A PERISHABLE INVENTORY MODEL WITH UNKNOWN TIME HORIZON

Traditionally, the time (planning) horizon over which the inventory for a particular item will be controlled is often assumed to be known (finite or infinite) and the total inventory cost is usually obtained by summing up the cost over the entire time horizon. However, in some inventory situations the period over which the inventory will be controlled are difficult to predict with certainty, as the inventory problems may not live up to or live beyond the assumed planning horizon, thereby affecting the optimality of the model. This paper presents a deterministic perishable inventory model for items with linear trend in demand and constant deterioration when time horizon is unknown, unspecified or unbounded. The heuristic model obtains replenishment policy by determining the ordering schedule to minimize the total cost per unit time over the duration of each schedule. A numerical example and sensitivity analysis are given to illustrate the model

Optimising Age-Replacement and Extended Non-Renewing Warranty Policies in Lifecycle Costing

This paper analyses the life cycle cost of equipment protected by both base and extended warranty policies from a consumer's perspective. We assume that the equipment has two types of failure: minor and catastrophic. A minor failure can be corrected with minimal repair whereas a catastrophic failure can only be removed by a replacement. It is assumed that equipment is maintained at no charge to the consumer during the warranty period, whereas the consumer is fully charged for any maintenance on failures after the extended warranty expires. We formulate the expected life cycle cost of the equipment under a general failure time distribution, and then for special cases we prove that the optimal replacement and extended warranty policies exists where the expected life cycle cost per unit time is minimised. This is examined with numerical examples. © 2011 Elsevier B.V. All rights reserved

Optimal maintenance strategies for systems with partial repair options and without assuming bounded costs

We study a repairable system with Markovian deterioration and partial repair options, carried out at fixed times $n=1,2,\ldots$ and look for optimal strategies under certain conditions. Two optimality criteria are considered: expected discounted cost and long-run average cost. Douer and Yechiali found conditions under which a policy in the class of generalized control limit policies is optimal. In this paper conditions are found under which an optimal policy is a control-limit policy. We explicitly explain how to derive this optimal policy; numerical examples are given, too

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach

Optimal replacement in the proportional hazards model and its applications in a product-service system

Condition-based maintenance is rapidly gaining favor as a way to prevent the failures of capital-intensive assets and to maintain them in good operating condition with minimum cost. A valuable and increasingly prevalent way to incorporate condition information into risk estimation is by the proportional hazards model (PHM), which explicitly includes both the age and the condition information in the calculation of the hazard function. This dissertation consists of three papers, in which the optimal replacement policies for systems whose deterioration process follows the PHM are developed under different settings; and a joint optimization of the asset and inventory management problem in the context of a product-service system is considered. In the first paper, a continuous time Markov covariate process is assumed to describe the condition of a system that is under periodic monitoring. Although the form of an optimal replacement policy for such a system in the PHM was developed previously, an approximation of the Markov process as constant within inspection intervals led to a counter-intuitive result that less frequent monitoring could yield a replacement policy with lower average cost. Accounting for possible state transitions between inspection epochs removes the approximation and eliminates the cost anomaly. A new recursive procedure to obtain the parameters of the optimal replacement policy is presented. By comparing the replacement and monitoring costs of different monitoring scheme, the value of condition information is evaluated. In the second paper, the optimal replacement policy for systems in the PHM with semi-Markovian covariate process and continuous monitoring is developed. Numerical examples and sensitivity analysis provide some insights about the suitability of a Markov approximation and the impact of the variations in the input parameters on the cost. In applying the optimal replacement policies to a product-service system, where the producers provide the use of the products to customers while retaining ownership, the coupling between the decision making for preventive replacement and the decision making for inventory management is evident. In the third paper, an integrated model is proposed for the preventive maintenance of a fleet of products and the inventory management of a hybrid manufacturing-remanufacturing system in the context of a product-service system. A joint optimization technique is developed to obtain the optimal parameters for the operational policy of the integrated model to minimize the long run average cost per unit time. In addition, the effect of the assumption that the replaced products are not sorted is evaluated

A Periodicity Metric for Assessing Maintenance Strategies

Organised by: Cranfield UniversityThe maintenance policy in manufacturing systems is devised to reset the machines functionality in an economical fashion in order to keep the products quality within acceptable levels. Therefore, there is a need for a metric to evaluate and quantify function resetting due to the adopted maintenance policy. A novel metric for measuring the functional periodicity has been developed using the complexity theory. It is based on the rate and extent of function resetting. It can be used as an important criterion for comparing the different maintenance policy alternatives. An industrial example is used to illustrate the application of the new metric.Mori Seiki – The Machine Tool Company; BAE Systems; S4T – Support Service Solutions: Strategy and Transitio

A geometric-process maintenance model for a deteriorating system under a random environment

This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time t, produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy N, by which the system is replaced at the time of the failure N, is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied.published_or_final_versio

Optimal Replacement in the Proportional Hazards Model with Semi-Markovian Covariate Process and Continuous Monitoring

Motivated by the increasing use of condition monitoring technology for electrical transformers, this paper deals with the optimal replacement of a system having a hazard function that follows the proportional hazards model with a semi-Markovian covariate process, which we assume is under continuous monitoring. Although the optimality of a threshold replacement policy to minimize the long-run average cost per unit time was established previously in a more general setting, the policy evaluation step in an iterative algorithm to identify optimal threshold values poses computational challenges. To overcome them, we use conditioning to derive an explicit expression of the objective in terms of the set of state-dependent threshold ages for replacement. The iterative algorithm is customized for our model to find the optimal threshold ages. A three-state example illustrates the computational procedure, as well as the effects of different sojourn time distributions of the covariate process on the optimal policy and cost. Numerical examples and sensitivity analysis provide some insights into the suitability of a Markov approximation, and the sources of variability in the cost. The optimization method developed here is much more efficient than the approach that approximates continuous monitoring as periodic, and then optimizes the periodic monitoring parameters

Optimal maintenance of multi-component systems: a review

In this article we give an overview of the literature on multi-component maintenance optimization. We focus on work appearing since the 1991 survey "A survey of maintenance models for multi-unit systems" by Cho and Parlar. This paper builds forth on the review article by Dekker et al. (1996), which focusses on economic dependence, and the survey of maintenance policies by Wang (2002), in which some group maintenance and some opportunistic maintenance policies are considered. Our classification scheme is primarily based on the dependence between components (stochastic, structural or economic). Next, we also classify the papers on the basis of the planning aspect (short-term vs long-term), the grouping of maintenance activities (either grouping preventive or corrective maintenance, or opportunistic grouping) and the optimization approach used (heuristic, policy classes or exact algorithms). Finally, we pay attention to the applications of the models.literature review;economic dependence;failure interaction;maintenance policies;grouping maintenance;multi-component systems;opportunistic maintenance;maintencance optimization;structural dependence