775 research outputs found
On the use of phase-type distributions for inventory management with supply disruptions
Cataloged from PDF version of article.Maintaining the continuity of operations becomes increasingly important for systems that are subject to disruptions due to various reasons. In this paper, we study an inventory system operating under a (q, r) policy, where the supply can become inaccessible for random durations. The availability of the supply is modeled by assuming a single supplier that goes through ON and OFF periods of stochastic duration, both of which are modeled by phase-type distributions (PTD). We provide two alternative representations of the state transition probabilities of the system, one with integral and the other employing Kolmogorov differential equations. We then use an efficient formulation for the analytical model that gives the optimal policy parameters and the long-run average cost. An extensive numerical study is conducted, which shows that OFF time characteristics have a bigger impact on optimal policy parameters. The ON time characteristics are also important for critical goods if disasters can happen. Copyright (C) 2011 John Wiley & Sons, Ltd
Loss systems in a random environment
We consider a single server system with infinite waiting room in a random
environment. The service system and the environment interact in both
directions. Whenever the environment enters a prespecified subset of its state
space the service process is completely blocked: Service is interrupted and
newly arriving customers are lost. We prove an if-and-only-if-condition for a
product form steady state distribution of the joint queueing-environment
process. A consequence is a strong insensitivity property for such systems.
We discuss several applications, e.g. from inventory theory and reliability
theory, and show that our result extends and generalizes several theorems found
in the literature, e.g. of queueing-inventory processes.
We investigate further classical loss systems, where due to finite waiting
room loss of customers occurs. In connection with loss of customers due to
blocking by the environment and service interruptions new phenomena arise.
We further investigate the embedded Markov chains at departure epochs and
show that the behaviour of the embedded Markov chain is often considerably
different from that of the continuous time Markov process. This is different
from the behaviour of the standard M/G/1, where the steady state of the
embedded Markov chain and the continuous time process coincide.
For exponential queueing systems we show that there is a product form
equilibrium of the embedded Markov chain under rather general conditions. For
systems with non-exponential service times more restrictive constraints are
needed, which we prove by a counter example where the environment represents an
inventory attached to an M/D/1 queue. Such integrated queueing-inventory
systems are dealt with in the literature previously, and are revisited here in
detail
Reliability applied to maintenance
The thesis covers studies conducted during 1976-79 under a
Science Research Council contract to examine the uses of reliability
information in decision-making in maintenance in the process industries.
After a discussion of the ideal data system, four practical studies
of process plants are described involving both Pareto and distribution
analysis. In two of these studies the maintenance policy was changed
and the effect on failure modes and frequency observed. Hyper-exponentially
distributed failure intervals were found to be common and were explained
after observation of maintenance work practices and development of
theory as being due to poor workmanship and parts. The fallacy that
constant failure rate necessarily implies the optimality of maintenance
only at failure is discussed.
Two models for the optimisation of inspection intervals are
developed; both assume items give detectable warning of impending failure.
The first is based upon constant risk of failure between successive
inspections 'and Weibull base failure distribution~ Results show that
an inspection/on-condition maintenance regime can be cost effective
even when the failure rate is falling and may be better than periodiC
renewals for an increasing failure situation. The second model is first-order Markov. Transition rate matrices are developed and solved
to compare continuous monitoring with inspections/on-condition
maintenance an a cost basis. The models incorporate planning delay
in starting maintenance after impending failure is detected.
The relationships between plant output and maintenance policy
as affected by the presence of redundancy and/or storage between stages
are examined, mainly through the literature but with some original
theoretical proposals.
It is concluded that reliability techniques have many applications
in the improvement of plant maintenance policy. Techniques abound,
but few firms are willing to take the step of faith to set up, even
temporarily, the data-collection facilities required to apply them.
There are over 350 references, many of which are reviewed in the
text, divided into chapter-related sectionso
Appendices include a review of Reliability Engineering Theory,
based on the author's draft for BS 5760(2) a discussion of the 'bath-tub
curves' applicability to maintained systems and the theory connecting
hyper-exponentially distributed failures with poor maintenance
practices
A review of the open queueing network models of manufacturing systems
"December 1990."Includes bibliographical references (p. 52-58).Research partially supported by the "Leaders for Manufacturing Program". Research partially supported by the UCLA Senate Committee on Grants. 99by Gabriel R. Bitran, Sriram Dasu
Modeling the supplier uncertainty with phase-type distributions in inventory problems
Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1996.Thesis (Master's) -- Bilkent University, 1996.Includes bibliographical references leaves 109-111.This study considers a stochastic inventory nnodel where the supply
availability is subject to random fluctuations. The periods in which the supplier
is available (ON) or unavailable (OFF) are modeled as a semi-Markov process.
During ON periods the {q,r) policy is applied. During OFF periods, the
amount enough to bring the inventory position to q + r is ordered as soon
as the supplier becomes available again. The regenerative cycles are identifled
by observing the inventory position and using the renewal reward theorem the
average cost per time objective function is derived. In our study, a K-stage
Phase-Type distribution for ON periods and a general distribution for OFF
periods are assumed. In our study, the problem is theoretically solved for Kstage
Phase-Type distributions; additionally numerical computations are made
for 2-stage Phase-Type distributions. For large q values the structure of the
objective function is investigated.Balcıoğlu, Ahmet BarışM.S
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