International Journal of Mathematics in Operational Research http://www.inderscience.com/browse/index.php?journalID=320&year=2012&vol=4&issue=1 Inderscience Publishers Ltd en-uk International Journal of Mathematics in Operational Research 1757-5850 1757-5869 © 2012 Inderscience Publishers Ltd editor@inderscience.com https://www.inderscience.com/images/files/coverImgs/ijmor_scoverijmor.jpg http://www.inderscience.com/browse/index.php?journalID=320&year=2012&vol=4&issue=1 http://www.inderscience.com/link.php?id=44469 Assembly lines are special flow-line production systems which are of great importance in the industrial mass production. This paper introduces the deterioration effects in assembly lines that the aim of the developed mathematical model and the proposed genetic algorithm is to minimise the working time of a product in a cycle of assembly. Task deterioration means that a task processed later consumes more time than the same task when it is processed earlier. At the end several well-known examples are solved and the results proved that the deterioration will affect both cycle time and working time, simultaneously. Working time evaluation in assembly lines
M. Karimi-Nasab; Unes Bahalke; H.R. Feili; A. Sheikhzadeh; K. Dolatkhahi
International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 1 - 17
Assembly lines are special flow-line production systems which are of great importance in the industrial mass production. This paper introduces the deterioration effects in assembly lines that the aim of the developed mathematical model and the proposed genetic algorithm is to minimise the working time of a product in a cycle of assembly. Task deterioration means that a task processed later consumes more time than the same task when it is processed earlier. At the end several well-known examples are solved and the results proved that the deterioration will affect both cycle time and working time, simultaneously.

]]> 10.1504/IJMOR.2012.044469 International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 1 - 17 M. Karimi-Nasab; Unes Bahalke; H.R. Feili; A. Sheikhzadeh; K. Dolatkhahi Department of Industrial Engineering, Iran University of Science and Technology, P.O. Box 1684613114, Narmak, Tehran, Iran. ' Department of Industrial Engineering, Iran University of Science and Technology, P.O. Box 1684613114, Narmak, Tehran, Iran. ' Faculty of Engineering, Department of Industrial Engineering, Alzahra University, P.O. Box 1993891176, Tehran, Iran. ' Department of Industrial Engineering, Amirkabir University of Technology, P.O. Box 1684613114, Tehran, Iran, Iran. ' Department of Industrial Engineering, Iran University of Science and Technology, P.O. Box 1684613114, Narmak, Tehran, Iran assembly line balancing working time sequencing task deterioration genetic algorithms GAs cycle time. 2011-12-26T23:20:50-05:00 4 1 1 17 2011-12-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=44470 Distributed software system consists of reused and newly developed software components. This paper presents testing-effort-dependent Software Reliability Growth Model (SRGM) for distributed environment. We have used logistic learning function for newly developed components with the assumption that the skill of the testing team grows as testing progresses. We assume that detected faults are not immediately removed but lag the fault detection process by debugging time lag. Thus, different debugging time lag functions have been used during removal process for newly developed components. The proposed model has been validated and is shown that the proposed model results are comparatively better than the existing ones. Testing-effort-dependent software reliability growth model for a distributed environment using debugging time lag functions
P.K. Kapur; Prashant Johri; Sunil Kumar Khatri
International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 18 - 30
Distributed software system consists of reused and newly developed software components. This paper presents testing-effort-dependent Software Reliability Growth Model (SRGM) for distributed environment. We have used logistic learning function for newly developed components with the assumption that the skill of the testing team grows as testing progresses. We assume that detected faults are not immediately removed but lag the fault detection process by debugging time lag. Thus, different debugging time lag functions have been used during removal process for newly developed components. The proposed model has been validated and is shown that the proposed model results are comparatively better than the existing ones.

]]> 10.1504/IJMOR.2012.044470 International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 18 - 30 P.K. Kapur; Prashant Johri; Sunil Kumar Khatri Amity International Business School, Amity University, Noida 201303, India. ' Department of Computer Science, Galgotias University, Greater Noida 201306, India. ' Amity Institute of Information Technology, Amity University, Noida 201303, India NHPP nonhomogeneous Poisson process distributed development environment testing effort debugging time lag functions software reliability distributed software fault detection software development. 2011-12-26T23:20:50-05:00 4 1 18 30 2011-12-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=44471 The paper studies the benchmark approach for pricing and hedging in incomplete markets where the investor has to filter the incomplete information. We consider a jump diffusion Markov modulated market model and derive the Growth Optimal Portfolio (GOP), by using the stochastic control method. Using GOP, we price and hedge European options where the existence of the equivalent martingale measure is not necessary. Growth Optimal Portfolio for unobservable Markov-modulated markets
I. Venkat Appal Raju; N. Selvaraju
International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 31 - 40
The paper studies the benchmark approach for pricing and hedging in incomplete markets where the investor has to filter the incomplete information. We consider a jump diffusion Markov modulated market model and derive the Growth Optimal Portfolio (GOP), by using the stochastic control method. Using GOP, we price and hedge European options where the existence of the equivalent martingale measure is not necessary.

