Analysis of the asset replacement level with an uncertain salvage value: a two-factor model

The aim of this article is to analyse the asset replacement problem from the perspective of optimal replacement level, given a specific tax environment and depreciation policy. Using a real options approach, our model minimizes current operation and maintenance costs and allows the definition of a new value of the replacement flexibility within a multi-cycle environment. The innovation on the valuation process comes from adding an autonomous salvage value’s factor. The results from partial differential equations reveal relevant differences from those observed in one-factor models, especially with regard to optimal replacement levels and in the non-monotonous effects of salvage value variation. The numerical case study also confirms that the salvage value is indeed a worthwhile element in the replacement process. It was possible to determine that, in terms of the magnitude of the cost replacement level, the key roles are played by changes in the speed of mean reversion, as well in the salvage factor volatility. This paper provides some improvements to the existing literature in equivalent annual cost by drawing up a cost minimization problem conditioned by a different salvage value dynamics, and contributes to real options literature by introducing a salvage value factor in the pricing model.     

The effect of tax depreciation on the stochastic replacement policy

The optimal replacement policy for an asset subject to a stochastic deteriorating operating cost is determined for three different tax depreciation schedules and a known re-investment cost, as the solution to a two-factor model using a quasi-analytical method. We find that tax depreciation exerts a critical influence over the replacement policy by lowering the operating cost thresholds. Although typically a decline in the corporate tax rate, increase in any initial capital allowance, or decrease in the depreciation lifetime (increase in depreciation rate) results in a lower operating cost threshold which justifies replacing older equipment, these results are not universal, and indeed for younger age assets the result may be the opposite. An accelerating depreciation schedule may incentivize early replacement in a deterministic context, but not necessarily for an environment of uncertainty.     

Optimization of a fully adaptive quality and maintenance model in the presence of multiple location and scale quality shifts

This paper presents a new model for the economic-statistical optimization of a Variable-Parameter Shewhart control scheme. The proposed model can be utilized to monitor processes where apart from multiple independent assignable causes, affecting both the mean and variance, failures can also occur. Each time an alarm is issued by the control scheme, preventive maintenance actions are initiated, whereas, corrective maintenance actions are required after a failure. The more realistic assumption of imperfect preventive maintenance actions has been considered. The optimal parameter values are selected through a bi-objective optimization problem formulated by the long-run average cost per time unit minimization, and the long-run expected availability maximization, subject to statistical constraints. A real case example is presented to illustrate the application of the model. An extended numerical investigation is utilized to evaluate the superiority of the proposed model.     

The dynamics of asset lifetime under technological change

The variable lifetime of assets is analyzed in a serial replacement problem. Technological change impacts the maintenance cost and new asset cost. The optimal asset lifetime appears to be constant only when both costs decrease with the same rate. We identify cases when the technological change decreases or increases the optimal lifetime.     

Optimal inspection and replacement policies for multi-state deteriorating systems

In this paper, a phase-type approach is proposed to derive optimal inspection and replacement policies for semi-Markovian deteriorating systems. In this approach, the general sojourn time distributions of a semi-Markovian maintenance model are approximated by acyclic phase-type distributions. Using the approximation, a semi-Markovian maintenance model can be transformed into a Markovian maintenance model such that the analytical tractability of Markov processes can be preserved. Based on the Markovian model, algorithms are provided to derive the optimal state-dependent and state-age-dependent inspection and replacement policies such that the expected long-run cost rate is minimized. Furthermore, procedures are developed to implement the optimal policies on semi-Markovian deteriorating systems. The implementation of the optimal policies are illustrated by numerical examples.     

Optimal policies for a delay time model with postponed replacement

We develop a delay time model (DTM) to determine the optimal maintenance policy under a novel assumption: postponed replacement. Delay time is defined as the time lapse from the occurrence of a defect up until failure. Inspections can be performed to monitor the system state at non-negligible cost. Most works in the literature assume that instantaneous replacement is enforced as soon as a defect is detected at an inspection. In contrast, we relax this assumption and allow replacement to be postponed for an additional time period. The key motivation is to achieve better utilization of the system’s useful life, and reduce replacement costs by providing a sufficient time window to prepare maintenance resources. We model the preventive replacement cost as a non-increasing function of the postponement interval. We then derive the optimal policy under the modified assumption for a system with exponentially distributed defect arrival time, both for a deterministic delay time and for a more general random delay time. For the settings with a deterministic delay time, we also establish an upper bound on the cost savings that can be attained. A numerical case study is presented to benchmark the benefits of our modified assumption against conventional instantaneous replacement discussed in the literature.     

Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.     

