Springer optimal control and dynamic games applications in finance management science and economics 2005 ISBN0387258043

Springer optimal control and dynamic games applications in finance management science and economics 2005 ISBN0387258043 Springer optimal control and dynamic games applications in finance management science and economics 2005 ISBN0387258043 Springer optimal control and dynamic games applications in finance management science and economics 2005 ISBN0387258043 Springer optimal control and dynamic games applications in finance management science and economics 2005 ISBN0387258043 Springer optimal control and dynamic games applications in finance management science and economics 2005 ISBN0387258043

OPTIMAL CONTROL AND DYNAMIC GAMES Advances in Computational Management Science VOLUME Optimal Control and Dynamic Games Applications in Finance, Management Science and Economics Edited by CHRISTOPHE DEISSENBERG Université de la Méditerrannée, Les Milles, France and RICHARD F HARTL University of Vienna, Austria A C.I.P Catalogue record for this book is available from the Library of Congress ISBN-10 0-387-25804-3 (HB) Springer Dordrecht, Berlin, Heidelberg, New York ISBN-10 0-387-25805-1 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York ISBN-13 978-0-387-25804-1 (HB) Springer Dordrecht, Berlin, Heidelberg, New York ISBN-13 978-0-387-25805-8 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York Published by Springer, P.O Box 17, 3300 AA Dordrecht, The Netherlands Printed on acid-free paper All Rights Reserved © 2005 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work Printed in the Netherlands Contents Foreword XI List of Contributors XV Introduction XIX Part I Applications to Marketing Advertising directed towards existing and new customers Richard F Hartl, Peter M Kort Advertising and Advertising Claims Over Time Charles S Tapiero 19 Part II Environmental Applications Capital Resource Substitution, Overshooting, and Sustainable Development Hassan Bencheckroun, Seiichi Katayama, Ngo Van Long 41 Hierarchical and Asymptotic Optimal Control Models Economic Sustainable Development Alain B Haurie 61 Common Property Resource and Private Capital Accumulation with Random Jump Masatoshi Fujisaki, Seiichi Katayama, Hiroshi Ohta 77 Transfer mechanisms inducing a sustainable forest exploitation Guiomar Mart´ın-Herr´ an, Mabel Tidball 85 Characterizing Dynamic Irrigation Policies via Green’s Theorem Uri Shani, Yacov Tsur, Amos Zemel 105 VIII Contents Part III Applications in Economics and Finance Volatility Forecasts and the Profitability of Automated Trading Strategies Engelbert J Dockner, Gă u ănter Strobl 121 Two-Part Tariff Pricing in a Dynamic Environment Gila E Fruchter 141 10 Numerical Solutions to Lump-Sum Pension Fund Problems That Can Yield Left-Skewed Fund Return Distributions Jacek B Krawczyk 155 11 Differentiated capital and the distribution of wealth Gerhard Sorger 177 12 Optimal Firm Contributions to Open Source Software Rong Zhang, Ernan Haruvy, Ashutosh Prasad, Suresh P Sethi 197 Part IV Production, Maintenance and Transportation 13 The Impact of Dynamic Demand and Dynamic Net Revenues on Firm Clockspeed Janice E Carrillo 215 14 Hibernation Durations for Chain of Machines with Maintenance Under Uncertainty Ali Dogramaci 231 15 Self-Organized Control of Irregular or Perturbed Network Trac Dirk Helbing, Stefan Lămmer, ă Jean-Patrick Lebacque 239 16 A stochastic optimal control policy for a manufacturing system on a finite time horizon Eugene Khmelnitsky, Gonen Singer 275 17 On a State-Constrained Control Problem in Optimal Production and Maintenance Helmut Maurer, Jang-Ho Robert Kimr, Georg Vossen 289 Part V Methodological Advances 18 Reliability Index A Bensoussan 311 Contents IX 19 The direct method for a class of infinite horizon dynamic games Dean A Carlson, George Leitmann 319 Curriculum Vitae - Prof Suresh P Sethi 335 Author Index 343 Foreword I am delighted to be invited to give a few remarks at this workshop honouring Suresh Sethi He was one of the most hardworking and