Comparing Markov Chains: Aggregation and Precedence Relations Applied to Sets of States, with Applications to Assemble-to-Order Systems

Published Online:https://doi.org/10.1287/moor.1110.0533

References

  • Adan I. J. B. F., van Houtum G. J., van der Wal J. Upper and lower bounds for the waiting time in the symmetric shortest queue system. Ann. Oper. Res. (1994) 48(2):197–217CrossrefGoogle Scholar
  • Baccelli F., Brémaud P.Elements of Queuing Theory (2003) (Springer-Verlag, Berlin/Heidelberg) CrossrefGoogle Scholar
  • Ben Mamoun M., Bušić A., Fourneau J.-M., Pekergin N., Langville A. N., Stewart W. J. Increasing convex monotone Markov chains: Theory, algorithm and applications. MAM 2006: Markov Anniversary Meeting (2006) (Boson Books, Raleigh, NC) 189–210Google Scholar
  • Bijvank M. Service inventory management: Solution techniques for inventory systems without backorders. (2009) . Ph.D. thesis, Vrije Universiteit, AmsterdamGoogle Scholar
  • Carrasco J. A. Bounding steady-state availability models with group repair and phase type repair distributions. Performance Evaluation (1999) 35(3–4):193–204CrossrefGoogle Scholar
  • Courtois P.-J., Semal P. Bounds for the positive eigenvectors of nonnegative matrices and for their approximations by decomposition. J. ACM (1984) 31(4):804–825CrossrefGoogle Scholar
  • Courtois P.-J., Semal P. On polyhedra of Perron-Frobenius eigenvectors. Linear Algebra Appl. (1985) 65:157–170CrossrefGoogle Scholar
  • Dayanik S., Song J.-S., Xu S. H. The effectiveness of several performance bounds for capacitated production, partial-order-service, assemble-to-order systems. Manufacturing Service Oper. Management (2003) 5(3):230–251LinkGoogle Scholar
  • Doğru M. K., Reiman M. I., Wang Q. A stochastic programming-based inventory policy for assemble-to-order systems with application to the W model. Oper. Res. (2010) 58(4, Part 1):849–864LinkGoogle Scholar
  • Fourneau J.-M., Lecoz M., Quessette F. Algorithms for an irreducible and lumpable strong stochastic bound. Linear Algebra Appl. (2004) 386:167–185CrossrefGoogle Scholar
  • Fourneau J.-M., Pekergin N., Calzarossa M., Tucci S. An algorithmic approach to stochastic bounds. Performance Evaluation of Complex Systems: Techniques and Tools (2002) 2459(Springer, Berlin/Heidelberg) 303–314Lecture Notes in Computer ScienceCrossrefGoogle Scholar
  • Hoen K. M. R., Güllü R., van Houtum G. J., Vliegen I. M. H. A simple and accurate approximation for the order fill rates in lost-sales assemble-to-order systems. Internat. J. Production Econom. (2011) 133(1):95–104CrossrefGoogle Scholar
  • Iravani S. M. R., Luangkesorn K. L., Simchi-Levi D. On assemble-to-order systems with flexible customers. IIE Trans. (2003) 35(5):389–403CrossrefGoogle Scholar
  • Kapuscinski R., Zhang R. Q., Carbonneau P., Moore R., Reeves B. Inventory decisions in Dell's supply chain. Interfaces (2004) 34(3):191–205LinkGoogle Scholar
  • Kelly F. P. Loss networks. Ann. Appl. Probab. (1991) 1(3):319–378CrossrefGoogle Scholar
  • Kemeny J. G., Snell J. L.Finite Markov Chains (1976) (Springer-Verlag, New York) Google Scholar
  • Kök A. G., Fisher M. L., Vaidyanathan R., Agrawal N., Smith S. A. Assortment planning: Review of literature and industry practice. Retail Supply Chain Management, International Series in Operations Research and Management Science (2009) (Springer, New York) 99–154Google Scholar
  • Koole G. Structural results for the control of queueing systems using event-based dynamic programming. Queueing Systems (1998) 30(3-4):323–339CrossrefGoogle Scholar
  • Koole G. Monotonicity in Markov reward and decision chains: theory and applications. Foundations Trends Stochastic Systems (2006) 1(1):1–82CrossrefGoogle Scholar
  • Leemans H. Provable bounds for the mean queue lengths in a heterogeneous priority queue. Queueing Systems (2000) 36(1–3):269–286CrossrefGoogle Scholar
  • Li H., Xu S. H. On the dependence structure and bounds of correlated parallel queues and their applications to synchronized stochastic systems. J. Appl. Probab. (2000) 37(4):1020–1043CrossrefGoogle Scholar
  • Lindvall T.Lectures on the Coupling Method (1992) (Wiley, New York) Google Scholar
  • Louth G., Mitzenmacher M., Kelly F. Computational complexity of loss networks. Theoret. Comput. Sci. (1994) 125(1):45–59CrossrefGoogle Scholar
  • Lu Y. Performance analysis for assemble-to-order systems with general renewal arrivals and random batch demands. Eur. J. Oper. Res. (2008) 185(2):635–647CrossrefGoogle Scholar
