Analysis of a multi-part spares inventory system subject to ambiguous fault isolation

This paper considers a multi-part spares inventory model for a maintenance system composed of a spares-stocking centre and a repair centre. In the maintenance system, multi-part spares are jointly needed to repair faulty end items determined by ambiguous fault isolation done by the built-in-test-equipment (BITE). If any operating end item breaks down, then all associated parts should be replaced either iteratively (one at a time) or altogether. In the case of iterative replacement, failed parts are detected in the field after fixing the broken end item. However, in the case of group (altogether) replacement, all removed parts are sent to the repair centre where the failed part is detected and fixed. The repaired or non-failed parts are then restocked at the spares-stocking centre. For the system, this paper is to derive the exact expressions for the distribution function and the expected numbers of the backlogged end items under the cannibalization policy. These expressions are then used in the optimization of the associated spares' inventory level. Illustrative numerical examples are also presented.     

On a Replacement Problem of a Cumulative Damage Model

Items are assumed to fail only by degradation. An appropriate stochastic model of such items is a cumulative process in which an item can fail only when the total amount of damage exceeds a prespecified failure level. This paper introduces a replacement policy in which an item is replaced at a certain level of damage before failure or at failure, whichever occurs first. The optimum replacement level of damage which will minimize the total expected cost per unit of time for an infinite time span is obtained. A numerical example is also presented. The total expected cost for a finite time span is also discussed.     

Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures

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.     

Repair-replace strategies for two-dimensional warranty policies

For repairable items sold with free replacement warranty, the actions available to the manufacturer to rectify failures under warranty are to

1. (1) repair the failed item or

2. (2) replace it with a new one.

A proper repair-replace strategy can reduce the expected cost of servicing the warranty. In this paper, we study repair-replace strategies for items sold with a two-dimensional free replacement warranty.     

Optimally maintaining a Markovian deteriorating system with limited imperfect repairs

We consider the problem of optimally maintaining a periodically inspected system that deteriorates according to a discrete-time Markov process and has a limit on the number of repairs that can be performed before it must be replaced. After each inspection, a decision maker must decide whether to repair the system, replace it with a new one, or leave it operating until the next inspection, where each repair makes the system more susceptible to future deterioration. If the system is found to be failed at an inspection, then it must be either repaired or replaced with a new one at an additional penalty cost. The objective is to minimize the total expected discounted cost due to operation, inspection, maintenance, replacement and failure. We formulate an infinite-horizon Markov decision process model and derive key structural properties of the resulting optimal cost function that are sufficient to establish the existence of an optimal threshold-type policy with respect to the system’s deterioration level and cumulative number of repairs. We also explore the sensitivity of the optimal policy to inspection, repair and replacement costs. Numerical examples are presented to illustrate the structure and the sensitivity of the optimal policy.     

Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering

In this paper, we consider the stochastic joint replenishment problem in an environment where transportation costs are dominant and full truckloads or full container loads are required. One replenishment policy, taking into account capacity restrictions of the total order volume, is the so-called QS policy, where replenishment orders are placed to raise the individual inventory positions of all items to their order-up-to levels, whenever the aggregate inventory position drops below the reorder level. We first provide a method to compute the policy parameters of a QS policy such that item target service levels can be met, under the assumption that demand can be modeled as a compound renewal process. The approximation formulas are based on renewal theory and are tested in a simulation study which reveals good performance. Second, we compare the QS policy with a simple allocation policy where replenishment orders are triggered by the individual inventory positions of the items. At the moment when an individual inventory position drops below its item reorder level, a replenishment order is triggered and the total vehicle capacity is allocated to all items such that the expected elapsed time before the next replenishment order is maximized. In an extensive simulation study it is illustrated that the QS policy outperforms this allocation policy since it results in lower inventory levels for the same service level. Although both policies lead to similar performance if items are identical, it can differ substantially if the item characteristics vary.     

A servicing strategy for items sold under warranty

When repairable items sold under warranty fail, the rectification action taken by the manufacturer can be either a repair or a replacement. In this paper a new repair–replacement strategy is proposed for the manufacturer when the items are sold with a non-renewing free replacement warranty policy. The strategy involves splitting the warranty period into two intervals where only repairs are carried out, separated by a third interval with at most one replacement.     

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchi’s on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is non-conforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure.     