prolific of any of my (45 or so PhD) students during the course of 42 years of teaching at GSIA I would like to discuss our interactions both during and after the completion of his doctoral thesis Suresh entered the PhD program in the fall of 1969 just after I had published a paper on the application of a new mathematical model called Optimal Control Theory which originated in Russia The paper was called: ”The Optimal Maintenance and Sale Date of a Machine” Suresh quickly absorbed the mathematics on which optimal control theory is base We wrote a joint paper called ”Applications of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems,” which was published before the end of 1970 At the same time Suresh wrote nine additional papers by himself (on topics which I have forgotten) He put these nine papers together with the dynamic cash balance paper above to complete his thesis in record time His PhD was awarded before the end of 1970 The nine additional chapters in his thesis were also published by him in subsequent years In 1970 it was uncommon for professors to write joint papers with either their colleagues or with their PhD students In GSIA we encouraged such joint work and other schools have since imitated this practice In order to analyze how Suresh has thrived in this environment, I did a quick count of the number of authors in each of the papers listed in the Professional Journal Articles section of his vita, obtaining the following amazing distribution: single author, 37; authors, 96; authors, 113; authors, 46; and authors, Note that three times as many papers having a single author is about the same as the number of papers having authors; half of the authored papers is about the same as the number of authored papers, etc In order to explain how Suresh could have created an environment in which made these results possible I would like to discuss some of his personal attributes as follows: (a) his congeniality; 328 From this we now compute, ˜ x, y ∗ (t), p˜) ˜, y ∗ (t), f˙(t) ± p˜) − L(˜ L1 (f (t) ± x = e−δt α2 ˙ α2 a2 ( f (t) ± p ˜ ) + 2s2 α2 + α (α(f (t) ± x ˜) + βy ∗ (t))2 α + (α(f (t) ± x ˜) + βy ∗ (t)) s α2 − (a − (α(f (t) ± x ˜) + βy ∗ (t))) (f˙(t) ± p˜) s + −a(α2 + α)(α(f (t) ± x ˜) + βy ∗ (t)) − e−δt = e−δt α2 α2 a2 p˜ + 2s2 2 α ˙ α2 + α [α(f (t) ± x ˜) + βy ∗ (t)]2 + f (t) 2s − a α2 + α [α(f (t) ± x ˜) + βy ∗ (t)] α2 α α2 a ˙ + [α(f (t) ± x ˜) + βy ∗ (t)] − f (t) s s s α2 ˙ α2 α α2 a f (t) + + [α(f (t) ± x ˜) + βy ∗ (t)] − ± e−δt s s s s ˜) ∂H1 (t, x ˜) ∂H1 (t, x + p˜ = ∂t ∂x ˜ + From this we compute the mixed partial derivatives to obtain, ∂ H1 (t, x ˜) = e−δt ±2 ∂x∂t ˜ α2 + α [α(f (t) ± x ˜) + βy ∗ (t)] α α2 α ˙ ∓aα(α2 + α) ± α + f (t) s s ˜) + α2 β(α + 2)y ∗ (t) = ±e−δt α3 (α + 2)(f (t) ± x −α2 (α + 1)a + α2 (α + 1)f˙(t) s p˜ 329 Direct Method – Infinite Horizon Games and ∂ H1 (t, x ) = et t x ă α2 α + f (t) + αf˙(t) + β y˙ ∗ (t) s2 s s α2 ˙ α(α + 1) ∓ δe−δt [α(f (t) ± x ˜) f (t) + s s α2 a +βy ∗ (t)] − s ă = et ( + 1)f(t) + (α + 1)y˙ ∗ (t) f (t) + s s s α2 δ ˙ δα2 − f (t) − (α + 1)f (t) s s δα2 δαβ α2 δ ∓ (α + 1)˜ x− (α + 1)y ∗ (t) + a s s s Assuming sufficient smoothness and equating the mixed partial derivatives we obtain the following equation: ) fă(t) f(t) (s2 ( + 2) + δs(α + 1))f (t) = h1 (t, x where δβs ∗ βs )y (t) − (α + 1)y˙ ∗ (t) α α x − a(s2 (α + 1) + δs) ± (αs2 (α + 2) − δs(α + 1))˜ h1 (t, x ˜) =(βs2 (α + 2) + A similar analysis for player yields: L2 (x, y, q) =e−δt β 2 β a2 β2 q + + + β (αx + βy)2 2s2 2 β β2 (αx + βy) − (a − (αx + βy) q (19.21) s s − a(β + β)(αx + βy) , and so choosing ˜ (˜ x, y˜, q˜) = e−δt L β 2 β a2 q + 2s2 gives us that the transformation z2 (·, ·) is obtained by solving the partial differential equation ∂z2 = 1, ∂ y˜ 330 which of course gives us, z2 (t, y˜) = g(t) ± y˜ Proceeding as above we arrive at the following differential equation for g(ã), gă(t) g(t) (s2 ( + 2) + δs(β + 1))g(t) = h2 (t, y˜) where δαs ∗ αs )x (t) − (1 + β)x˙ ∗ (t) β β ± (βs2 (β + 2) − δs(β + 1))˜ y − a(s2 (β + 1) + δs) h2 (t, y˜) =(αs2 (β + 2) + Now the auxiliary variational