Comparing Markov Chains: Aggregation and Precedence Relations Applied to Sets of States, with Applications to Assemble-to-Order Systems
Published Online:20 Mar 2012https://doi.org/10.1287/moor.1110.0533
References
- Upper and lower bounds for the waiting time in the symmetric shortest queue system. Ann. Oper. Res. (1994) 48(2):197–217Crossref, Google Scholar
- Elements of Queuing Theory (2003) (Springer-Verlag, Berlin/Heidelberg) Crossref, Google Scholar
- , 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
- Service inventory management: Solution techniques for inventory systems without backorders. (2009) . Ph.D. thesis, Vrije Universiteit, AmsterdamGoogle Scholar
- Bounding steady-state availability models with group repair and phase type repair distributions. Performance Evaluation (1999) 35(3–4):193–204Crossref, Google Scholar
- Bounds for the positive eigenvectors of nonnegative matrices and for their approximations by decomposition. J. ACM (1984) 31(4):804–825Crossref, Google Scholar
- On polyhedra of Perron-Frobenius eigenvectors. Linear Algebra Appl. (1985) 65:157–170Crossref, Google Scholar
- The effectiveness of several performance bounds for capacitated production, partial-order-service, assemble-to-order systems. Manufacturing Service Oper. Management (2003) 5(3):230–251Link, Google Scholar
- A stochastic programming-based inventory policy for assemble-to-order systems with application to the W model. Oper. Res. (2010) 58(4, Part 1):849–864Link, Google Scholar
- Algorithms for an irreducible and lumpable strong stochastic bound. Linear Algebra Appl. (2004) 386:167–185Crossref, Google Scholar
- , 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 ScienceCrossref, Google Scholar
- A simple and accurate approximation for the order fill rates in lost-sales assemble-to-order systems. Internat. J. Production Econom. (2011) 133(1):95–104Crossref, Google Scholar
- On assemble-to-order systems with flexible customers. IIE Trans. (2003) 35(5):389–403Crossref, Google Scholar
- Inventory decisions in Dell's supply chain. Interfaces (2004) 34(3):191–205Link, Google Scholar
- Loss networks. Ann. Appl. Probab. (1991) 1(3):319–378Crossref, Google Scholar
- Finite Markov Chains (1976) (Springer-Verlag, New York) Google Scholar
- , 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
- Structural results for the control of queueing systems using event-based dynamic programming. Queueing Systems (1998) 30(3-4):323–339Crossref, Google Scholar
- Monotonicity in Markov reward and decision chains: theory and applications. Foundations Trends Stochastic Systems (2006) 1(1):1–82Crossref, Google Scholar
- Provable bounds for the mean queue lengths in a heterogeneous priority queue. Queueing Systems (2000) 36(1–3):269–286Crossref, Google Scholar
- On the dependence structure and bounds of correlated parallel queues and their applications to synchronized stochastic systems. J. Appl. Probab. (2000) 37(4):1020–1043Crossref, Google Scholar
- Lectures on the Coupling Method (1992) (Wiley, New York) Google Scholar
- Computational complexity of loss networks. Theoret. Comput. Sci. (1994) 125(1):45–59Crossref, Google Scholar
- Performance analysis for assemble-to-order systems with general renewal arrivals and random batch demands. Eur. J. Oper. Res. (2008) 185(2):635–647Crossref, Google Scholar
- Order fill rate, leadtime variability, and advance demand information in an assemble-to-order system. Oper. Res. (2003) 51(2):292–308Link, Google Scholar
- Backorder minimization in multiproduct assemble-to-order systems. IIE Trans. (2005) 37(8):763–774Crossref, Google Scholar
- No-holdback allocation rules for continuous-time assemble-to-order systems. Oper. Res. (2010) 58(3):691–705Link, Google Scholar
- Computing bounds on steady state availability of repairable computer systems. J. ACM (1994) 41(4):676–707Crossref, Google Scholar
- Bound computation of dependability and performance measures. IEEE Trans. Comput. (2001) 50(5):399–413Crossref, Google Scholar
- Comparison Methods for Stochastic Models and Risks (2002) (Wiley, New York) Google Scholar
- Bounding availability of repairable computer systems. IEEE Trans. Comput. (1989) 38(12):1714–1723Crossref, Google Scholar
- Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (1981) (Johns Hopkins University Press, Baltimore) Google Scholar
- Multiservice Loss Models for Broadband Telecommunication Networks (1995) (Springer-Verlag, Berlin) Crossref, Google Scholar
- Refinable bounds for large Markov chains. IEEE Trans. Comput. (1995) 44(10):1216–1222Crossref, Google Scholar
- Stochastic Orders and Their Applications (1994) (Academic Press, San Diego) Google Scholar
- On the order fill rate in a multi-item, base-stock inventory system. Oper. Res. (1998) 46(6):831–845Link, Google Scholar
- Order-based backorders and their implications in multi-item inventory systems. Management Sci. (2002) 48(4):499–516Link, Google Scholar
- Performance analysis and optimisation of assemle-to-order systems with random lead times. Oper. Res. (2002) 50(5):889–903Link, Google Scholar
- , 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) 561–596Crossref, Google Scholar
- Order-fulfillment performance measures in an assemble-to-order system with stochastic leadtimes. Oper. Res. (1999) 47(1):131–149Link, Google Scholar
- Join minimum cost queue for multiclass customers: Stability and performance bounds. Probab. Engrg. Informational Sci. (2004) 18(4):445–472Google Scholar
- Coupling, stationarity and regeneration. Probability and Its Applications (2000) (Springer-Verlag, New York) Google Scholar
- Bounds and error bounds for queueuing networks. Ann. Oper. Res. (1998) 79:295–319Crossref, Google Scholar
- Simple bounds and monotonicity results for finite multi-server exponential tandem queues. Queueing Systems (1989) 4(1):1–16Crossref, Google Scholar
- Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism. OR Spectrum (2001) 23(3):411–427Crossref, Google Scholar
- Bounds for performance characteristics: A systematic approach via cost structures. Comm. Statist.—Stochastic Models (1998) 14(1 and 2):205–224Crossref, Google Scholar
- Approximate evaluation of order fill rates for an inventory system of service tools. Internat. J. Production Econom. (2009) 118(1):339–351Crossref, Google Scholar
- The benefits of reevaluating real-time order fulfillment decisions. Manufacturing Service Oper. Management (2009) 11(2):340–355Link, Google Scholar
- Structural analysis of a queueing system with multiclasses of correlated arrivals and blocking. Oper. Res. (1999) 47(2):264–276Link, Google Scholar
- , Song J.-S., Yao D. D. Dependence analysis of assemble-to-order systems. Supply Chain Structures: Coordination, Information and Optimization (2002) (Kluwer Academic, Boston) 359–414Crossref, Google Scholar

