Solution algorithms for the parallel replacement problem under economy of scale

Chen, Zhilong

doi:10.1002/(sici)1520-6750(199804)45:3<279::aid-nav3>3.0.co;2-4

Cited by 24 publications

(12 citation statements)

References 6 publications

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“…This approach is slightly more efficient than that of [7] because it is only necessary to specify replacement options for the stage and state combinations that are consistent with the ages of the initial clusters that comprise the population. Unfortunately, the size of the optimization problem grows exponentially with the number of stages, T. Finally, Chen [2] proposes shortest path algorithms that exploit the AONR for infinite-horizon problems with stationary parameters and for finite-horizon problems with time-varying parameters. These algorithms are efficient but rely on overly restrictive assumptions to ensure that the AONR applies, as discussed earlier.…”

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

“…In addition to the aforementioned algorithms, Chen [2] formulates the finite horizon PMRP with fixed plus variable replacement costs and time-varying parameters as a zeroone integer program. He proposes an exact solution proce- dure based on Benders' decomposition.…”

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

“…Except for the zero-one integer program of [2] that relies on the fixed plus variable cost structure, the computational approaches described above can be used to find optimal replacement policies for deterministic problems with general classes of replacement cost functions. 3 That is, the linear programming approach of [7] or the forward dynamic programming approach of [9] can be used for the deterministic PMRP with nonincreasing marginal costs because the NSR applies.…”

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

“…The OCRR is also required for the forward dynamic programming approach of [9]. Also, one may use the shortest path algorithms of [2] if the assumptions required for the AONR hold. These algorithms, however, cannot be used to solve the stochastic PMRP because they assume that the number of clusters in the population does not increase over the planning horizon (a corollary to the NSR).…”

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

“…In the stochastic PMRP, clusters can be split even if the same actions are applied to them. In addition, the forward dynamic programming formulation of [9] and the zero-one integer program of [2] rely on the fact that machines deteriorate deterministically.…”

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

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On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

Childress

Durango-Cohen

2005

Naval Research Logistics

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Abstract:The parallel machine replacement problem consists of finding a minimum cost replacement policy for a finite population of economically interdependent machines. In this paper, we formulate a stochastic version of the problem and analyze the structure of optimal policies under general classes of replacement cost functions. We prove that for problems with arbitrary cost functions, there can be optimal policies where a machine is replaced only if all machines in worse states are replaced (Worse Cluster Replacement Rule). We then show that, for problems with replacement cost functions exhibiting nonincreasing marginal costs, there are optimal policies such that, in any stage, machines in the same state are either all kept or all replaced (No-Splitting Rule). We also present an example that shows that economies of scale in replacement costs do not guarantee optimal policies that satisfy the No-Splitting Rule. These results lead to the fundamental insight that replacement decisions are driven by marginal costs, and not by economies of scale as suggested in the literature. Finally, we describe how the optimal policy structure, i.e., the No-Splitting and Worse Cluster Replacement Rules, can be used to reduce the computational effort required to obtain optimal replacement policies.

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Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

Section: Solving the Deterministic Pmrpmentioning

confidence: 99%

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On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

Childress

Durango-Cohen

2005

Naval Research Logistics

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The parallel replacement problem with demand and capital budgeting constraints

Hartman

2000

Naval Research Logistics

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A generalized parallel replacement problem is considered with both fixed and variable replacement costs, capital budgeting, and demand constraints. The demand constraints specify that a number of assets, which may vary over time, are required each period over a finite horizon. A deterministic, integer programming formulation is presented as replacement decisions must be integer. However, the linear programming relaxation is shown to have integer extreme points if the economies of scale binary variables are fixed. This allows for the efficient computation of large parallel replacement problems as only a limited number of 0–1 variables are required. Examples are presented to provide insight into replacement rules, such as the “no‐splitting‐rule” from previous research, under various demand scenarios. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 40–56, 2000

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A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

2010

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This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.Keywords Project management · Scheduling · Genetic algorithms · Random keys · Forward-backward improvement · Resource constrained project scheduling problem Supported by Fundação para a Ciência e Tecnologia (FCT) project PTDC/GES/72244/2006.

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Solution algorithms for the parallel replacement problem under economy of scale

Cited by 24 publications

References 6 publications

On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

The parallel replacement problem with demand and capital budgeting constraints

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

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