problem we must solve consists of minimizing the two functionals, +∞ t0 e−δt α2 ˙ αa2 x ˜ (t) + 2s2 +∞ dt and e−δt t0 β2 ˙2 βa2 y ˜ (t) + 2s2 dt over some appropriately chosen initial conditions We observe that these two minimization problems are easily solved if these conditions take the form, x ˜(t0 ) = c1 and y˜(t0 ) = c2 for arbitrary but fixed constants c1 and c2 The solutions are in fact, x ˜∗ (t) ≡ c1 and y˜∗ (t) ≡ c2 According to our theory we then have that the solution to our variational game is, x∗ (t) = f (t) ± c1 and y ∗ (t) = g(t) ± c2 In particular, using this information in the equations for f (·) and g(·) with x ˜ = c1 and with y˜ = c2 we obtain the following equations for x∗ (·) and y (ã), x ă (t) x (t) − [αs2 (α + 2) + δs(α + 1)]x∗ (t) =h1 (t, 0) yă (t) y (t) − [βs2 (β + 2) + δs(β + 1)]y ∗ (t) =h2 (t, 0) with the initial conditions, x∗ (t0 ) = P0 and y ∗ (t0 ) = P0 These equations coincide exactly with the Euler-Lagrange equations, as derived by the Maximum Principle for the open-loop variational game without constraints Additionally we note that as these equations are derived here via the direct method we see that they become sufficient conditions for a Nash equilibrium of the unconstrained system, and hence 331 Direct Method – Infinite Horizon Games for the constrained system for solutions which satisfy the constraints Moreover, we also observe that we can recover the functions Hj (·, ·), for j = 1, 2, since we can recover both f (·) and g(·) by the formulas f (t) = x∗ (t) ∓ c1 and g(t) = y ∗ (t) ∓ c2 The required functions are now recovered by integrating the partial derivatives of H1 (·, ·) and H2 (·, ·) which can be computed Moreover, if the functions x∗ (·) and y ∗ (·) are bounded, which implies that f (·) and g(·) are also bounded, we further have that, lim H1 (t, x ˜∗ (t)) = and t→+∞ lim H2 (t, y˜∗ (t)) = t→+∞ Consequently, we see that in this instance the solution to our variational game is given by the solutions of the above Euler-Lagrange system, provided the resulting strategies and the price satisfy the requisite constraints Finally, we can obtain the solution to the original problem by taking, P ∗ (t) = αx∗ (t) + βy ∗ (t), u∗1 (t) = α a − P ∗ (t) − x˙ ∗ (t) , s and u∗2 (t) = β a − P ∗ (t) − y˙ ∗ (t) s Of course, we still must check that these functions meet whatever constraints are required (i.e., ui (t) ≥ and P (t) ≥ 0) There is one special case of the above analysis in which the solution can be obtained easily This is the case when α = β = 12 In this case the above Euler-Lagrange system becomes, x ă (t) x (t) yă (t) y (t) 3δ s + s x∗ (t) = 3 s + δs y ∗ (t) − sy˙ ∗ (t) − a s + δs 2 3δ s + s y ∗ (t) = 3 s + δs x∗ (t) − sx˙ ∗ (t) − a s + δs 2 Using the fact that P ∗ (t) = 12 (x∗ (t) + y ∗ (t)) for all t ∈ [t0 , +∞) we can multiply each of these equations by 12 an add them together to obtain 332 the following equation for P (ã), Pă (t) + s − δ P˙ ∗ (t) − (s + δ) sP ∗ (t) = − 2 s + δ as, for t0 ≤ t This equation is an elementary non-homogeneous second order linear equation with constant coefficients whose general solution is given by P ∗ (t) = Aer1 (t−t0 ) + Ber2 (t−t0 ) + 3s + 2δ 5(s + δ) a in which r1 and r2 are the characteristic roots of the equation and A and B are arbitrary constants More specifically, the characteristic roots are roots of the polynomial r2 + s − δ sr − (s + δ) s = 2 and are given by r1 = s and r2 = δ − s Thus, to solve the dynamic game in this case we select A and B so that P ∗ (·) satisfies the fixed initial condition and remains bounded That is, we require ≤ δ < 52 s, we put A = 0, and choose B to be, B = P0 − (3s + 2δ)a 5(δ + s) Further, we note that we can also take x∗ (t) = y ∗ (t) = P ∗ (t) and so obtain the optimal strategies as u∗1 (t) = u∗2 (t) = a − P ∗ (t) − P˙ ∗ (t) s and of course subject to the requirement that the control constraints given by (19.14) and state constraints (19.15) are met Regarding these conditions it is an easy matter to see that the optimal price (as chosen above) satisfies P ∗ (t) ≥ for all t ≥ since P0 ≥ To satisfy the 