressions for several performance measures. One such measure (cost benefit) is used as the basis for optimal determination of the maintenance parameters. The model application is explained via detailed study of 21 variants of a numerical example problem. The optimal maintenance policies (obtained using a numerical search technique) vary widely depending on the problem parameters. Plots of the cost benefit versus the system characteristic parameters (such as, demand arrival rate, failure rate, production rate, etc.) reveal the parameter sensitivities. The results show that the actual values of the failure and maintenance costs, and their ratio are significant in determining the sensitivities of the system parameters.     

Production, operating risk and market uncertainty: a valuation perspective on controlled policies

This paper develops a contingent claims model of an optimally controlled production process characterized by financial and operational risks. Financial risk is depicted by the uncertainty in output prices as determined in competitive markets. Operational uncertainty is portrayed through the risk of system failures which we represent by a nonhomogeneous Poisson process. In the analysis, failure propensity is functionally specified by the system's age, rate of production, and system maintenance expenditures. In this environment, the model obtains an optimal production and maintenance policy maximizing the value of the production effort. Determination of the optimal policies results through the application of stochastic control techniques where production and maintenance expenditure rates are taken as adapted real-valued processes. Further extensions of the model include the analysis of an insurance option on failure repairs and the consequent moral hazard implications. We demonstrate that an appropriately established insurance premium must reflect the producer's operating policy in place and the extent to which operating policies may be modified to maintain the same level of operating risk, as in the absence of an insurance option. The framework presented provides insight into key strategic factors that affect the management of process operations, operating flexibility issues and their resulting economic value.     

Joint production and maintenance planning with machine deterioration and random yield

Production, yield and maintenance are three key components for sustaining the competitiveness of a manufacturing firm. In this paper, we investigate a joint production and maintenance planning problem in a periodic review environment subject to stochastic demand and random yields. The manufacturing system deteriorates from period to period according to a discrete-time Markov chain. The objective is to find an integrated lot sizing and maintenance policy for the system such that the aggregate cost associated with production, holding, backlogging and maintenance is minimised. We formulate this integrated planning problem as a Markov decision process and analyse the structural properties of the optimal policies. We prove that the optimal production and the maintenance policies both exhibit a control limit structure and show that the solution to the finite-horizon problems converges to that of the infinite-horizon problem.     

Dynamic vs static pricing in a make-to-stock queue with partially controlled production

We consider a capacitated make-to-stock production system that offers a product to a market of price-sensitive users. The production process is partially controlled. On the one hand, the decision-maker controls the production of a single facility. On the other hand, an uncontrolled flow of items arrives at the stock. Such a situation occurs in several contexts; for example, when there is a return flow of products or a fixed delivery contract. We model the system as a make-to-stock queue with lost sales. We address the static pricing problem and the dynamic pricing problem with the objective of maximizing the average profit over an infinite horizon. For both problems, we characterize the optimal production and pricing policy. We also obtain analytical results for the static pricing problem. From numerical results, we show that dynamic pricing might be much more beneficial when the production is not totally controlled.      

Maintenance scheduling of a manufacturing system subject to deterioration

This paper presents an integrated model for the joint determination of both optimal inspection strategy and optimal repair policy for a manufacturing system whose resulting output is subject to system state. An appropriate maintenance strategy is essential to optimize revenue from a manufacturing system which is in continuous operation and subject to deterioration. The optimum policy balances the amount of maintenance required to increase availability against the loss of revenue arising from the down time: insufficient maintenance leads to an increase in the number of defective items, low profit and low maintenance cost; excessive maintenance results in a reduction in the proportion of defective items, high profit and high maintenance cost. In this paper, an intensity control model adapted to partial information provides an optimal inspection intensity and repair degree of the system as an optimal control process to yield maximum revenue. The solution is obtained through formulating an equivalent deterministic Hamilton-Jacobi equation. A numerical example is provided to illustrate the behavior of the optimal control process. The optimal control process determines a solution to both optimum inspection frequency and optimal replacement policy which results in an optimal production run length of the system.     

A piecewise nonlinear model for a production system under maintenance,trade credit and limited warehouse space

Small and medium size manufacturers exist commonly in developing countries. Limited warehouse space is a characteristic in small and medium size manufacturers. In today’s business environment, many upstream companies offer a credit period to downstream companies. In production system, a manufacturer usually adopts the system maintenance when the system is in the out-of-control state. Therefore, this paper considers a production-inventory model for a manufacturer under system maintenance, trade credit and limited warehouse space. The objective is to determine the optimal production run time to minimise the total cost. We develop an algorithm based on several theorems for solving the problem described. We provide several examples to illustrate the solution procedure and discuss how system parameters affect the manufacturer’s decision behaviour. Computational analysis demonstrates that the results of the proposed model are consistent with economic insights.     

