Conveyor Merges in Zone Picking Systems: A Tractable and Accurate Approximate Model

References

• Baskett F, Chandy KM, Muntz RR, Palacios FG (1975) Open, closed, and mixed networks of queues with different classes of customers. J. ACM 22(2):248–260.Crossref, Google Scholar
• Bastani AS (1988) Analytical solution of closed-loop conveyor systems with discrete and deterministic material flow. Eur. J. Oper. Res. 35(2):187–192.Crossref, Google Scholar
• Bastani AS, Elsayed EA (1986) Blocking in closed-loop conveyor systems connected in series with discrete and deterministic material flow. Comput. Indust. Engrg. 11(1):40–45.Crossref, Google Scholar
• Bolch G, Greiner S, de Meer H, Trivedi KS (2006) Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications, 2nd ed. (Wiley-Interscience, Hoboken, NJ).Crossref, Google Scholar
• Boucherie RJ, van Dijk NM (1993) A generalization of Norton’s theorem for queueing networks. Queueing Systems 13(1–3):251–289.Crossref, Google Scholar
• Bozer YA, Hsieh YJ (2005) Throughput performance analysis and machine layout for discrete-space closed-loop conveyors. IIE Trans. 37(1):77–89.Crossref, Google Scholar
• Bright L, Taylor PG (1995) Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes. Stochastic Models 11(3):497–525.Crossref, Google Scholar
• Bryant RM, Krzesinski AE, Lakshmi MS, Chandy KM (1984) The MVA priority approximation. ACM Trans. Comput. Systems 2(4): 335–359.Crossref, Google Scholar
• Buzen JP (1973) Computational algorithms for closed queueing networks with exponential servers. Comm. ACM 16(9):527–531.Crossref, Google Scholar
• Chandy KM, Herzog U, Woo L (1975) Parametric analysis of queuing networks. IBM J. Res. Development 19(1):36–42.Crossref, Google Scholar
• Chao X, Miyazawa M, Pinedo M (1999) Queueing Networks: Customers, Signals and Product Form Solutions (Wiley, Chichester, UK).Google Scholar
• Coffman EG Jr, Gelenbe E, Gilbert EN (1988) Analysis of a conveyor queue in a flexible manufacturing system. Eur. J. Oper. Res. 35(3):382–392.Crossref, Google Scholar
• Dallery Y, Gershwin SB (1992) Manufacturing flow line systems: A review of models and analytical results. Queueing Systems 12(1): 3–94.Crossref, Google Scholar
• De Koster MBM (1994) Performance approximation of pick-to-belt orderpicking systems. Eur. J. Oper. Res. 72(3):558–573.Crossref, Google Scholar
• De Koster MBM, Le-Duc T, Roodbergen KJ (2007) Design and control of warehouse order picking: A literature review. Eur. J. Oper. Res. 182(2):481–501.Crossref, Google Scholar
• Disney RL (1962) Some multichannel queueing problems with ordered entry. J. Indust. Engrg. 13(1):46–48.Google Scholar
• Economou A, Fakinos D (1998) Product form stationary distributions for queueing networks with blocking and rerouting. Queueing Systems 30(3):251–260.Crossref, Google Scholar
• Eisenstein DD (2008)Analysis and optimal design of discrete order picking technologies along a line. Naval Res. Logist. 55(4):350–362.Crossref, Google Scholar
• Gordon WJ, Newell GF (1967) Closed queuing systems with exponential servers. Oper. Res. 15(2):254–265.Link, Google Scholar
• Gu J, Goetschalckx M, McGinnis LF (2010) Research on warehouse design and performance evaluation: A comprehensive review. Eur. J. Oper. Res. 203(3):539–549.Crossref, Google Scholar
• Hsiao MT, Lazar AA (1989) An extension to Norton’s equivalent. Queueing Systems 5(4):401–411.Crossref, Google Scholar
• Hsieh YJ, Bozer YA (2005) Analytical modeling of closed-loop conveyors with load recirculation. Gervasi O, Gavrilova ML, Kumar V, Lagana A, Lee HP, Mun Y, Taniar D, Tan CJK, eds. Computational Science and Its Applications—ICCSA 2005, Lecture Notes Comput. Sci., Vol. 3483 (Springer, Berlin Heidelberg), 437–447.Crossref, Google Scholar
• Jackson JR (1963) Jobshop-like queueing systems. Management Sci. 10(1):131–142.Link, Google Scholar
• Jane CC (2000) Storage location assignment in a distribution center. Internat. J. Phys. Distribution Logist. Management 30(1):55–71.Crossref, Google Scholar
• Jewkes E, Lee C, Vickson R (2004) Product location, allocation and server home base location for an order picking line with multiple servers. Comput. Oper. Res. 31(4):623–636.Crossref, Google Scholar