A queueing model for general group screening policies and dynamic item arrivals

Classification of items as good or bad can often be achieved more economically by examining the items in groups rather than individually. If the result of a group test is good, all items within it can be classified as good, whereas one or more items are bad in the opposite case. Whether it is necessary to identify the bad items or not, and if so, how, is described by the screening policy. In the course of time, a spectrum of group screening models has been studied, each including some policy. However, the majority ignores that items may arrive at random time epochs at the testing center in real life situations. This dynamic aspect leads to two decision variables: the minimum and maximum group size. In this paper, we analyze a discrete-time batch-service queueing model with a general dependency between the service time of a batch and the number of items within it. We deduce several important quantities, by which the decision variables can be optimized. In addition, we highlight that every possible screening policy can, in principle, be studied, by defining the dependency between the service time of a batch and the number of items within it appropriately.     

Optimal replacement policy based on maximum repair time for a random shock and wear model

We study a \(\delta \) shock and wear model in which the system can fail due to the frequency of the shocks caused by external conditions, or aging and accumulated wear caused by intrinsic factors. The external shocks occur according to a Bernoulli process, i.e., the inter-arrival times between two consecutive shocks follow a geometric distribution. Once the system fails, it can be repaired immediately. If the system is not repairable in a pre-specific time D, it can be replaced by a new one to avoid the unnecessary expanses on repair. On the other hand, the system can also be replaced whenever its number of repairs exceeds N. Given that infinite operating and repair times are not commonly encountered in practical situations, both of these two random variables are supposed to obey general discrete distribution with finite support. Replacing the finite support renewal distributions with appropriate phase-type (PH) distributions and using the closure property associated with PH distribution, we formulate the maximum repair time replacement policy and obtain analytically the long-run average cost rate. Meanwhile, the optimal replacement policy is also numerically determined by implementing a two-dimensional-search process.     

A stocking policy for spare part provisioning under age based preventive replacement

A new policy, called stocking policy for ease of reference, has been advanced for joint optimization of age replacement and spare provisioning. It combines age replacement policy with continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The policy is generally applicable to any operating situation having either a single item or a number of identical items. A simulation model has been developed to determine the optimal values of the decision variables by minimizing the total cost of replacement and inventory. The behaviour of the stocking policy has been studied for a number of case problems specifically constructed by 5-factor second order rotatory design and the effects of different cost elements and item failure characteristics have been highlighted. For all case problems, optimal (s, S) policies to-support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate that the optimal stocking policy is, in general, more cost-effective than the Barlow-Proschan policy.     

An impulse control problem of a production model with interruptions to follow stochastic demand

The paper deals with the stochastic optimal intervention problem which arises in a production & storage system involving identical items. The requests for items arrive at random and the production of an item can be interrupted during production to meet the corresponding demand. The operational costs considered are due to the stock/backlog, running costs and set up costs associated to interruptions and re-initializations. The process presents distinct behaviour on each of two disjoint identical subsets of the state space, and the state process can only be transferred from one subset to the other by interventions associated to interruptions/re-initializations. A characterization is given in terms of piecewise deterministic Markov process, which explores the aforementioned structure, and a method of solution with assured convergence, that does not require any special initialization, is provided.Additionally, we demonstrate that under conditions on the data, the optimal policy is to produce the item completely in a certain region of the state space of low stock level.     

多货栈及变质情形下两种可替代物品的经济订货批量模型

研究了多货栈及变质情形下两种可替代物品的经济订货批量问题.在计划期内,若某一种易变质物品发生缺货,则可以被另一种易变质物品以一定的替代率代替补充,不同物品有不同的变质率,且要决定租用货栈的数量.以库存系统的总费用最小为目标函数,分别对货栈容量无限与有限的情形建立模型,证明了最优策略存在的唯一性,并分别给出了求解最优订购策略的算法,最后通过一个算例验证了算法的最优性.     

Joint Replenishment in Multi-Item Inventory Systems

A multi-item inventory system is considered which has the property that, for each single item, a reorder policy using the E.O.Q. formula would be appropriate. Holding costs are linear, and fixed ordering costs are assumed to be composed of a major set-up cost reflecting the pure fact of placing an order, and a sum of minor set-up costs corresponding to the items included in the order. If it is desirable to form a certain number of groups of items where all items of one group share the same order cycle, it is shown that there is always an optimal grouping in which items are arranged in increasing order of their ratio of yearly holding costs and minor set-up costs.A heuristic for forming the groups is given which turns out to be an optimal algorithm for the case that there are no major set-up costs. After an initial sorting of ratios, the worst-case complexity of this procedure is linear in the number of items.     

Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization

The joint economic lot sizing problem (JELP) model provides a global view to facilitate the development of a production-inventory policy for an integrated system. However, when a deteriorating item is involved, previous studies have neglected the following two important issues: (1) the deterioration quantity increases the demand for the supplier's capacity, which consequently requires the supplier to recalculate the corresponding average cost and reevaluate the capacity utilization, and (2) given the supplier's production rate, in-transit deterioration imposes restrictions on the delivery distance or in-transit time. Therefore, the existing integrated policies may lead to infeasible solutions for the distribution channel when a deterioration item is included. In view of these two issues, a generalized JELP model under delay in payments is formulated to investigate the integrated production-inventory policy for an item with two-stage deterioration (in-transit and retail deterioration) while incorporating both transportation time and capacity utilization. By developing the average cost functions of the supply chain members and employing several new definitions (e.g., variable capacity utilization), this paper provides a mechanism for measuring the influence of two-stage deterioration on the supplier's capacity utilization for the JELP. Three algorithms are proposed to obtain optimal decisions based on the theoretical results. This paper demonstrates that the supplier's variable capacity utilization is relevant to transportation time and two-stage deterioration, which can be applied to evaluate the feasibility of the integrated production-inventory policy for the deteriorating item. Furthermore, there is a maximum allowable value for the retailer's order cycle.     

A dyadic age-replacement policy for a periodically inspected equipment item subject to random deterioration

A periodic review replacement system is considered. The amount of deterioration over successive periods forms a sequence of i.i.d. random variables. A replacement policy of the dyadic type is in effect whereby the used equipment item is discarded and immediately replaced by a new identical equipment item if at the end of a period the old equipment has service aged by an amount in excess of S or has been in operation for exactly N periods whichever comes first. Using a theorem on renewal reward processes, an expression for the total steady-state expected cost per period is derived, consisting of a fixed replacement cost and a linear cost of operation. Optimal values of S and N that minimize this steady state cost are computed for a few numerical examples, when the service aging per period has a gamma distribution.     

两种可替代物品的经济订货批量模型

研究了两种可替代物品的经济订货批量问题.在计划期内,若某一种物品发生缺货,则可以被另一种物品以一定的替代率代替补充,以库存系统的总费用最小为目标函数,证明了最优策略存在的唯一性,并给出了求解最优订购策略的算法,最后通过两个算例验证了算法的最优性.     

A scheduling policy for adjusting economic lot quantities to a feasible solution

A heuristic scheduling policy is introduced for a multi-item, single-machine production facility. The scheduling policy uses the presumed optimal order quantities derived from solving an Economic Lot Size Problem and checks that the quantities obtain a feasible production schedule according to current inventory levels and expected demand rates. If not, the scheduling policy modifies the order quantities to achieve a possible solution without shortages. The scheduling policy is inspired by modification of the similar heuristic Dynamic Cycle Lengths Policy by Leachman and Gascon from 1988, 1991. The main characteristics of this scheduling policy are successive batches of the same item are treated explicitly, due to that it is quite possible that one item be manufactured several times before one other item is manufactured once more; the batches are ordered in increasing run-out time; if the existing situation creates stock-outs with ordinary order quantities, then the order quantities are decreased with a common scaling factor to try to prevent inventory shortages; in case the decrease of the order quantities changes expected run-out times, the batches are reordered after new run-out times; no filling up to an explicit inventory level is done, the filling up is done by the desirable order quantity; to prevent possible excess inventory the policy suggests time periods where no production should be performed. The scheduling policy contains no economical evaluation; this is supposed to be done when the order quantities are calculated, the policy prevents shortages and excess inventory. A numerical example illustrates the suggested scheduling policy. Finally, it is discussed as to how the policy can also take into account stochastic behaviour of the demand rates and compensate the schedule by applying appropriate safety times.     

易变质产品的可替代库存模型的最优订购策略研究

研究了易变质产品的可替代库存模型.在有限计划期内,供应商面临两种不同产品的需求,当一种产品发生短缺时,另一种产品可以以一定的替代率代替短缺产品.通过分析系统的总成本函数的性质,提出了最优订购策略.最后通过算例验证了算法的最优性.     

Optimal repair–replacement policies for a system with two types of failures

In this paper, the optimal replacement problem is investigated for a system with two types of failures. One type of failure is repairable, which is conducted by a repairman when it occurs, and the other is unrepairable, which leads to a replacement of the system at once. The repair of the system is not “as good as new”. The consecutive operating times of the system after repair form a decreasing geometric process, while the repair times after failure are assumed to be independent and identically distributed. Replacement policy N is adopted, where N is the number of repairable failures. The system will be replaced at the Nth repairable failure or at the unrepairable failure, whichever occurs first. Two replacement models are considered, one is based on the limiting availability and the other based on the long-run average cost rate of the system. We give the explicit expressions for the limiting availability and the long-run average cost rate of the system under policy N, respectively. By maximizing the limiting availability A(N) and minimizing the long-run average cost rate C(N), we theoretically obtain the optimal replacement policies N^∗ in both cases. Finally, some numerical simulations are presented to verify the theoretical results.