  • Lu Y., Song J.-S., Yao D. D. Order fill rate, leadtime variability, and advance demand information in an assemble-to-order system. Oper. Res. (2003) 51(2):292–308LinkGoogle Scholar
  • Lu Y., Song J.-S., Yao D. D. Backorder minimization in multiproduct assemble-to-order systems. IIE Trans. (2005) 37(8):763–774CrossrefGoogle Scholar
  • Lu Y., Song J.-S., Zhao Y. No-holdback allocation rules for continuous-time assemble-to-order systems. Oper. Res. (2010) 58(3):691–705LinkGoogle Scholar
  • Lui J. C. S., Muntz R. R. Computing bounds on steady state availability of repairable computer systems. J. ACM (1994) 41(4):676–707CrossrefGoogle Scholar
  • Mahevas S., Rubino G. Bound computation of dependability and performance measures. IEEE Trans. Comput. (2001) 50(5):399–413CrossrefGoogle Scholar
  • Müller A., Stoyan D.Comparison Methods for Stochastic Models and Risks (2002) (Wiley, New York) Google Scholar
  • Muntz R. R., de Souza e Silva E., Goyal A. Bounding availability of repairable computer systems. IEEE Trans. Comput. (1989) 38(12):1714–1723CrossrefGoogle Scholar
  • Neuts M. F.Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (1981) (Johns Hopkins University Press, Baltimore) Google Scholar
  • Ross K. W.Multiservice Loss Models for Broadband Telecommunication Networks (1995) (Springer-Verlag, Berlin) CrossrefGoogle Scholar
  • Semal P. Refinable bounds for large Markov chains. IEEE Trans. Comput. (1995) 44(10):1216–1222CrossrefGoogle Scholar
  • Shaked M., Shanthikumar J. G.Stochastic Orders and Their Applications (1994) (Academic Press, San Diego) Google Scholar
  • Song J.-S. On the order fill rate in a multi-item, base-stock inventory system. Oper. Res. (1998) 46(6):831–845LinkGoogle Scholar
  • Song J.-S. Order-based backorders and their implications in multi-item inventory systems. Management Sci. (2002) 48(4):499–516LinkGoogle Scholar
  • Song J.-S., Yao D. D. Performance analysis and optimisation of assemle-to-order systems with random lead times. Oper. Res. (2002) 50(5):889–903LinkGoogle Scholar
  • Song J.-S., Zipkin P., de Kok A. G., Graves S. C. Supply chain operations: Assemble-to-order systems. Supply Chain Management: Design, Coordination and Operation, Handbooks in Operations Research and Management Science (2003) 11(North-Holland, Amsterdam) 561–596CrossrefGoogle Scholar
  • Song J.-S., Xu S. H., Liu B. Order-fulfillment performance measures in an assemble-to-order system with stochastic leadtimes. Oper. Res. (1999) 47(1):131–149LinkGoogle Scholar
  • Tandra R., Hemachandra N., Manjunath D. Join minimum cost queue for multiclass customers: Stability and performance bounds. Probab. Engrg. Informational Sci. (2004) 18(4):445–472Google Scholar
  • Thorisson H. Coupling, stationarity and regeneration. Probability and Its Applications (2000) (Springer-Verlag, New York) Google Scholar
  • van Dijk N. M. Bounds and error bounds for queueuing networks. Ann. Oper. Res. (1998) 79:295–319CrossrefGoogle Scholar
  • van Dijk N. M., van der Wal J. Simple bounds and monotonicity results for finite multi-server exponential tandem queues. Queueing Systems (1989) 4(1):1–16CrossrefGoogle Scholar
  • van Houtum G. J., Adan I. J. B. F., Wessels J., Zijm W. H. M. Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism. OR Spectrum (2001) 23(3):411–427CrossrefGoogle Scholar
  • van Houtum G. J., Zijm W. H. M., Adan I. J. B. F., Wessels J. Bounds for performance characteristics: A systematic approach via cost structures. Comm. Statist.—Stochastic Models (1998) 14(1 and 2):205–224CrossrefGoogle Scholar
  • Vliegen I. M. H., van Houtum G. J. Approximate evaluation of order fill rates for an inventory system of service tools. Internat. J. Production Econom. (2009) 118(1):339–351CrossrefGoogle Scholar
  • Xu P. J., Allgor R., Graves S. C. The benefits of reevaluating real-time order fulfillment decisions. Manufacturing Service Oper. Management (2009) 11(2):340–355LinkGoogle Scholar
  • Xu S. H. Structural analysis of a queueing system with multiclasses of correlated arrivals and blocking. Oper. Res. (1999) 47(2):264–276LinkGoogle Scholar
  • Xu S. H., Song J.-S., Yao D. D. Dependence analysis of assemble-to-order systems. Supply Chain Structures: Coordination, Information and Optimization (2002) (Kluwer Academic, Boston) 359–414CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.