333 Direct Method – Infinite Horizon Games control constraints, we observe that u∗i (t) = → (3s + 2δ)a a − P0 − 5(δ + s) 5s (3s + 2δ)a − δ− s 5(δ + s) (3s + 2δ) 1− a 5(δ + s) 5s e(δ− )(t−t0 ) − (3s + 2δ)a 5(δ + s) 5s e(δ− )(t−t0 ) as t → +∞ so that a necessary condition for the optimal stratiegies to remain positive would be that (3s + 2δ) 1− ≥ 0, 5(δ + s) or that s ≤ 3δ In addition, we observe that since the optimal strategies have the form E + Der(t−t0 ) with E and D cosntants it follows that they must be strictly monotonic This implies that for the control constraints to be satisfied all we need check is that their initial values, ui (t0 ), be positive Thus we must choose the parameters so that, 2u∗i (t0 ) (3s + 2δ)a (3s + 2δ)a − 5(δ + s) 5(δ + s) 5s (3s + 2δ)a − δ− s 5(δ + s) 5s (3s + 2δ)a = a − P0 − δ− s 5(δ + s) 5s (3s + 2δ) = 1− δ− a − P0 s 5(δ + s) 25s2 + 14sδ − 4δ = a − P0 10s(s + δ) = a − P0 − ) + 51δ 25(s + 25 10s(s + δ) = a − P0 ≥ Summarizing, the direct method provides an open-loop Nash equilibrium for this example whenever the parameters, s, a, P0 , and δ, are chosen so that < 3s < δ < 5s and P0 < ) + 51δ 25(s + 25 10s(s + δ) a 334 References C Carath´ ´eodory Calculus of Variations and Partial Differential Equations Chelsea, New York, New York, 1982 Dean A Carlson An observation on two methods of obtaining solutions to variational problems Journal of Optimization Theory and Applications, 114:345–362, 2002 Dean A Carlson and George Leitmann A direct method for open-loop dynamic games for affine control systems too appear in Dynamic Games: Theory and Applications, G Zaccour and Alain Haurie (eds.) 2005 Dean A Carlson and George Leitmann An extension of the coordinate transformation method for open-loop Nash equilibria Journal of Optimization Theory and Applications, 123(1): 27 - 47, 2004 E J Dockner and G Leitmann Coordinate transformation and derivation of open-loop nash equilibrium Journal of Optimization Theory and Applications, 110(1):1–16, 2001 G Leitmann A Direct Method of Optimization and Its Application to a Class of Differential Games Dynamics of Continuous, Discrete, and Impulsive Systems, Series A: Mathematical Analysis, 11:191–204, 2004 G Leitmann Some Extensions of a Direct Optimization Method Journal of Optimization Theory and Applications, 111(1):1–6, 2001 G Leitmann On a Class of Direct Optimization Problems Journal of Optimization Theory and Applications, 108(3):467–481, 2001 G Leitmann A note on absolute extrema of certain integrals International Journal of Non-Linear Mechanics, 2:55–59, 1967 Suresh P Sethi Suresh Sethi (www.utdallas.edu/∼sethi), Ashbel Smith Professor and Director of Center for Intelligent Supply Networks at University of Texas at Dallas, has made fundamental contributions in a number of disciplines including operations management, finance, marketing, operations research (applied mathematics), industrial engineering, and optimal control Suresh Sethi was born in Ladnun, India in 1945 He received his B.Tech in Mechanical Engineering from the Indian Institute of Technology, Bombay, in 1967 He graduated with an M.B.A from Washington State University, Pullman, WA in 1969 In that same year, he joined the Graduate School of Industrial Administration at Carnegie Mellon University and there he received his M.S.I.S in 1971 and his Ph.D in 1972 He became a Full Professor at University of Toronto at the age of 33, where he served from 1973-1997 in various positions including General Motors Research Professor and Director of Laboratory for Manufacturing Research There, he founded the Doctoral Program in Operations Management He joined the University of Texas at Dallas in 1997 to build the Operations Management area including a doctoral program Currently, the area has about 10 faculty and 20 doctoral students Sethi’s doctoral thesis at Carnegie Mellon explored the applications of optimal control theory to functional areas of management Sethi extended the theory to deal with the peculiarities of management problems, such as the nonnegativity constraints and time lags