### Personal Web

### Education

BS degree Econometrics Erasmus University Rotterdam, The Netherlands 1974

MSc degree Mathematics University of Utrecht,The Netherlands 1979

Ph.D degree, Erasmus Unıversity Rotterdam,The Netherlands , 1983

### Areas of Interest

### Publications

__Frenk, Hans__and

__Javadi Khatab, Sonya__and Pourakbar, Morteza and

__Sezer, Semih Onur__(2019) "An exact static solution approach for the service parts end-of-life inventory problem",

*European Journal of Operational Research*, Vol.272, No.2, 496-504 (SCI, SSCI)

__Frenk, Hans__and Pourghannad, Behrooz and

__Sezer, Semih Onur__(2017) "A static model in single leg flight airline revenue management",

*Transportation Science*, Vol.51, No.1, 214-232 (SCI)

__Birbil, Ş. İlker__and

__Bülbül, Kerem__and

__Frenk, Hans__and Mulder, H. M. (2015) "On EOQ cost models with arbitrary purchase and transportation costs",

*Journal of Industrial and Management Optimization*, Vol.11, No.4, 1211-1245 (SCI)

__Frenk, Hans__and Dekker, Rommert (2015) "The role of contract expirations in service parts management",

*Production and Operations Management*, Vol.24, No.10, 1580-1597 (SCI)

__Frenk, Hans__and

__Sezer, Semih Onur__(2015) "On the single-leg airline revenue management problem in continuous time",

*Mathematical Methods of Operations Research*, Vol.81, No.1, 27-52 (SCI)

__Birbil, Ş. İlker__and

__Frenk, Hans__and Gromicho, Joaquim A. S. and Zhang, Shuzhong (2014) "A network airline revenue management framework based on decomposition by origins and destinations",

*Transportation Science*, Vol.48, No.3, 313-333 (SCI)

__Aydın, Nursen__and

__Birbil, Ş. İlker__and

__Frenk, Hans__and

__Noyan, Nilay__(2013) "Single-leg airline revenue management with overbooking",

*Transportation Science*, Vol.47, No.4, 560-583 (SCI)

__Frenk, Hans__and Gabor, Adriana (2013) "Increasing the revenue of self-storage warehouses by facility design",

*Production and Operations Management*, Vol.22, No.3, 555-570 (SCI)

__Birbil, Ş. İlker__and

__Frenk, Hans__and

__Noyan, Nilay__(2012) "Tractable open loop policies for joint overbooking and capacity control over a single flight leg with multiple fare classes",

*Transportation Science*, Vol.46, No.4, 460-481 (SCI)

__Frenk, J. B. G.__and Dekker, R. (2012) "End-of-life inventory decisions for consumer electronics service parts",

*Production and Operations Management*, Vol.21, No.5, 889-906 (SCI)

__Frenk, Hans J.B.G.__(2011) "Renewal theory for random variables with a heavy tailed distribution and finite variance",

*Statistics and Probability Letters*, Vol.81, No.1, 77-82 (SCI)

__Frenk, Hans__and

__Kaya, Murat__and

__Pourghannad, Behrooz__, "Generalizing the ordering cost and holding-backlog cost rate functions in EOQ-type inventory models",

__Handbook of EOQ Inventory Problems: Stochastic and Deterministic Models and Applications__, Choi, Jason (ed.), New York, NY: Springer 2014, 79-119

__Birbil, Ş. İlker__and

__Frenk, Hans__and Gromicho, Joaquim A. S. and Zhang, Shuzhong, "A network airline reveneu management framework based on decomposition by origins and destinations", December 2011, Sabancı University ID:SU_FENS_2011/0013

On Renewal Theory and Regenerative Processes.

1. The behaviour of the renewal sequence in case the tail of the waiting time distribution is regularly varying with index -1, Advances of Applied Probability 14, 870-884, 1982

2.On Banach Algebras, Renewal Measures and Regenerative Processes, CWI tract 38, Center of Mathematics and Computer Science, Amsterdam, 1987 (ISBN 90 6196 321 4)

3. Some monotonicity properties of the delayed renewal function ( with B.Hansen), Journal of Applied Probability 28, 811-821, 1991

Convex analysis. Duality theory and Nonlinear Programming

4. A deep cut ellipsoid algorithm for convex programming; theory and applications, (with J.Gromicho and S.Zhang), Mathematical Programming 63,83-108,1994.

5. Generalized fractional programming and cutting plane algorithms (with A.I.Barros), Journal of Optimization Theory and Applications 87 (1), 103-120, 1995.

