A Discrete Maintenance and Replacement Model under Technological Breakthrough Expectations
TL;DR: Two cases of the discrete time finite horizon technology replacement problem are solved and it is demonstrated that management may improve profitability by delaying (but not necessarily foregoing) replacement with an available better machine.
Abstract: Two cases of the discrete time finite horizon technology replacement problem are solved. The first deals with two available machines, one in use and a better one that can be purchased to replace it. The second case considers, in addition, a third machine of future technology that will be available at some random future time. The maintenance level of each used machine is chosen for each period in order to economically control performance deterioration. For solving the model, we first derive an optimal preventive maintenance policy by showing that “bang-bang” (i.e., full or non), non-increasing, maintenance efforts are optimal. Employing the optimal maintenance policy, we reformat the problem and conduct a numerical search in order to derive the replacement policy that will maximize the expected net present profit. Numerical examples demonstrate that management may improve profitability by delaying (but not necessarily foregoing) replacement with an available better machine.
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TL;DR: A solution algorithm is presented and replacement considerations under technological change are incorporated into a well-known optimal control model for maintenance under uncertainty.
Abstract: How should a manager make replacement decisions for a chain of machines over time if each is maintained by an optimal control model addressing uncertainty of machine breakdowns? A network representation of the problem involves arcs with interdependent costs. A solution algorithm is presented and replacement considerations under technological change are incorporated into a well-known optimal control model for maintenance under uncertainty (that of Kamien and Schwartz 1971). The method is illustrated by an example.
43 citations
Additional excerpts
...The way this problem differs from replacement models that use deterministic (optimal control) maintenance segments such as, say, those of Sethi and Morton (1972) or Mehrez et al. (2000), can be summarized as follows....
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...More recently, building on Kamien and Schwartz’s ideas, Mehrez and Berman (1994) and Mehrez et al. (2000) developed deterministic maintenance models allowing for as much as three replacements over time....
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TL;DR: In this article, the authors develop a real options framework to analyse the impact of technological, policy and electricity price uncertainty on the decision to invest sequentially in successively improved versions of a renewable energy (RE) technology.
31 citations
TL;DR: A cost function is considered, which takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and-or production) cost, with a constant rate per unit time.
Abstract: Identical components are considered, which become obsolete once new-type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old-type components by the new-type ones: either purely preventive, where all old-type components are replaced as soon as the new-type ones are available; either purely corrective, where the old-type ones are replaced by new-type ones only at failure; or a mixture of both strategies, where the old-type ones are first replaced at failure by new-type ones and next simultaneously preventively replaced after a fixed number of failed old-type components.
To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and-or production) cost, with a constant rate per unit time.
A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long-time run. Numerical experiments conclude the paper. Copyright © 2008 John Wiley & Sons, Ltd.
28 citations
TL;DR: Through a numerical study, insights are derived on which of the two upgrading policies is the best one and it is shown how this depends on the lifetime of the systems, the reliability of the old components, the improvement level in the reliability, the increase in the unit price, downtime costs, the size of installed base, and the batch size.
17 citations
TL;DR: In this article, an efficient discrete-time algorithm for serial asset replacement under incomplete data about technological change that affects the capital cost, operating cost and salvage value of newer assets is presented.
Abstract: We analyse the serial asset replacement problem under incomplete data about technological change that that affects the capital cost, operating cost and salvage value of newer assets. We construct an efficient discrete-time algorithm for this problem in the case where only partial information is available about future costs of new assets. The algorithm is based on introducing a corrected annual capital recovery factor into the classic Economic Life method. It produces the same lifetime of the first asset as the benchmark infinite-horizon cost minimisation when the operating cost, capital cost and salvage value of new assets decrease proportionally. The algorithm has the same complexity as the Economic Life method but performs much better under improving technology. Numeric simulation demonstrates a superior efficiency of the suggested algorithm vs. existing methods in practical situations when only few discrete measurements of technological change are available.
15 citations
Cites background from "A Discrete Maintenance and Replacem..."
...…assets (Karabakal, Lohmann, and Bean 1994; Scarf and Bouamra 1999; Büyüktahtakın and Hartman 2015); (2) Discrete-time (Kusaka and Suzuki 1990; Mehrez, Rabinowitz, and Shemesh 2000; Regnier, Sharp, and Tovey 2004; Rogers and Hartman 2005) and continuous-time (Grinyer 1973; Scarf and Hashem…...