He has made pioneering applications in the areas of operations management, marketing and finance Few individuals have contributed more toward the application of optimal control theory to managerial problems than Sethi His work has been extensive in coverage and penetrating in analysis His thesis and the subsequent work eventually led to the 1981 Sethi-Thompson book (481 pages) that brought the theory of optimal control to management schools The second edition (505 pages) of this classic text became available in Fall 2000 336 In the areas of operations management, Sethi has applied optimal control theory to HMMS-type production planning problems, machine maintenance and replacement problems, simultaneous production and pricing problems, etc Sethi has surveyed this area in a 1978 paper Sethi has made numerous applications of optimal control in the area of marketing His application of Green’s Theorem to solve for optimal advertising expenditures in the Vidale-Wolfe model is now a classic In 1983, Sethi also introduced stochastic optimal control to the marketing area This paper has found a number of interesting extensions Prasad and Sethi develops a competitive extension of the Vidale-Wolfe advertising model, and solves explicitly the resulting stochastic differential game Bass et al introduces generic advertising in the model and solve the resulting differential game explicitly to obtain the Nash equilibrium levels of both brand and generic advertising expenditures by the competitors Sethi and Feichtinger, Hartl, and Sethi have provided extensive reviews of the literature of optimal control of advertising models in 1977 and 1994, respectively In 1978, Sethi began to look into the fundamental problem of how long-term planning influences immediate decisions His work on decision, forecast and rolling horizons has provided a logical foundation for the practice of finite horizon assumptions and the choice of horizon Sethi has published extensively on the topic, and he is considered to be one of the foremost scholars in the area Recently, Chand, Hsu, and Sethi have surveyed the field in an article commissioned by Manufacturing Services & Operations Management (2002), a leading journal in the area Among his contributions in the finance/economics area, the most important is his work on the classical consumption-portfolio problem He is responsible for bringing the realistic features of subsistence consumption and bankruptcy into the classical problem His 1986 paper with Karatzas, Lechozky and Shreve published in Mathematics of Operations Research broadens the scope of the classical problem and provides an explicit solution of the problem It represents a landmark paper in the area It gave new life to the classical problem, which lay dormant for 15 years, and it inspired mathematicians and mathematical economists to study the problem with new perspectives Sethi’s further work on the problem includes risk-averse behaviour of agents subject to bankruptcy The work of Sethi and co-authors on the problem has appeared in a 428-page book by Sethi, published by Kluwer In its Fellow citation, the New York Academy of Sciences mentions that Harry Markowitz, a 1990 Nobel Laureate in Economics, places Dr Sethi ”among the leaders in financial theory.” Suresh P Sethi 337 Sethi has also made significant contributions to the area of sequencing and scheduling In a seminal co-authored 1992 paper, a new paradigm for scheduling jobs and sequencing of robot moves simultaneously in a robotic cell is introduced and analyzed A deep conjecture regarding the optimality of the solution, referred to as the Sethi conjecture among the co-authors, generated considerable research interest including at least five doctoral theses and over 40 papers The conjecture is now partially resolved A book co-authored by Dawande, M., Geismar, H., and Sriskandarajah, C on the topic is forthcoming in 2005 In the area of flexible manufacturing systems, two surveys by Sethi has defined and surveyed the various concepts of manufacturing flexibility (Browne et al and