6. A new algorithm for generalized fractional programs (with A.I.Barros, S.Schaible and S.Zhang), Mathematical Programming 72, 147-175, 1996.

7.Using duality to solve generalized fractional programming problems (with A.I.Barros,S.Schaible and S.Zhang), Journal of Global Optimization 8, 139-170, 1996.

8. An interior point based subgradient method for nondifferentiable convex programming (with J.F.Sturm and S. Zhang), Optimization methods and Software 10, 197-215, 1998.

9. A duality theory for a class of generalized fractional programs (with J.R.Jefferson and S.C.Scott), Journal of Global Optimization 12, 239-245, 1998.

10. Dominating sets for convex functions with some applications (with E.Carrizosa), Journal of Optimization Theory and Applications 96 (2), 281-295, 1998.

11. On classes of generalized convex functions,Gordan-Farkas type theorems and Lagrangian duality (with G.Kassay), Journal of Optimization Theory and Applications 102(2), 315-343, 1999.

12. Minimax results and finite dimensional separation (with G.Kassay), Journal of Optimization Theory and Applications 113 (2), 409-421, 2002.

13. On equivalent results in minimax theory (with G.Kassay, J.Kolumban), European Journal of Operational Research 157(1), 46-58, 2004.

14. Recursive approximation of the high dimensional max function (with Ş.I. Birbil, S.Fang and S.Zhang), Operations Research Letters 33, 450-458, 2005.

15. On Borel probability Measures and noncooperative game theory (with G.Kassay and V.Protassov), Optimization 54 (1), 81-101, 2005.

16. The level set method of Joo and its use in minimax theory (with G.Kassay), Mathematical Programming 105 (1), 145-155, 2006.

17. Equilibrium constrained optimization problems (with G.Bouza, G.J.Still and Ş.I.Birbil), European Journal of Operational Research 169, 110-1127, 2006.

18. A note on the paper Fractional programming with convex quadratic forms and functions by H.P.Benson, European Journal of Operational Research 176, 641-642, 2007.

19. An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming (with Ş.I.Birbil and G.J.Still), European Journal of Operational Research 180, 479-484, 2007.

20. On linear programming duality and necessary and sufficient conditions in minimax theory (with P.Kas and G.Kassay), Journal of Optimization Theory and Applications 132, 423-439, 2007.

21. Lagrangean duality and cone convexlike functions (with G.Kassay),Journal of Optimization Theory and Applications 134, 207-222, 2007.

Applications to Engineering, Operations Research and Economics.

Combinatorial Optimization and Probability Theory.

22. Randomly degenerated polytopes for testing mathematical programming algorithms (with J.W. van Dam and J.Telgen), Mathematical Programming 26, 172-181, 1983.

23. The asymptotic behavior of a distributive sorting model (with J.W. van Dam and A.H.G. Rinnooy Kan), Computing 31, 287-303, 1983.

24. Asymptotic properties of the quadratic assignment problem (with M. van Houweninge and A.H.G.Rinnooy Kan ), Mathematics of Operations Research 10, 100-116, 1985.

25. Order statistics and the linear assignment problem (with M. van Houweninge and A.H.G.Rinnooy Kan), Computing 39, 165-174, 1987.

26. A probabilistic analysis of the next fit decreasing bin packing heuristic (with J.Csirik, A.Frieze, G.Galambos and A.H.G.Rinnooy Kan), Operations Research Letters 5, 233-236,1986.

27. Probabilistic analysis of algorithms for dual bin packing problems (with J.Csirik, G.Galambos and A.H.G.Rinnooy Kan), Journal of Algorithms 12,189-203,1991.

Insurance Mathematics

28. Optimal claim behaviour for third party liability insurances or to claim or not to claim: that is the question (with N.P.Dellaert, A.van Kouwenhoven and B.S.van der Laan), Insurance: Mathematics and Economics 9, 59-76, 1990.

29. İnsurers profits in the third party liability insurance (with N.P. Dellaert and B.S.van der Laan), Insurance: Mathematics and Economics 10, 165-172, 1991.

30. Optimal claim behaviour for third-party liability insurances with perfect information (with N.P.Dellaert and E.Voshol), Insurance: Mathematics and Economics 10, 145-151, 1991.

31. Optimal claim behaviour for insurances for vehicle damage insurances (with N.P.Dellaert and L.P.Rijsoort), Insurance: Mathematics and Economics 12, 225-244, 1993.

I

Inventory Control.

32. An efficient optimal solution method for the joint replenishment problem (with R.Dekker and R.E.Wildeman), European Journal of Operational Research 99, 433-444, 1997.