]]> 10.1504/IJMOR.2012.044471 International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 31 - 40 I. Venkat Appal Raju; N. Selvaraju Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781 039, India. ' Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781 039, India ?nancial markets jump diffusions contingent claims pricing hedging GOP growth optimal portfolio stochastic control incomplete information Markov modulated markets. 2011-12-26T23:20:50-05:00 4 1 31 40 2011-12-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=44472 Excessive systems' usage leads to failure and hence necessitates repair or replacement. Many types of repair actions could be implemented after failure. In this work, the performance of a system that is upon failure could undergo one of several repairs; imperfect repair, minimal repair, or replacement (perfect repair), is examined. An analytical expression for the availability of the general system and three special cases are derived along with the long run probabilities of the different states of the system. An example is presented to illustrate and compare the performance of the three cases. Availability of a system with different repair options
Mohammed A. Hajeeh
International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 41 - 55
Excessive systems' usage leads to failure and hence necessitates repair or replacement. Many types of repair actions could be implemented after failure. In this work, the performance of a system that is upon failure could undergo one of several repairs; imperfect repair, minimal repair, or replacement (perfect repair), is examined. An analytical expression for the availability of the general system and three special cases are derived along with the long run probabilities of the different states of the system. An example is presented to illustrate and compare the performance of the three cases.

]]> 10.1504/IJMOR.2012.044472 International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 41 - 55 Mohammed A. Hajeeh Techno-Economics Division, Kuwait Institute for Scientific Research, P.O. Box 24885, Safat-13109, Kuwait imperfect repair minimal repair replacement system failure analytical expression repair options system availability. 2011-12-26T23:20:50-05:00 4 1 41 55 2011-12-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=44473 This paper analyses a discrete-time Geo<SUP align="right">X</SUP>/Geo/1 queue with unreliable server and working vacation. During the vacation period, the server renders service to the primary job at lower rate rather than completely stopping service; this type of vacation is considered as working vacation. For modelling the queueing problem, the inter-arrival time, service time and repair time are treated as discrete random variables. The customers are assumed to arrive at the system in batches according to a geometric process during the consecutive slots. Using the probability generating function method, we obtain the steady-state distribution of the number of the customers in the system. Furthermore, Maximum Entropy Approach (MEA) is employed to obtain the approximate formulae for the probability distributions of the number of customers and the expected waiting time in the system in terms of several well-known results. Finally, the sensitivity analysis is also carried out to illustrate the effect of different parameters on several performance characteristics. Maximum Entropy Approach for discrete-time unreliable server GeoX/Geo/1 queue with working vacation
Madhu Jain; G.C. Sharma; Richa Sharma
International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 56 - 77
This paper analyses a discrete-time Geo<SUP align="right">X</SUP>/Geo/1 queue with unreliable server and working vacation. During the vacation period, the server renders service to the primary job at lower rate rather than completely stopping service; this type of vacation is considered as working vacation. For modelling the queueing problem, the inter-arrival time, service time and repair time are treated as discrete random variables. The customers are assumed to arrive at the system in batches according to a geometric process during the consecutive slots. Using the probability generating function method, we obtain the steady-state distribution of the number of the customers in the system. Furthermore, Maximum Entropy Approach (MEA) is employed to obtain the approximate formulae for the probability distributions of the number of customers and the expected waiting time in the system in terms of several well-known results. Finally, the sensitivity analysis is also carried out to illustrate the effect of different parameters on several performance characteristics.

]]> 10.1504/IJMOR.2012.044473 International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 56 - 77 Madhu Jain; G.C. Sharma; Richa Sharma Department of Mathematics, IIT, Roorkee 247667, India. ' Department of Mathematics, I.B.S., Khandari, Agra 282002, India. ' Department of Mathematics, St. Johns College, Agra 282002, India discrete-time queues unreliable servers working vacations geometric batch arrivals generating functions maximum entropy queue size waiting times modelling. 2011-12-26T23:20:50-05:00 4 1 56 77 2011-12-26T23:20:50-05:00 http://www.inderscience.com/link.php?id=44474 This investigation deals with single server state dependent queuing systems, wherein the arrivals of units are in batches and follow the Poisson process with state dependent arrival rates. After availing of the First Regular Vacation (FRV) in a case when there is no customer in the system, the server may also take a Second Optional Vacation (SOV). By using supplementary variable techniques, the probability generating function of the queue length distribution is established to study various performance measures. The maximum entropy approach is also used to find queue length distribution for evaluation of steady state probabilities in all different states. Numerical illustrations are provided to verify the tractability of performance measures obtained analytically. MX/G/1 queuing model with state dependent arrival and Second Optional Vacation
Charan Jeet Singh; Madhu Jain; Binay Kumar
International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 78 - 96
This investigation deals with single server state dependent queuing systems, wherein the arrivals of units are in batches and follow the Poisson process with state dependent arrival rates. After availing of the First Regular Vacation (FRV) in a case when there is no customer in the system, the server may also take a Second Optional Vacation (SOV). By using supplementary variable techniques, the probability generating function of the queue length distribution is established to study various performance measures. The maximum entropy approach is also used to find queue length distribution for evaluation of steady state probabilities in all different states. Numerical illustrations are provided to verify the tractability of performance measures obtained analytically.

]]> 10.1504/IJMOR.2012.044474 International Journal of Mathematics in Operational Research, Vol. 4, No. 1 (2012) pp. 78 - 96 Charan Jeet Singh; Madhu Jain; Binay Kumar Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India. ' Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India. ' Department of Mathematics, M.L.U. DAV College, Phagwara 144402, India M right" >X/G/1 bulk arrivals queue length state dependent rate optional vacations supplementary variables maximum entropy queuing models modelling. 2011-12-26T23:20:50-05:00 4 1 78 96 2011-12-26T23:20:50-05:00