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Prof. Dr. Johannes Bartholomeus Gerardus FRENK
Endüstri Mühendisliği

Johannes Bartholomeus Gerardus FRENK
Telefon
(262) 6052063
E-Posta
frenk@gtu.edu.tr
Web sayfası
https://www.researchgate.net/profile/Hans-Frenk
Ofis
F Blok, 111
Çalışma alanları
Doğrusal, Doğrusal Olmayan ve Tam Sayılı Programlama, Stokastik Süreçler, Konveks Analiz, İşbirlikçi Olmayan Oyun Teorisi
1. The behaviour of the renewal sequence in case the tail of the waiting timedistribution is regularly varying with index −1, Advances of AppliedProbability 14, 870 − 884, 1982.

2. On renewal theory, Banach algebras and Functions of Bounded Increase,
Ph.D. Thesis, 1983.

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

4. Renewal theory for random variables with a heavy tailed distribution
and finite variance (with J.Geluk), Statistics and Probability Letters 81,
77 − 82, 2011.

Topic: Statistics

1. On the method of moments approach applied to a (generalized) Gamma
population (with Hadi Abbaszadehpeivasti), Communications in Statistics and Probabality: Theory and Methods 52 (11), 3685-3708, 2023,
https:// doi.org/10.1080/03610926.2021.

Topic: Multivariate probability theory.

1. On computing the multivariate Poisson probability distribution (with S
Javadi and B Cekyay) Methodology and Computing in Applied Probability. published online 20 June 2023 https://doi.org/10.1007/s11009-
023-10036

Topic: Convex Analysis, Duality Theory and Nonlinear Programming.

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

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

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

4. 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.

5. 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.

6. 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.

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

8. 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.

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

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

11. Recursive approximation of the high dimensional max function (with
S¸.˘I. Birbil, S.Fang and S.Zhang), Operations Research Letters 33, 450−
458, 2005.

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

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

14. Equilibrium constrained optimization problems (with G.Bouza, G.J.Still
and S¸.˘I.Birbil), European Journal of Operational Research 169, 1108 −
1127, 2006.

15. 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.

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

17. 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.

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

19. Quasiconvex functions: How to separate if you must! (with J.A Gromicho and S.Zhang), Stud.Univ.Babes Bolyai Math. 67 (1), 105 − 128,
2022.

Applications to Operations Research and Economics.

Topic: Combinatorial Optimization and Probability Theory.

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

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

3. 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.

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

5. 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.

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.

Topic: Insurance Mathematics.

1. 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.

2. Insurers 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.

3. 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.

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.

Topic: Inventory Control.

1. 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.

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

3. 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.;

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

5. 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.

6. The joint replenishment problem with variable production costs (with
Z.P. Bayindir and S¸.˘I. Birbil), European Journal of Operational Research
175, 622 − 640, 2006.

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

8. End-of-life inventory decisions for consumer electronics service parts
(with M. Pourakbar and R. Dekker), Production and Operations Management (POMS), Vol 21-No 5, 889 − 206, September-October 2012.

9. On EOQ cost models with arbitrary purchase and transportation costs
(with Ilker Birbil , K , Bulbul and H.M. Mulder), Journal of Industrial
and Management Optimization (J˙IMO) Vol 11, No-4, October 2015.

10. The Role of Contract Expirations in Service Parts Management (with
C.Pince and R.Dekker), Production and Operations Management, volume 24 (Issue 10): 1580-1597, 2015.

11. An exact static solution approach for the service life parts end-of-life inventory problem (with Morteza Pourakbar, Sonya Javadi Khatab, Semih
O., Sezer), European Journal of Operational Research 272, 496−504, 2019

12. An optimal stopping approach for the end-of-life inventory problem (with
Sonya Javadi Khatab and Semih O., Sezer), Mathematical Methods of
Operations Research 90, 329 − 363, 2019.

Topic: Location Theory.

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

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

3. 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.

4. On Miehle’s algorithm and the perturbed Lp-distance multifacility location problem (with M.J.Kleijn), Studies in Locational Analysis 7, 61 −75, 1994.

5. 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.

6. 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.

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

Topic: Machine Scheduling and Probability Theory.

1. 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.

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

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

4. 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.

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

6. 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.

Topic: Maintenance.

1. 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.

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

3. 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.

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

Topic: Economics

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

Topic: Revenue Management.