Sethi and Sethi) These are very well-known and highly cited papers in the area In addition, Sethi has published research on flexible transfer lines and flexible robotic cells Over the last fifteen years, Sethi has been looking into the complex problem of production planning in stochastic manufacturing systems The work has resulted in a new theory of hierarchical decision making in stochastic manufacturing systems While the work is still continuing, a significant plateau reached by Sethi and co-authors resulted in a 1994 book by Sethi and Zhang (419 pages) In reviews, the book is variously described as impressive, pathbreaking, and profound The late Herbert A Simon, the 1978 Nobel Laureate in Economics, stated, ”Suresh Sethi has clearly made a series of important extensions to the treatment of hierarchical systems and applications to management science problems, and the book with Zhang is an impressive piece of work.” A review in Discrete Event Dynamic Systems (July 1996) states: ”This is a truly remarkable book, in which Sethi and Zhang have contributed enormously to the area of hierarchical controls in manufacturing.” The theory leads to a reduction of the intractable stochastic optimization problem into simpler problems, which could then be solved to obtain a provably near-optimal solution of the original problem More specifically, the theory gives rise to a relatively simpler model for higher-level management decisions and a reduced model for lower level decisions on the shop floor The importance of the scheme lies in the facts that the simpler higher-level model is realistic enough so that it captures the essential features of the manufacturing process, and the lower level model can be reduced since it is guided by higher-level decisions In his 1994 text Manufacturing Systems Engineering, Gershwin mentions: ”There have been many hierarchical scheduling and planning algorithms, some quite practical and successful However, outside of the work of Sethi and his colleagues, there had been little systematic justification of this 338 structure.” A follow-up of the 1994 book dealing with the average cost criteria, co-authored with Zhang and Zhang, is soon to appear More recently, Sethi has been studying inventory problems with Markovian demands or world-driven demands with discounted as well as average cost criteria In addition, he has generalized the assumption on cost functions to include those having polynomial growth Moreover; he has analyzed the case when the demand depends on a Markov process, which in turn depends on other decisions such as promotion A book titled Markovian Demand Inventory Models is currently in progress to appear in the International Series on Operations Research and Management Science published by Springer Beginning with his 2001 paper, Sethi started studying the optimality of base-stock and (s,S) type policies in cases of forecast updates and multiple delivery modes In this paper, Sethi, Yan and Zhang introduce a general forecast updating scheme, termed peeling layers of an onion, and show the optimality of a forecast-dependent base-stock policy with two delivery modes Fix cost was introduced in a subsequent paper Finally, it is shown that the base-stock policy is no longer optimal for other than the two fastest modes when there are three or more consecutive delivery modes Sethi had studied a variety of supply chain contracts with demand forecast updates Gan, Sethi and Yan look at the issue of coordination in a supply chain consisting of risk-averse agents They develop a definition of coordination in this case, and obtain coordinating contracts in a variety of supply chains with agents observing different risk-averse objectives Bensoussan, Feng and Sethi generalize the standard newsvendor problem to include two ordering stages, a forecast update at the second stage, and an overall service constraint A book titled Inventory and Supply Chain Management with Forecast Updates is to appear in the International Series on Operations Research and Management Science published by Springer