Central European Journal of Operations Research

, Volume 25, Issue 4, pp 831–858 | Cite as

Evaluating the quality of online optimization algorithms by discrete event simulation

Original Paper

Abstract

A key feature of dynamic problems which offer degrees of freedom to the decision maker is the necessity for a goal-oriented decision making routine which is employed every time the logic of the system requires a decision. In this paper, we look at optimization procedures which appear as subroutines in dynamic problems and show how discrete event simulation can be used to assess the quality of algorithms: after establishing a general link between online optimization and discrete event systems, we address performance measurement in dynamic settings and derive a corresponding tool kit. We then analyze several control strategies using the methodologies discussed previously in two real world examples of discrete event simulation models: a manual order picking system and a pickup and delivery service.

Keywords

Online optimization Algorithm analysis Discrete event simulation Order picking Pickup and delivery 

References

  1. Angelopoulos S, Dorrigiv R, López-Ortiz A (2007) On the separation and equivalence of paging strategies. In: Proceedings of the 18th annual ACM-SIAM symposium on discrete algorithms, pp 229–237Google Scholar
  2. Becchetti L, Leonardi S, Marchetti-Spaccamela A, Schäfer G, Vredeveld T (2006) Average-case and smoothed competitive analysis of the multilevel feedback algorithm. Math Oper Res 31(1):85–108CrossRefGoogle Scholar
  3. Ben-David S, Borodin A (1994) A new measure for the study of on-line algorithms. Algorithmica 11(1):73–91CrossRefGoogle Scholar
  4. Blom M, Krumke S, de Paepe W, Stougie L (2000) The online TSP against fair adversaries. In: Bongiovanni G, Petreschi R, Gambosi G (eds) Algorithms and complexit. Springer, Berlin, pp 137–149CrossRefGoogle Scholar
  5. Borodin A, El-Yaniv R (1998) Online computation and competitive analysis. Cambridge University Press, CambridgeGoogle Scholar
  6. Boyar J, Favrholdt L (2007) The relative worst order ratio for online algorithms. In: ACM transactions on algorithms, 3(2), article no. 22Google Scholar
  7. Boyar J, Favrholdt L, Larsen K, Nielsen M (2003) Extending the accommodating function. Acta Inform 40(1):3–35CrossRefGoogle Scholar
  8. Boyar J, Larsen K, Nielsen M (2002) The accommodating function: a generalization of the competitive ratio. SIAM J Comput 31(1):233–258CrossRefGoogle Scholar
  9. Cassandras C, Lafortune S (2008) Introduction to discrete event systems, 2nd edn. Springer, BerlinCrossRefGoogle Scholar
  10. Coffman E, So K, Hofri M, Yao A (1980) A stochastic model of bin-packing. Inf Control 44(2):105–115CrossRefGoogle Scholar
  11. Cordeau J, Laporte G (2003) A tabu search heuristic for the static multi-vehicle dial-a-ride problem. Transp Res B Methodol 37(6):579–594CrossRefGoogle Scholar
  12. Croes GA (1958) A method for solving traveling-salesman problems. Oper Res 6(6):791–812CrossRefGoogle Scholar
  13. Csirik J, Woeginger G (2002) Resource augmentation for online bounded space bin packing. J Algorithms 44(2):308–320CrossRefGoogle Scholar
  14. Dorrigiv R, Lopez-Ortiz A (2007) Adaptive analysis of on-line algorithms. In: Fekete S, Fleischer R, Klein R, Lopez-Ortiz A (eds) Robot navigation, number 06421 in Dagstuhl Seminar Proceedings, Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI). Schloss Dagstuhl, GermanyGoogle Scholar
  15. Dorrigiv R, López-Ortiz A (2008) Closing the gap between theory and practice: new measures for on-line algorithm analysis. In: Proceedings of the 2nd international conference on algorithms and computation, pp 13–24Google Scholar
  16. Dorrigiv R, López-Ortiz A, Munro J (2009) On the relative dominance of paging algorithms. Theor Comput Sci 410(38–40):3694–3701CrossRefGoogle Scholar
  17. Dunke F (2014) Online Optimization with Lookahead. Ph.D. thesis, Karlsruhe Institute of TechnologyGoogle Scholar
  18. Fiat A, Woeginger G (1998) Competitive odds and ends. In: Fiat A, Woeginger G (eds) Online algorithms: the state of the art. Springer, Berlin, pp 385–394CrossRefGoogle Scholar
  19. Franaszek P, Wagner T (1974) Some distribution-free aspects of paging algorithm performance. J ACM 21(1):31–39CrossRefGoogle Scholar
  20. Ghiani G, Laporte G, Musmanno R (2004) Introduction to logistics systems planning and control. Wiley, HobokenGoogle Scholar
  21. Grötschel M, Krumke S, Rambau J (eds) (2001) Online optimization of large scale systems, SpringerGoogle Scholar