A new MIP model for mine equipment scheduling by minimizing maintenance cost

Mining investment has been recognized as capital intensive due mainly to the cost of large equipment. Equipment capital costs for a given operation are usually within the order of hundreds of million dollars but may reach to billion dollars for large companies operating multiple mines. Such large investments require the optimum usage of equipment in a manner that the operating costs are minimized and the utilization of equipment is maximized through optimal scheduling. This optimum usage is required to ensure that the business remains sustainable and financially stable. Most mining operations utilize trucks to haul the mined material. Maintenance is one of the major operating cost items for these fleets as it can reach approximately one hundred million dollars yearly. There is no method or application in the literature that optimizes the utilization for truck fleet over the life of mine. A new approach based on mixed integer programming (MIP) techniques is used for annually scheduling a fixed fleet of mining trucks in a given operation, over a multi-year time horizon to minimize maintenance cost. The model uses the truck age (total hours of usage), maintenance cost and required operating hours to achieve annual production targets to produce an optimum truck schedule. While this paper focuses on scheduling trucks for mining operation, concept can be used in most businesses using equipment with significant maintenance costs. A case study for a large scale gold mine showed an annual discounted (10% rate) maintenance cost saving of over $2M and more than 16% ($21M) of overall maintenance cost reduction over 10 years of mine life, compared with the spreadsheet based approach used currently at the operation.     

Optimal fleet replacement: A case study on a Spanish urban transport fleet

Optimizing the average annual cost of a bus fleet has become an increasing concern in transport companies management around the world. Nowadays, there are many tools available to assist managerial decisions, and one of the most used is the cost analysis of the life cycle of an asset, known as “life cycle cost”. Characterized by performing deterministic analysis of the situation, it allows the administration to evaluate the process of fleet replacement but is limited by not contemplating certain intrinsic variations related to vehicles and for disregarding variables related to exigencies of fleet use. The main purpose of this study is to develop a combined model of support to asset management based in the association of the life cycle cost tool and the mathematical model of Monte Carlo simulation, by performing a stochastic analysis considering both age and average annual mileage for optimum vehicle replacement. The utilized method was applied in a Spanish urban transport fleet, and the results indicate that the use of the stochastic model was more effective than the use of the deterministic model.     

Optimal number of minimal repairs before ordering spare for preventive replacement

This paper presents a model for determining the optimal number of minimal repairs before ordering spare for preventive replacement. By introducing the costs of ordering, repair, downtime, replacement, and the salvage value of an un-failed system, the expected long-term cost rates and cost effectiveness are derived. It is shown that, under certain conditions, the optimal number of minimal repairs, which minimizes the cost rate or maximizes the cost effectiveness, is given by a unique solution of an equation. A numerical example is also given for illustration of the proposed model.     

A real options approach for entering the Internet securities trading businesses with start‐up time

This paper uses a real options approach to establish a new evaluation model under uncertainty of both the volume of Internet securities transactions and the total transaction volume of a securities firm. The proposed approach can assist securities firms in evaluating the optimal thresholds for entering the Internet securities trading business and withdrawing from the conventional securities trading business. This paper assumes that the annual number of Internet securities transactions and the total annual number of securities transactions both follow a geometric Brownian motion. Besides, this model considers a start‐up time to complete the entry project's procedure. Accordingly, a decision model based on the real options approach is introduced, and the closed form solutions for the optimal threshold values of the entry or withdrawal models are determined. The conclusions provide some valuable references to help strategic managers of securities firms in making decisions on entering the Internet securities trading business or withdrawing from the conventional trading business. Copyright © 2003 John Wiley & Sons, Ltd.     

Cyber vulnerability maintenance policies that address the incomplete nature of inspection

In cybersecurity, incomplete inspection, resulting mainly from computers being turned off during the scan, leads to a challenge for scheduling maintenance actions. This article proposes the application of partially observable decision processes to derive cost‐effective cyber maintenance actions that minimize total costs. We consider several types of hosts having vulnerabilities at various levels of severity. The maintenance cost structure in our proposed model consists of the direct costs of maintenance actions in addition to potential incident costs associated with different security states. To assess the benefits of optimal policies obtained from partially observable Markov decision processes, we use real‐world data from a major university. Compared with alternative policies using simulations, the optimal control policies can significantly reduce expected maintenance expenditures per host and relatively quickly mitigate the most important vulnerabilities.     

增长期权对最优资本结构的影响研究：企业生命周期的视角

资产构成和生命周期的动态关系决定了企业最优资本结构的变化趋势。本文在利息税盾和破产成本的权衡理论框架下,运用实物期权方法,理论上揭示了增长期权动态执行导致最优资本结构随企业生命周期的变化规律,扩展分析了股东-债权人代理冲突对最优资本结构的影响,并提供了基于中国沪深A股上市公司的经验证据。结果表明：随着企业由年轻走向成熟,增长期权不断执行和在位资产逐渐累积会降低企业总体的破产风险,从而企业最优财务杠杆呈现上升趋势且增长速度逐渐放缓;股东和债权人在增长期权执行决策上的代理冲突导致的投资不足会降低最优财务杠杆,但代理成本随企业生命周期推进呈递减趋势。     

Numerical solution of variational inequalities for pricing Asian options by higher order Lagrange–Galerkin methods

Asian options prices can be modelled in the Black–Scholes framework leading to two-factor models depending on the asset price, the average of the asset price and the time. They can also involve inequality constraints, as in the case of Amerasian options, leading to variational inequalities (VI). In the first section, we completely describe the pricing model for fixed-strike Eurasian and Amerasian options and list some properties satisfied by the option value function. Then, since no solutions in closed form are known, we deal with the numerical solution of the above problems proposing a general methodology: an iterative algorithm for the VI, combined with higher order Lagrange–Galerkin methods for partial differential equations. Finally, numerical results are shown.     