Integrated maintenance and production control of a deteriorating production system

We consider a make-to-stock production/inventory system consisting of a single deteriorating machine which produces a single item. We formulate the integrated decisions of maintenance and production using a Markov Decision Process. The optimal dynamic policy is shown to have a rather complex structure which leads us to consider more implementable policies. We present a double-threshold policy and derive exact and approximate methods for evaluating the performance of this policy and computing its optimal parameters. A detailed numerical study demonstrates that the proposed policy and our approximate method for computing its parameters perform extremely well. Finally, we show that policies which do not address maintenance and production control decisions in an integrated manner can perform rather badly.     

A multi-objective mixed-integer programming model for a multi-floor facility layout

We consider a multi-floor facility layout problem in which the overall length and width of the facility, the size and location of each department, the number and the location of elevators and the number of floors in the facility are all modelled as decision variables. We adapt a linear approximation scheme to represent the area of each department. We consider two objective functions in our model, namely minimising material handling and facility building costs, and propose a lexicographic ordering technique to handle multiple objectives. The numerical experiments show that the slack used in the lexicographic ordering approach has a significant impact on the optimal solution. The experiments also show that the material handling cost can be significantly reduced in a multi-floor facility compared with a single-floor facility.     

Investigating reliability improvement of second-hand production equipment considering warranty and preventive maintenance strategies

A cost model for optimal reliability improvement of warranted second-hand production equipment is developed. The second-hand production equipment of age x is subjected to an upgrade action of a certain level u before it is sold with a Free Repair Warranty. We look at determining the optimal upgrade level when not performing and when performing periodic preventive maintenance (PM) during the warranty period. Two different PM strategies are considered: (a) periodic PM actions having the same efficiency level; (b) periodic multi-phase PM actions with a maintenance efficiency level which varies according to the phase. The proposed model aims at helping the dealer to find the optimal upgrade level to perform before selling the second-hand equipment, and to assess whether performing PM actions during the warranty period, according to a specific maintenance strategy, is worthwhile in terms of cost reduction. Numerical experimentations considering each PM scenario are performed in order to investigate how each PM strategy impacts the improvement level to be performed and the associated total expected cost. The obtained results showed that the expected total cost incurred by the dealer is governed by a sensitive trade-off between the warranty servicing cost and the costs associated with the reliability improvement, and with the PM performed during the warranty period. It is also found that the proposed new periodic multi-phase PM policy with an increasing maintenance efficiency level yields lower upgrade levels, inducing lower costs for the dealer.     

Effects of maintenance policy on an imperfect production system under trade credit

The traditional production model development assumed that all products are perfect quality and did not consider maintenance, which is far from reality. In practice, the production process may shift randomly from an in-control state to an out-of-control state during a production run, i.e. process deterioration. This paper considers both preventive maintenance and corrective maintenance which are used to increase the system reliability. The objective of this paper is to determine the optimal production run time and maintenance frequency while minimising the total cost under process deterioration and trade credit. This paper develops a theorem and an algorithm to solve the problem described, provides numerical analysis to illustrate the proposed solution procedure, and discusses the impact of various system parameters. A real case of hi-tech manufacturer is used to verify the model. It predicts a 10.36% decrease in total cost if the preventive maintenance decision is considered.     

Risk-based maintenance of ethylene oxide production facilities

This paper discusses a methodology for the design of an optimum inspection and maintenance program. The methodology, called risk-based maintenance (RBM) is based on integrating a reliability approach and a risk assessment strategy to obtain an optimum maintenance schedule. First, the likely equipment failure scenarios are formulated. Out of many likely failure scenarios, the ones, which are most probable, are subjected to a detailed study. Detailed consequence analysis is done for the selected scenarios. Subsequently, these failure scenarios are subjected to a fault tree analysis to determine their probabilities. Finally, risk is computed by combining the results of the consequence and the probability analyses. The calculated risk is compared against known acceptable criteria. The frequencies of the maintenance tasks are obtained by minimizing the estimated risk. A case study involving an ethylene oxide production facility is presented. Out of the five most hazardous units considered, the pipeline used for the transportation of the ethylene is found to have the highest risk. Using available failure data and a lognormal reliability distribution function human health risk factors are calculated. Both societal risk factors and individual risk factors exceeded the acceptable risk criteria. To determine an optimal maintenance interval, a reverse fault tree analysis was used. The maintenance interval was determined such that the original high risk is brought down to an acceptable level. A sensitivity analysis is also undertaken to study the impact of changing the distribution of the reliability model as well as the error in the distribution parameters on the maintenance interval.