in 2005 Sethi has published over 300 papers in the areas of operations research, operations management, optimal control, mathematical finance and economics, industrial engineering, and semiconductor manufacturing He has presented his work at many scholarly conferences, universities and research institutions He serves on several editorial boards of journals in the areas of operations research, operations management, applied mathematics, and optimal control Over the years, Sethi’s research has been supported by a number of sponsors including NSERC, SSHRC, Manufacturing Research Corporation of Ontario, and Research Grant Council (Hong Kong) In recognition of his contributions, Sethi has received many honors The Canadian OR Society recognized his work on operations research by Suresh P Sethi 339 bestowing on him the 1996 CORS Award of Merit In 1997 he gave a distinguished Bartlett Memorial lecture in mathematics at the University of Tennessee In 1999 he was elected a Fellow of New York Academy of Sciences for his outstanding contributions in a variety of research areas In 2001 the Institute of Electrical and Electronics Engineers named him IEEE Fellow for his extraordinary accomplishments in optimal control Suresh Sethi was awarded an INFORMS Fellow in 2003 The American Association for the Advancement of Science elected him an AAAS Fellow in that same year Other honors include C.Y O’Connor Fellow, Curtin University, Perth, Australia (1998); Honorary Professor at Zhejiang University of Technology, Hangzhou, China (appointed in 1996); Fellow of the Canadian Academy of Sciences and Humanities or The Royal Society of Canada (1994); Visiting Erskine Fellow at the University of Canterbury, Christchurch, New Zealand (1991); Connaught Senior Research Fellow at the University of Toronto (1984-85) He is listed in Canadian Who’s Who, Marquis Who’s Who in the World and Marquis Who’s Who in America (2001) Sethi is a member of INFORMS, MSOM, SIAM, IEEE, CORS, POMS, ORSI, DSI, AAAS, NYAS, Royal Society of Canada, Phi Kappa Phi, and Beta Gamma Sigma Sethi has been very successful at mentoring post-doctoral fellows and PhD students These researchers have gone on to make important contributions to both teaching and research in Operations Management This list includes Dr Sita Bhaskaran (General Motors), Professor Richard Hartl (University of Vienna), Professor Qing Zhang (University of Georgia), Professor Steef van de Velde (Erasmus University), Dr Dirk Beyer (Hewlett Packard), Dr Feng Cheng (IBM), Dr Hanqin Zhang (Chinese Academy of Sciences), Professor Gerhard Sorger (University of Vienna), Professor Abel Cadenillas (University of Alberta), Dr Wulin Suo (Queens University), Professor Houmin Yan and Dr Xun Yu Zhou (Chinese University of Hong Kong), Professor Suresh Chand and Dr Arnab Bisi (Purdue University), Professor Chelliah Sriskandarajah (University of Texas at Dallas), Dr Ruihua Liu (University of Dayton) References Bass, F.M., Krishnamoorthy, A., Prasad, A., and Sethi, S.P., ”Generic and Brand Advertising Strategies in a Dynamic Duopoly,” Marketing Science, forthcoming Bensoussan, A., Feng, Q., and Sethi, S.P., ”A Two-Stage Newsvendor Problem with a Service Constraint.” 340 Beyer, D., Cheng, F and Sethi, S.P., Markovian Demand Inventory Models, Springer, 2005 Browne, J., Dubois, D., Rathmill, K., Sethi, S.P., and Stecke, K., ”Classification of Flexible Manufacturing Systems,” The FMS Magazine, April 1984, 114-117 Chand, S., Hsu, V.N., and Sethi, S.P., ”Forecast, Solution and Rolling Horizons in Operations Management Problems: A Classified Bibliography,” Manufacturing & Service Operations Management, 4, 1, Winter 2002, 25-43 Dawande, M., Geismar, H.N., Sethi, S.P., and Sriskandarajah, C., Throughput Optimization in Robotic Cells, Springer, 2005 Feichtinger, G., Hartl, R.F and Sethi, S.P., ”Dynamic Optimal Control Models in Advertising: Recent Developments,” Management Science, 40, 2, Feb 1994, 195-226 Feng, Q., Gallego, G., Sethi, S.P., Yan, H., and Zhang, H ”Optimality and Nonoptimality of the Base-stock Policy in