A Mean Variance Approach to the Optimal Machine Maintenance and Replacement Problem

This paper considers a simultaneous maintenance and replacement problem under uncertainty. The effects of maintenance and deterioration are assumed to have a probabilistic effect (of the Markovian type) on a machine's salvage value. This leads to the definition of a non-stationary stochastic process of the machine's salvage value whose mean and variance evolutions are found. These evolutions together with an expected discounted profit functional (as that given by Thompson) allows us to apply the tools of optimal control theory to determine a "certainty-equivalent" maintenance program and the optimum replacement date of the machine. A discussion of the uncertain effects of deterioration and maintenance and managers attitudes towards risk is included as well.     

考虑残值变化和消费者低碳偏好的生产定价与销售激励机制

在消费者低碳偏好和产品残值变化下,研究制造商的碳减排、生产及定价联合决策、以及对销售商的销售激励契约设计问题。不同于以往的研究假设残值不变,本文考虑残值依赖于清仓期库存以及碳减排问题。提出委托代理模型,求解模型并从理论上分析残值的变化和碳减排成本对双方决策和收益的影响。研究表明,残值变化率的增加只导致制造商的收益和生产量下降,不影响制造商的碳减排、定价、销售契约及零售商的决策和收益,但碳减排成本将导致制造商的收益和双方决策变量的下降。最后通过算例分析验证了结论,对供应链的运营实践有指导意义。     

Optimal decision policy for real options under general Markovian dynamics

The Least-Squares Monte Carlo Method (LSM) has become the standard tool to solve real options modeled as an optimal switching problem. The method has been shown to deliver accurate valuation results under complex and high dimensional stochastic processes; however, the accuracy of the underlying decision policy is not guaranteed. For instance, an inappropriate choice of regression functions can lead to noisy estimates of the optimal switching boundaries or even continuation/switching regions that are not clearly separated. As an alternative to estimate these boundaries, we formulate a simulation-based method that starts from an initial guess of them and then iterates until reaching optimality. The algorithm is applied to a classical mine under a wide variety of underlying dynamics for the commodity price process. The method is first validated under a one-dimensional geometric Brownian motion and then extended to general Markovian processes. We consider two general specifications: a two-factor model with stochastic variance and a rich jump structure, and a four-factor model with stochastic cost-of-carry and stochastic volatility. The method is shown to be robust, stable, and easy-to-implement, converging to a more profitable strategy than the one obtained with LSM.     

Age-dependent production planning and maintenance strategies in unreliable manufacturing systems with lost sale

In this paper, we formulate an analytical model for the joint determination of an optimal age-dependent buffer inventory and preventive maintenance policy in a production environment that is subject to random machine breakdowns. Traditional preventive maintenance policies, such as age and periodic replacements, are usually studied based on simplified and non-realistic assumptions, as well as on the expected costs criterion. Finished goods inventories and the age-dependent likelihood of machine breakdowns are usually not considered. As a result, these policies could significantly extend beyond the anticipated financial incomes of the system, and lead to crises. In order to solve this problem, a more realistic analysis model is proposed in this paper to consider the effects of both preventive maintenance policies and machine age on optimal safety stock levels. Hence, a unified framework is developed, allowing production and preventive maintenance to be jointly considered. We use an age-dependent optimization model based on the minimization of an overall cost function, including inventory holdings, lost sales, preventive and corrective maintenance costs. We provide optimality conditions for the manufacturing systems considered, and use numerical methods to obtain an optimal preventive maintenance policy and the relevant age-dependent threshold level production policy. In this work, this policy is called the multiple threshold levels hedging point policy. We include numerical examples and sensitivity analyses to illustrate the importance and the effectiveness of the proposed methodology. Compared with other available optimal production and maintenance policies, the numerical solution obtained shows that the proposed age-dependent optimal production and maintenance policies significantly reduce the overall cost incurred.     

Optimal maintenance strategy for non‐renewing replacement–repair warranty

In this paper, we study the maintenance policy following the expiration of the non‐renewing replacement–repair warranty (NRRW). For such purposes, we first define the non‐renewing free replacement–repair warranty and the non‐renewing pro rata replacement–repair warranty. Then the maintenance model following the expiration of the NRRW is discussed from the user's point of view. As the criterion to determine the optimal maintenance strategy, we formulate the expected cost rate per unit time from the user's perspective. All system maintenance costs incurred after the warranty is expired are paid by the user. Given the cost structures during the life cycle of the system, we determine the optimal maintenance period following the expiration of the NRRW. Finally, a few numerical examples are given for illustrative purposes. Copyright © 2012 John Wiley & Sons, Ltd.