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

2. Tractable open loop policies with joint overbooking and capacity control
over a single flight leg with multiple fare classes (with S¸.˘I., Birbil, N.,
Noyan and H., Topaloglu), Transportation Science 46(4), 460 − 481,
November 2012.

3. Increasing the revenue of self storage warehouses by facility design (with
Y.Yong (Marseille), A. Gabor (EUR Rotterdam) and R. De Koster (EUR
Rotterdam), Production and Operations Management (POM) 22(3), 555−
570, (May-June) 2013.

4. Single-leg revenue management with overbooking (with N. Aydin, S¸.˘I.
Birbil, N. Noyan), Transportation Science 47(4), 560 − 583, November
2013.

5. A Network airline based revenue management framework based on decomposition by origins and destinations (with S¸.˘I. Birbil, G., Gromicho
and S., Zhang), Transportation Science 48(3), 313 − 333,August 2014,
ISSN 0041 − 1655 (print).

6. On the single-leg airline revenue management problem in continuous
time (with S.O., Sezer, A.M., Arslan) Mathematical Methods of Operations Research 81(1), 27 − 52,2015.

7. A static model in single-leg flight airline revenue management (with
S.O., Sezer and B.P., Pourghannad), Transportation Science 51 (1), 214−
232, 2017, ISSN 0041 − 1655 (print).

8. Order and exit decisions under non-decreasing price curves for products with short life cycles (with Canan Pehlivan and Semih Onur Sezer),
Mathematical Methods of Operations Research 90, 365 − 397, 2019.

Topic: Spare parts management

1. On spare parts demand and the installed base concept: A theoretical approach (with A.Amniattalab and M.Hekiomoglu) International Journal ˘
of Production economics 266, December 2023, article 109043

Topic: Worst case analysis of Algorithms.

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

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

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

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

5. 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.

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

7. Improved Algorithms for machine allocation in manufacturing systems
(with M.Labbe, M. van Vliet and S.Zhang), Operations Research 42, 523−
530, 1994

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

Book Chapters.

1. 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.

2. 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.

3. 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

4. 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.Ozekici, ¨ 239 − 280, Springer Verlag, Berlin, 1996.

5. 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.

6. 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.(on invitation)

;7. 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. (on invitation)

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

9. 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.
(on invitation)

10. On noncooperative games, minimax theorems and equilibrium problems
(with G.Kassay (Cluj)) 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 (on invitation)

11. Risk measures and Their Application in Asset Management, (with S¸.˘I.
Birbil, N. Noyan and B. Kaynar), Chapter 15 of The VAR IMPLEMENTATION HANDBOOK (editor G.N.Gregoriou, McGraw Hill, 2009. (on invitation)

12. Generalizing the Ordering cost and Holding-Backlog Cost Rate Functions in EOQ-type Inventory Models (with M, Kaya and B, Pourghannad), In Handbook of EOQ Inventory Problems (Stochastic and Deterministic Models and Applications), editor Tsan-Ming Choi,79-120 Series: International Series in Operational Research and Management Science, Springer Verlag, New York 2014, ISBN 978-1-4614-7638-2.

13. On the Principle of Lagrange in Optimization Theory and its applications in Transportation and Location Problems (with S. Javadi)r In New
Perspectives in Operations Research and Management Science (Essays
in honor of Fusun Elegin), editors Y. ˙Ilker Topcu et al page 31 − 67.
International Series in Operations Research and Management Science
volume 326, Springer Verlag, 2022, ISBN 978-3-030-91850-7

Books.

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

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

  • Doktora: Ph.D. in Economics, EUR, Rotterdam, September 1983, Title Ph.D
    thesis: On renewal theory, Banach algebras and functions of bounded
    increase (promotor: Prof.Dr. L.F.M. de Haan, co promotors Prof.
    Dr D.van Dulst, Prof. Dr. W. Vervaat)
  • Yüksek lisans: Master’s Degree in Mathematics (specialization stochastic processes),
    University of Utrecht, Utrecht, March 1979, Title master thesis:
    Brownian motion and optimal stopping, master thesis supervisor
    Prof. Dr J.W.Cohen.)
  • Lisans: 1. Candidate’s (Bachelor) Degree in Mathematics, University of Utrecht,
    Utrecht, The Netherlands, september 1977.
    2. Candidate’s (Bachelor) degree in Econometrics, EUR, Rotterdam,
    The Netherlands, august 1979.
• Wickham Skinner best paper award published in Production and Operations Management 2012.