Inventory Problems with Multiple Delivery Modes,” Operations Research, February 2004 Gan, X., Sethi, S.P., and Yan, H., ”Channel Coordination with a RiskNeutral Supplier and a Downside-Risk-Averse Retailer,” POM; Special Issue on Risk Management in Operations, in press Karatzas, I., Lehoczky, J.P., Sethi, S.P and Shreve, S.E., ”Explicit Solution of a General Consumption/Investment Problem,” Mathematics of Operations Research, 11, 2, May 1986, 261-294 Prasad, A and Sethi, S.P., ”Competitive Advertising under Uncertainty: Stochastic Differential Game Approach,” Journal of Optimization Theory and Applications, 123, 1, October 2004, in press Sethi, A and Sethi, S.P., ”Flexibility in Manufacturing: A Survey,” International Journal of Flexible Manufacturing Systems, 2, 1990, 289-328 Sethi, S.P., Optimal Consumption and Investment with Bankruptcy, Kluwer Academic Publishers, Norwell, MA, 1997 Sethi, S.P., ”Deterministic and Stochastic Optimization of a Dynamic Advertising Model,” Optimal Control Application and Methods, 4, 2, 1983, 179-184 Sethi, S.P., ”A Survey of Management Science Applications of the Deterministic Maximum Principle,” TIMS Studies in the Management Science, 9, 1978, 33-68 Sethi, S.P., ”Dynamic Optimal Control Models in Advertising: A Survey,” SIAM Review, 19, 4, Oct 1977, 685-725 Sethi, S.P., ”Optimal Control of the Vidale-Wolfe Advertising Model,” Operations Research, 21, 4, 1973, 998-1013 Suresh P Sethi 341 Sethi, S.P., Sriskandarajah, C., Sorger, G., Blazewicz, J., and Kubiak, W., ”Sequencing of Parts and Robot Moves in a Robotic Cell,” International Journal of Flexible Manufacturing Systems, 4, 1992, 331-358 Sethi, S.P and Thompson, G.L., Optimal Control Theory: Applications to Management Science and Economics, Second Edition, Kluwer Academic Publishers, Boston, 2000 Sethi, S.P and Thompson, G.L., Optimal Control Theory: Applications to Management Science, Martinus Nijhoff, Boston, 1981 Sethi, S.P., Yan, H., and Zhang, H., Inventory and Supply Chain Management with Forecast Updates, Springer, 2005 Sethi, S.P., Yan, H., and Zhang, H., ”Inventory Models with Fixed Costs, Forecast Updates, and Two Delivery Modes,” Operations Research, 51, 2, March-April 2003, 321-328 Sethi, S.P., Yan, H., and Zhang, H., ”Peeling Layers of an Onion: Inventory Model with Multiple Delivery Modes and Forecast Updates,” Journal of Optimization Theory and Applications, 108, 2, Feb 2001, 253-281 Sethi, S.P and Zhang, Q., Hierarchical Decision Making in Stochastic Manufacturing Systems, in series Systems and Control: Foundations and Applications, Birkhauser ă Boston, Cambridge, MA, 1994 Sethi, S.P., Zhang, H., and Zhang, Q., Average-Cost Control of Stochastic Manufacturing Systems, Springer, 2005 Author Index A Bensoussan, 311 Alain B Haurie, 61 Ali Dogramaci, 231 Amos Zemel, 105 Ashutosh Prasad, 197 Charles S Tapiero, 19 Dean A Carlson, 319 Dirk Helbing, 239 Engelbert J Dockner, 121 Ernan Haruvy, 197 Eugene Khmelnitsky, 275 Gunter ă Strobl, 121 Georg Vossen, 289 George Leitmann, 319 Gerhard Sorger, 177 Gila E Fruchter, 141 Gonen Singer, 275 Guiomar Mart´n-Herr´ ´ ´ an, 85 Hassan Bencheckroun, 41 Helmut Maurer, 289 Hiroshi Ohta, 77 Jacek B Krawczyk, 155 Jang-Ho Robert Kimr, 289 Janice E Carrillo, 215 Jean-Patrick Lebacque, 239 Mabel Tidball, 85 Masatoshi Fujisaki, 77 Ngo Van Long, 41 Peter M Kort, Richard F Hartl, Rong Zhang, 197 Seiichi Katayama, 41, 77 Stefan Lă a ămmer, 239 Suresh P Sethi, 197, 335 Uri Shani, 105 Yacov Tsur, 105 .. .OPTIMAL CONTROL AND DYNAMIC GAMES Advances in Computational Management Science VOLUME Optimal Control and Dynamic Games Applications in Finance, Management Science and Economics Edited... economics, forecasting and rolling horizons, sequencing and scheduling, flexible manufacturing systems, hierarchical decision making in stochastic manufacturing systems, and complex inventory problems,... contributions of Sethi in the domain of Introduction XXI finance, manufacturing and resource management can also serve to better understand the stakes of sustainability in economic growth and to assess