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...…so our analysis is also restricted to one-asset settings (Grinyer 1973; Kusaka and Suzuki 1990; Bean, Lohmann, and Smith 1994; Bethuyne 1998; Mehrez, Rabinowitz, and Shemesh 2000; Cheevaprawatdomrong and Smith 2003; Regnier, Sharp, and Tovey 2004; Rogers and Hartman 2005; Yatsenko and…...
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...…features, such as: (1) Serial replacement of a single asset (Grinyer 1973; Kusaka and Suzuki 1990; Bean, Lohmann, and Smith 1994; Bethuyne 1998; Mehrez, Rabinowitz, and Shemesh 2000; Cheevaprawatdomrong and Smith 2003; Regnier, Sharp, and Tovey 2004; Rogers and Hartman 2005; Hritonenko and…...
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...…horizons (Kusaka and Suzuki 1990; Scarf and Hashem 1997; Yatsenko and Hritonenko 2015); (6) Models with continuous and discontinuous technological change (Hopp and Nair 1991; Rajagopalan, Singh, and Motron 1998; Mehrez, Rabinowitz, and Shemesh 2000; Yatsenko and Hritonenko 2009), and others....
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References
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TL;DR: Disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full N periods and desire a minimum total cost inventory management scheme which satisfies known demand in every period.
Abstract: (This article originally appeared in Management Science, October 1958, Volume 5, Number 1, pp. 89-96, published by The Institute of Management Sciences.)
A forward algorithm for a solution to the following dynamic version of the economic lot size model is given: allowing the possibility of demands for a single item, inventory holding charges, and setup costs to vary over N periods, we desire a minimum total cost inventory management scheme which satisfies known demand in every period. Disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full N periods.
2,114 citations
Book•
31 Jul 2000
TL;DR: In this article, the authors present an alternative derivation of the maximum principle of continuous time for optimal control, which they call the continuous time maximization principle (CTP), which is defined in the Calculus of Variations.
Abstract: Preface to First Edition.- Preface to Second Edition.- What is Optimal Control Theory?.- The Maximum Principle: Continuous Time.- The Maximum Principle: Mixed Inequality Constraints.- The Maximum Principle: General Inequality Constraints.- Applications to Finance.- Applications to Production and Inventory.- Applications to Marketing.- The Maximum Principle: Discrete Time.- Maintenance and Replacement.- Applications to Natural Resources.- Economic Applications.- Differential Games, Distributed Systems, and Impulse Control.- Stochastic Optimal Control.- Solutions of Linear Differential Equations.- Calculus of Variations and Optimal Control Theory.- An Alternative Derivation of the Maximum Principle.- Special Topics in Optimal Control.- Answers to Selected Exercises.- Bibliography.- Index.- List of Figures.- List of Tables.
804 citations
TL;DR: The literature on maintenance models is surveyed and includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.
Abstract: The literature on maintenance models is surveyed. The focus is on work appearing since the 1965 survey "Maintenance Policies for Stochastically Failing Equipment: A Survey" by John McCall and the 1965 book", "The Mathematical Theory of Reliability", by Richard Barlow and Frank Proschan. The survey includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.
709 citations
"A Discrete Maintenance and Replacem..." refers background in this paper
...Thus, simple stochastic single-machine (see, e.g., Pierskalla and Voelker [ 11 ] and their references) or deterministic multiple-machines (see, e.g., Leung and Tanchoco [7] and their references) may provide a useful insight into the machine replacement problem....
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TL;DR: This document summarizes current capabilities, research and operational priorities, and plans for further studies that were established at the 2015 USGS workshop on quantitative hazard assessments of earthquake-triggered landsliding and liquefaction.
Abstract: Solutions for Chapter 1.- Solutions for Chapter 2.- Solutions for Chapter 3.- Solutions for Chapter 4.- Solutions for Chapter 5.- Solutions for Chapter 6.- Solutions for Chapter 7.- Solutions for Chapter 8.- Solutions for Chapter 9.- Solutions for Chapter 10.- Solutions for Chapter 11.- Solutions for Chapter 12.
194 citations