• Kritzinger PS, Van Wyk S, Krzesinski AE (1982) A generalisation of Norton’s theorem for multiclass queueing networks. Performance Evaluation 2(2):98–107.Crossref, Google Scholar
• Kwo TT (1958) A theory of conveyors. Management Sci. 5(1):51–71.Link, Google Scholar
• Latouche G, Ramaswami V (1999) Introduction to Matrix Analytic Methods in Stochastic Modeling, Vol. 5 (SIAM, Philadelphia).Crossref, Google Scholar
• Malmborg CJ (1996) Storage assignment policy tradeoffs. Internat. J. Production Res. 34(2):363–378.Crossref, Google Scholar
• Marie RA (1979) An approximate analytical method for general queueing networks. IEEE Trans. Software Engrg. 5(5):530–538.Crossref, Google Scholar
• Melacini M, Perotti S, Tumino A (2010) Development of a framework for pick-and-pass order picking system design. Internat. J. Adv. Manufacturing Tech. 53(9):841–854.Google Scholar
• Muth EJ (1977) A model of a closed-loop conveyor with random material flow. AIIE Trans. 9(4):345–351.Crossref, Google Scholar
• Neuse D, Chandy KM (1982) HAM: The heuristic aggregation method for solving general closed queueing network models of computer systems. ACM SIGMETRICS Performance Evaluation Rev. 11(4):195–212.Crossref, Google Scholar
• Osorio C, Bierlaire M (2009) An analytic finite capacity queueing network model capturing the propagation of congestion and blocking. Eur. J. Oper. Res. 196(3):996–1007.Crossref, Google Scholar
• Park BC (2012) Order picking: Issues, systems and models. Manzini R, ed. Warehousing in the Global Supply Chain: Advanced Models, Tools and Applications for Storage Systems, 1st ed. (Springer-Verlag, London), 1–30.Crossref, Google Scholar
• Petersen CG (2000) An evaluation of order picking policies for mail order companies. Production Oper. Management 9(4):319–335.Google Scholar
• Petersen CG (2002) Considerations in order picking zone configuration. Internat. J. Oper. Production Management 22(7):793–805.Crossref, Google Scholar
• Pittel B (1979) Closed exponential networks of queues with saturation: The Jackson-type stationary distribution and its asymptotic analysis. Math. Oper. Res. 4(4):357–378.Link, Google Scholar
• Reiser M, Lavenberg SS (1980) Mean-value analysis of closed multichain queuing networks. J. ACM 27(2):313–322.Crossref, Google Scholar
• Schassberger R (1984) Decomposable stochastic networks: Some observations. Baccelli F, Fayolle G, eds. Modelling and Performance Evaluation Methodology. Lecture Notes in Control and Information Sciences, Vol. 60 (Springer, Berlin), 135–150.Crossref, Google Scholar
• Schmidt LC, Jackman J (2000) Modeling recirculating conveyors with blocking. Eur. J. Oper. Res. 124(2):422–436.Crossref, Google Scholar
• Serfozo R (1999) Introduction to Stochastic Networks (Springer-Verlag, New York).Crossref, Google Scholar
• Sonderman D (1982) An analytical model for recirculating conveyors with stochastic inputs and outputs. Internat. J. Production Res. 20(5):591–605.Crossref, Google Scholar
• Van der Gaast JP, De Koster MBM, Adan IJBF, Resing JAC (2012) Modeling and performance analysis of sequential zone picking systems. Working paper, Erasmus University, Rotterdam, Netherlands. http://alexandria.tue.nl/repository/books/751517.pdf.Google Scholar
• Van Dijk NM (1988) On Jackson’s product form with “jump-over” blocking. Oper. Res. Lett. 7(5):233–235.Crossref, Google Scholar
• Van Dijk NM (1993) Queueing Networks and Product Forms: A Systems Approach, Vol. 4 (John Wiley & Sons, Chichester, UK).Google Scholar
• Walrand J (1983) A note on Norton’s theorem for queuing networks. J. Appl. Probab. 20(2):442–444.Crossref, Google Scholar
• Whitt W (1982) Approximating a point process by a renewal process, I: Two basic methods. Oper. Res. 30(1):125–147.Link, Google Scholar
• Yu M, De Koster MBM (2008) Performance approximation and design of pick-and-pass order picking systems. IIE Trans. 40(11):1054–1069.Crossref, Google Scholar
• Zijm WHM, Adan IJBF, Buitenhek R, Van Houtum GJ (2000) Capacity analysis of an automated kit transportation system. Ann. Oper. Res. 93(1–4):423–446.Crossref, Google Scholar