33. On Regenerative Processes and Inventory Control (with M.J.Kleijn), Pure and Applied Mathematics 9(1-2), 61-94, 1998.

34. An efficient algorithm for a generalized joint replenishment problem (with R.Dekker and M.J.Kleijn), European Journal of Operational Research 118, 413-428,1999.

35. On the newsboy model with a cutoff transaction size (with R.Dekker, T. de Kok and M.Kleijn), IIE transactions 32, 461-469, 2000.

36. Modeling of inventory control with regenerative processes (with E.M. Bazsa and P.W. den Iseger), International Journal of Production Economics 71, 263-276, 2001.

37. The joint replenishment problem with variable production costs (with Z.P. Bayindir and Ş.I. Birbil), European Journal of Operational Research 175, 622-640, 2006.

38. A deterministic inventory/production model with a general inventory cost rate function and piecewise linear concave production costs (with Z.P. Bayindir and Ş.I. Birbil), European Journal of Operational Research 179, 114-123, 2007.

Location Theory

39. A note on a stochastic location problem (with M.Labbe and S.Zhang), Operations Research Letters 13, 213-214,1993.

40. The Weiszfeld method in single facility location (with M.T.Melo and S.Zhang), Investigacao Operacional 14, 35-59,1994.

41. A Weiszfeld method for a generalized Lp-distance minisum location model in continuous space (with M.T.Melo and S.Zhang), Location Science 2,111-127,1994.

42. On Miehle's algorithm and the perturbed $L_{p}$-distance multifacility location problem (with M.J.Kleijn), Studies in Locational Analysis 7, 61-75,1994.

43. General models in min-max continuous location:theory and solution techniques (with J.Gromicho and S.Zhang), Journal of Optimization Theory and Applications 89 (1), 39-63, 1996.

44. General models in min-max planar location: checking optimality conditions (with J.Gromicho and S.Zhang), Journal of Optimization Theory and Applications 89 (1), 65-87,1996.

45. Fractional location problems (with A.I.Barros and J.Gromicho), Location Science 5 (1), 47-58,1997.

Machine Scheduling and Probability Theory.

46. A hierarchical scheduling problem with a well-solvable second stage (with A.H.G.Rinnooy Kan and L.Stougie), Annals of Operations Research 1, 43-58,1984.

47. The rate of convergence to optimality of the LPT rule (with A.H.G.Rinnooy Kan), Discrete Applied Mathematics 14, 187-197, 1986.

48. The asymptotic optimality of the LPT rule (with A.H.G.Rinnooy Kan), Mathematics of Operations Research 12, 241-254, 1987.

49. Single machine scheduling subject to stochastic breakdowns (with J.Birge, J.Mittenthal and A.H.G.Rinnooy Kan), Naval Research Logistics 37, 661-677, 1990.

50. A note on one-machine scheduling problems with imperfect information, Probability in the Engineering and Informational Sciences 5, 317-331, 1991.

51. A general framework for stochastic one-machine scheduling problems with zero release times and no partial ordering, Probability in the Engineering and Informational Sciences 5, 297-315, 1991

Maintenance.

52. Optimizing a general optimal replacement model by fractional programming techniques (with A.I.Barros, R.Dekker and S. van Weeren), Journal of Global Optimization 10, 405-423, 1997.

53. A unified treatment of single component replacement models (with R. Dekker and M.J.Kleijn), Mathematical Methods of Operations Research 45, 437-454,1997.

54. On the marginal cost approach in maintenance (with R. Dekker and M.J.Kleijn), Journal of Optimization Theory and Applications 94 (3), 771-781, 1997.

55. Modelling and optimizing imperfect maintenance of coatings on steel structures (with R. Nicolai and R. Dekker), Structural Safety 31, 234-$244, 2009.

Revenue Management.

56. Labour costs and queueing theory in retailing (with A.R.Thurik and C.A. Bout), European Journal of Operational Research 55, 260-267, 1991.

57. The role of robust optimization in single leg airline revenue management (with Ş.I. Birbil, J.Gromicho and S.Zhang), Management Science 55 (1), 148-163$, 2009

Worst case analysis of Algorithms.

58. A hybrid next-fit algorithm for the two-dimensional rectangle bin packing problem (with G.Galambos), Computing 39, 201-217, 1987.