  22. Grötschel M, Krumke S, Rambau J, Winter T, Zimmermann U (2001) Combinatorial online optimization in real time. In: Grötschel M, Krumke S, Rambau J (eds) Online optimization of large scale systems. Springer, Berlin, pp 679–704CrossRefGoogle Scholar
  23. Henn S, Koch S, Wäscher G (2012) Order batching in order picking warehouses: a survey of solution approaches. In: Manzini R (ed) Warehousing in the global supply chain. Springer, Berlin, pp 105–137CrossRefGoogle Scholar
  24. Hiller B (2009) Online optimization: probabilistic analysis and algorithm engineering. Ph.D. thesis, Technische Universität BerlinGoogle Scholar
  25. Huber C (2011) Throughput analysis of manual order picking systems with congestion consideration. Ph.D. thesis, Karlsruher Institut für TechnologieGoogle Scholar
  26. Jaynes E (1957) Information theory and statistical mechanics. Phys Rev 106(4):620–630CrossRefGoogle Scholar
  27. Jaynes E (1957) Information theory and statistical mechanics II. Phys Rev 108(2):171–190CrossRefGoogle Scholar
  28. Kallrath J (2005) Online storage systems and transportation problems with applications: optimization models and mathematical solutions. Springer, BerlinGoogle Scholar
  29. Kalyanasundaram B, Pruhs K (2000) Speed is as powerful as clairvoyance. J ACM 47(4):617–643CrossRefGoogle Scholar
  30. Karlin A, Manasse M, Rudolph L, Sleator D (1988) Competitive snoopy caching. Algorithmica 3(1–4):79–119CrossRefGoogle Scholar
  31. Karlin A, Phillips S, Raghavan P (2000) Markov paging. SIAM J Comput 30(3):906–922CrossRefGoogle Scholar
  32. Kenyon C (1996) Best-fit bin-packing with random order. In: Proceedings of the 7th annual ACM-SIAM symposium on discrete algorithms, pp 359–364Google Scholar
  33. Kirkpatrick S, Gelatt CD, Vecchi P (1983) Optimization by simulated annealing. Science 220(4598):671–680CrossRefGoogle Scholar
  34. Koutsoupias E, Papadimitriou C (2000) Beyond competitive analysis. SIAM J Comput 30(1):300–317CrossRefGoogle Scholar
  35. Krumke S, Laura L, Lipmann M, Marchetti-Spaccamela A, Paepe Wd, Poensgen D, Stougie L (2002) Non-abusiveness helps: An o(1)-competitive algorithm for minimizing the maximum flow time in the online traveling salesman problem. In: Proceedings of the 5th international workshop on approximation algorithms for combinatorial oimization, APPROX ’02, 200–214, SpringerGoogle Scholar
  36. Lawler E, Lenstra J, Rinnooy Kan A, Shmoys D (eds.) (1985) The traveling salesman problem: a guided tour of combinatorial optimization. WileyGoogle Scholar
  37. Miller C, Tucker A, Zemlin R (1960) Integer programming formulation of traveling salesman problems. J ACM 7(4):326–329CrossRefGoogle Scholar
  38. Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, HobokenGoogle Scholar
  39. März L, Krug W (2011) Kopplung von Simulation und Optimierung. In: Krug W, Rose O, Weigert G (eds) Simulation und Optimierung in Produktion und Logistik: Praxisorientierter Leitfaden mit Fallbeispielen. Springer, Berlin, pp 41–45CrossRefGoogle Scholar
  40. Psaraftis H (1995) Dynamic vehicle routing: status and prospects. Ann Oper Res 61(1):143–164CrossRefGoogle Scholar
  41. Raghavan P (1991) A statistical adversary for on-line algorithms. DIMACS Ser Discrete Math Theor Comput Sci 7:79–83CrossRefGoogle Scholar
  42. Scharbrodt M, Schickinger T, Steger A (2006) A new average case analysis for completion time scheduling. J ACM 53(1):121–146CrossRefGoogle Scholar
  43. Sleator D, Tarjan R (1985) Amortized efficiency of list update and paging rules. Commun ACM 28(2):202–208CrossRefGoogle Scholar
  44. Spielman D, Teng S (2004) Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time. J ACM 51(3):385–463CrossRefGoogle Scholar
  45. Stadtler H, Kilger C (eds.) (2008) Supply chain management and advanced planning: concepts, models, sftware, and case studies. Springer, 4th ednGoogle Scholar
  46. Toth PM, Vigo D (eds.) (2002) The vehicle routing problem. SIAMGoogle Scholar
  47. Verein Deutscher Ingenieure (VDI) (1996) VDI-Richtlinie 3633. Simulation von Logistik-, Materialfluß- und Produktionssystemen: Begriffsdefinitionen. In: VDI-Handbuch Materialfluß und Fördertechnik, BeuthGoogle Scholar
  48. Young N (1994) The k-server dual and loose competitiveness for paging. Algorithmica 11(6):525–541CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Operations Research, Discrete Optimization and LogisticsKarlsruhe Institute of TechnologyKarlsruheGermany

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