An optimal ordering policy for a spare unit with lead time

doi:10.1016/0377-2217(78)90136-4

European Journal of Operational Research

Volume 2, Issue 6, November 1978, Pages 409-419

https://doi.org/10.1016/0377-2217(78)90136-4 Get rights and content

Abstract

We consider a generalised ordering policy in which a spare unit for replacement can be delivered only by order after a constant lead time. Introducing the costs for ordering, shortage and holding, we derive the expected cost per unit time in the steady-state. We discuss the optimal ordering policy which minimises the expected cost, and show in a main theorem that the optimal policy is reduced to either one of two typical ordering policies depending on some conditions. We further discuss a similar ordering policy with varying lead times.

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Numerical study of inventory management under various maintenance policies
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However, in this literature, costs for spare parts inventories are not incorporated. Although the importance of the joint optimisation of maintenance and inventory policies has been raised before (see e.g., [23,26,34,37]), to the best of our knowledge, an inventory cost comparison of multiple maintenance policies combined with inventory control policies has not been performed in the literature; we believe to be the first to do so. In our study we consider three different maintenance policies.
Capital assets, such as manufacturing equipment, require maintenance to remain functioning. Maintenance can be performed when a component breaks down and needs replacement (i.e., corrective maintenance), or the maintenance and part replacement can be performed preventively. Preventive maintenance can be planned on a periodic basis (periodic maintenance), or it can be triggered by a certain monitored condition (condition-based maintenance). Preventive maintenance policies are gaining traction in the business world, but for many companies it is unclear what their impact is on the resulting inventory requirements for the spare parts that are used for the maintenance interventions. We study the impact of the maintenance policy on the inventory requirements and the corresponding costs for a setting that is realistic at an OEM in the compressed air industry. Preventive policies increase the total demand for spare parts compared to corrective maintenance, since the former do not exploit the entire useful life of the components. This leads to higher inventory requirements. At the same time, the preventive policies inhibit advance demand information, as the interventions, and correspondingly the spare parts demands, are planned in advance. Using a simulation study, we show that by using this advance demand information in managing the spare part inventory, the increase in inventory requirements of preventive maintenance policies can to a large extent be offset; for condition-based maintenance, we find that inventories can even be lower compared to corrective maintenance, provided that the advance demand information is used correctly when managing inventories. Our analysis sheds light on the behaviour of the inventory related costs under various maintenance policies.
Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures
2014, European Journal of Operational Research
Citation Excerpt :
As a result they conclude that the optimal replacement policy is extreme and similar to that studied by Osaki (1977). Armstrong and Atkins (1996) extend the analysis of Thomas and Osaki (1978) assuming that preventive replacement is generally less expensive than failure replacement. Other extensions of the model proposed by Thomas and Osaki (1978) are also studied in Dohi, Kaio, and Osaki (1998) and Giri, Dohi, and Kaio (2005).
In this paper the joint maintenance and spare parts ordering problem for more than one identical operating items is studied. The operating items may suffer two types of silent failures: a minor failure, which results in item malfunctioning, and a major failure, which renders the item completely out-of-function. Inspections are periodically held to detect any failures and the inspected items are preventively maintained, repaired or replaced according to their condition. Two ordering policies are investigated to supply the necessary spare parts: a periodic review and a continuous review policy. The expected total maintenance and inventory cost per time unit is derived and the proposed models are optimized for real case data. In addition, the sensitivity of the proposed models is studied through numerical examples and the effect of some key problem characteristics on the optimal decisions is discussed.
Age replacement policy with lead-time for a system subject to non-homogeneous pure birth shocks
2013, Applied Mathematical Modelling
A system is subject to shocks that arrive according to a non-homogeneous pure birth process. Whenever a shock occurs, the system enters one of the two types of failure states. Type I failure (minor failure) is fixed by a minimal repair. Type II failure (catastrophic failure) is removed by a replacement. We consider an age replacement policy which replaces the system whenever its age reaches $T$ and a spare for replacement is available. The optimal cost minimization age $T^{*}$ is derived under a cost structure. We demonstrate that this model includes more realistic factors and is a generalization of several previous models in the literature.
Optimal spare ordering policy for preventive replacement under cost effectiveness criterion
2010, Applied Mathematical Modelling
This paper presents a spare ordering policy for preventive replacement with age-dependent minimal repair and salvage value consideration. The spare unit for replacement is available only by order and the lead-time for delivering the spare due to regular or expedited ordering follows general distributions. To analyze the ordering policy, the failure process is modelled by a non-homogeneous Poisson process. By introducing the costs due to ordering, repairs, replacements and downtime, as well as the salvage value of an un-failed system, the expected cost effectiveness in the long run are derived as a criterion of optimality. It is shown, under certain conditions, there exists a finite and unique optimum ordering time which maximizes the expected cost effectiveness. Finally, numerical examples are given for illustration.
Cost-effective ordering policies for inventory systems with emergency order
2009, Computers and Industrial Engineering
Most of the studies on inventory control reported in earlier contributions deal with the optimization problems minimizing an expected cost criterion such as the long-run average cost. However, when the plant engineers design the inventory systems in practical situations, they must take account of reliability into the inventory system as well as economical aspect, where reliability can be defined as the probability that the stock is not depleted until a pre-specified time. In this paper, we discuss the inventory control policies that provide a balance between economical and reliability requirements. By applying the cost effectiveness criterion, which simultaneously includes the effects of system availability and expected cost, as optimality one, we derive the optimal inventory replenishment policies of two kinds of inventory models. Finally, with a set of numerical examples, we show that the optimal inventory policies of the models under consideration make the stationary availability increase.
Optimal age-replacement policy of a system subject to shocks with random lead-time
2004, European Journal of Operational Research
Citation Excerpt :
Nakagawa and Osaki [22] and Osaki and Yamada [24] also assume that the random lead-time is start at time 0. If the random lead-time is not started at time 0, then one must consider an ordering policy for the unit (see [21,25–28,34,39,40], for example). The idea of minimal repair was introduced by Barlow and Hunter [6]; the r(t) remains undisturbed by any minimal repair.
This paper considers a generalized age-replacement policy of a system subject to shocks with random lead-time. A system is subject to shocks that arrive according to a non-homogeneous Poisson process. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. The minimum-cost policy time is described and discussed. Various special cases are considered. Because the model and its analysis are general, several existing results are shown to be subsumed by this model.

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An optimal ordering policy for a spare unit with lead time

Abstract

An ordering policy for repairable stock items

Operations Res.

An ordering policy for stock items when delivery can be expedited

Operations Res.

Mathematical Theory of Reliability

Statistical Theory of Reliability and Life Testing: Probability Models