59. A dual version of the binpacking problem (with J.Csirik), Algorithms Review 1, 87-95,1990.

60. On the multidimensional vector binpacking (with J.Csirik, M.Labbe and S.Zhang), Acta Cybernetica 9, 361-369,1990.

61. Heuristics for the 0-1 min-knapsack problem (with J.Csirik, M.Labbe and S.Zhang), Acta Cybernetica 10, 15-20,1991.

62. A simple proof of Liang's lower bound for on-line bin packing and the extension to the parametric case (with G.Galambos), Discrete Applied Mathematics 41, 173-178,1993.

63. Two-dimensional rectangle packing:on-line methods and results (with J.Csirik and M.Labbe), Discrete Applied Mathematics 45, 197-204,1993.

64. Improved Algorithms for machine allocation in manufacturing systems (with M.Labbe, M. van Vliet and S.Zhang), Operations Research 4, 523-530,1994

65. Two simple algorithms for bincovering (with J.Csirik, S.Zhang and M.Labbe) Acta Cybernetica 14, 13-25, 1999.

Publications in Proceedings .

66. On noncooperative games and minimax theory (with G.Kassay), Proceedings of the $4$th Twente workshop on Cooperative Game theory joint with 3rd Dutch-Russian symposium, CTIT Workshop Proceedings, 61-69, $2005.

Publications in Books.

67. The theory for convex/quasiconvex functions and its application to optimization (with D.M.L.Dias and J.Gromicho), Lecture Notes in Economics and Mathematical Systems, Vol. 405, ed. S.Komlosi, T.Rapcak and S.Schaible, 153-170, Springer Verlag, Berlin, 1994.

68. A deep cut ellipsoid algorithm and quasiconvex programming (with J. Gromicho, F.Plastria and S.Zhang), Lecture Notes in Economics and Mathematical Systems, Volume 405, ed. S.Komlosi, T.Rapcak and S. Schaible, 62-76, Springer Verlag, Berlin, 1994.

69. An elementary rate of convergence proof for the deep cut ellipsoid algorithm (with J. Gromicho), In recent Advances in Nonsmooth Optimization, eds. D-Z.Du, L.Qi and R.S Womersley, World Scientific Publishers, 106-120, 1995.

70. How to determine maintenance frequencies for multi-component systems? A general Approach. (with R.Dekker and R.E.Wildeman), in Reliability and maintenance of complex Systems (NATO ASI series), editor: S. Özekici, 239-280, Springer Verlag, Berlin, 1996.

71. High Performance Optimization, editor (with S.Zhang, K.Roos, T. Terlaky), series Applied Optimization vol 33, Kluwer Academic publishers, Dordrecht, 2000.

72. A general approach for the coordination of maintenance frequencies (with R. Dekker, R.E. Wildeman and R. van Egmond), in Maintenance, modelling and optimization, editors: S.O. Duffuaa and A. Raouf, 245-282, Kluwer Academic Publishers, Boston, 2000.

73. Fractional Programming (with S.Schaible), in Encyclopedia of Optimization vol II, editors: C.A. Floudas and P.M. Pardalos, 162-172, Kluwer Academic Publishers, Dordrecht, 2001, ISBN $0-7923-7027-9.

74. Introduction to convex and quasiconvex analysis (with G.Kassay), Chapter 1 in Handbook of Generalized Convexity and Generalized Monotonicity, editors N. Hadjisavvas, S. Komlosi and S. Schaible, 3-87, series Nonconvex Optimization and Its Applications vol 76, Springer Verlag, 2004, ISBN 0-387-23255-9.

75. On noncooperative games and minimax theory (with G.Kassay), Proceedings of the $4$th Twente workshop on Cooperative Game theory joint with 3$rd Dutch-Russian symposium, CTIT Workshop Proceedings, 61-69, 2005.

76. Modeling imperfect maintenance of coating systems protecting steel structures (with R.P.Nicolai), In Safety and Reliability for managing risk, editors Guedes Soares\& Zio, 563-570, Taylor \& Francis Group, 2006.

77. On noncooperative games, minimax theorems and equilibrium problems (with G.Kassay (Cluj)) In Pareto Optimality, Game Theory and Equilibria, editors Athanasios Migdalas (Crete), Panos Pardalos (Florida), Leonidas Pitsoulis (London) and Altannar Chinchuluun (Florida), 211-255, Series: Springer Optimization and Its Applications vol 17, Springer Verlag, New York, 2008, ISBN: 978-0-387-77246-2

78. Risk measures and Their Application in Asset Management, (with Ş.I. Birbil, N. Noyan and B. Kaynar), Chapter 15 of The VAR IMPLEMENTATION\ HANDBOOK (editor G.N.Gregoriou, McGraw Hill, 2009. ISBN 978-0-07-161513-6