references - springer978-1-4612-1356... · 2017-08-26 · references 451 [26] r. bellman and s....
TRANSCRIPT
References
[I] 1. Abate and W. Whitt. Numerical inversion of probability generating functions. Operations Research leiters, 12:245-251, 1992.
[2] J. Abate and W. Whitt. Numerical inversion of Laplace transfonns ofprobability distributions. ORSA Journal on Computing, 7:36-43,1995.
[3] R. L. Ackotf. The meaning, scope and methods of operations research. In R. L. Ackotf, editor, Progress in Operations Research, volume I. John Wiley, New York, 1961.
[4] R. L. Ackotf and M. W. Sasieni. Fundamentals of Operations Research. John Wiley, New York, 1968.
[5] R. M. Adelson. Compound Poisson distributions. Operational Research Quarterly, 17:73-75, 1966.
[6] S. C. Aggarwal. A review of current inventory theory and its applications. International Journal of Production Research, 12:443482, 1974.
[7] H. Anton. Elementary Linear Algebra. John Wiley, New York, 6th edition, 1991.
[8] T. M. Apostol. Mathematical Analysis. Addison-Wesley, Reading, Mass., 1969.
[9] K. 1. Arrow. Historical background. In K. J. Arrow, S. Karlin, and H. Scarf, editors, Studies in the Mathematical Theory of Inventory and Production, pages 3-15. Stanford University Press, Stanford, California, 1958.
450 References
[10] K. J. Arrow. Essays in the Theory of Risk-Bearing. Markham, Chicago, 1971.
[11] K. J. Arrow, T. Harris, and J. Marschak. Optimal inventory policy. Econometrica, 19:250-272, 1951.
[12] J. Banks, J. S. Carson, and B. L. Nelson. Discrete-Event System Simulation. Prentice Hall, Upper Saddle River, N.J., 2nd edition, 1996.
[13] J. Banks and W. J. Fabrycky. Procurement and Inventory Systems Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1987.
[14] S. K. Bar-Lev, M. Parlar, and D. Perry. Optimal sequential decisions for incomplete identification of group-testable items. Sequential Analysis, 14(1):41-57, 1995.
[15] E. Barancsi, G. Banki, R. Borloi, A. Chikan, P. Kelle, T. Kulcsar, and G. Meszena. Inventory Models. Kluwer Academic Publishers, Dordrecht, 1990.
[16] D. J. Bartholomew. Stochastic Models for Social Processes. John Wiley, Chichester, 1982.
[17] M. Baxter and A. Rennie. Financial Calculus: An Introduction to Derivative Pricing. Cambridge University Press, Cambridge, 1996.
[18] M. S. Bazaraa and C. M. Shetty. Nonlinear Programming: Theory and Algorithms. John Wiley, New York, 1979.
[19] M. J. Beckmann. Dynamic Programming of Economic Decisions. Springer-Verlag, Berlin, 1968.
[20] S. Beer. Decision and Control. John Wiley, New York, 1966.
[21] R. Bellman. On the theory of dynamic programming. Proceedings of National Academy of Sciences, 38:716-719,1952.
[22] R. Bellman. Dynamic progamming and a new formalism in the calculus of variations. Proceedings of the National Academy of Sciences, 39: 1 077-1082, 1953.
[23] R. Bellman. Dynamic Programming. Princeton University Press, Prince-ton, N.J., 1957.
[24] R. Bellman. Adaptive Control Processes: A Guided TOUT. Princeton University Press, Princeton, N.J., 1961.
[25] R. Bellman and K. L. Cooke. Modern Elementary Differential Equations. Dover, New York, 2nd edition, 1971.
References 451
[26] R. Bellman and S. Dreyfus. Dynamic programming and the reliability of multicomponent devices. Operations Research, 6:200-206,1958.
[27] R. Bellman and R. E. Kalaba. Dynamic programming and statistical communication theory. Proceedings of the National Academy of Sciences, USA, 43:749-751, 1957.
[28] R. Bellman and R. E. Kalaba. On the role of dynamic programming in statistical communication theory. IRE Transactions on Information Theory, IT-3:197-203,1957.
[29] A. Bensoussan, E. G. Hurst, and B. Naslund. Management Applications of Modern Control Theory. North-Holland, Amsterdam, 1974.
[30] D. P. Bertsekas. Dynamic Programming: Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs, 1987.
[31] D. P. Bertsekas. Dynamic Programming and Optimal Control, volume I. Athena Scientific, Belmont, Massachusetts, 1995.
[32] U. N. Bhat. A controlled transportation queueing process. Management Science, 16(7):446-452, 1970.
[33] U. N. Bhat. Elements of Applied Stochastic Processes. John Wiley, New York, 2nd edition, 1984.
[34] F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Econamy, 81 :637-659, May-June 1973.
[35] J. H. Bookbinder and D. L. Martell. Time-dependent queueing approach to helicopter allocation for forest fire initial attack. INFOR, 17:58-70, 1979.
[36] G. E. P. Box and M. F. Muller. A note on the generation of random normal deviates. Annals of Mathematical Statistics, 29:610-611, 1958.
[37] L. Breiman. Stopping-rule problems. In E. F. Beckenbach, editor, Applied Combinatorial Mathematics, pages 284-319. John Wiley, New York, 1964.
[38] R. S. Brooks and J. Y. Lu. On the convexity of the backorder function for an EOQ policy. Management &ience, 15(7):453-454, 1969.
[39] A. E. Bryson and Y.-C. Ho. Applied Optimal Control. Halstead, New York,1975.
[40] G. Carter, J. M. Chaiken, and E. J. Ignall. Response areas for two emergency units. Operations Research, 20:571-594,1972.
[41] S. <;etinkaya and M. Parlar. Optimal nonmyopic gambling strategy for the generalized Kelly criterion. Naval Research Logistics, 44(4):639-654, 1997.
452 References
[42] S. Cetinkaya and M. Parlar. Nonlinear programming analysis to estimate implicit inventory backorder costs. Journal of Optimization Theory and Applications, 97(1):71-92, 1998.
[43] Y. S. Chow, H. Robbins, and D. Siegmund. The Theory of Optimal Stopping. Houghton MitHin, Boston, 1971.
[44] C. W. Churchman. The Systems Approach. Delta, New York, 1968.
[45] C. W. Churchman, R. L. Ackoff, and E. L. Arnoff. Introduction to Operations Research. John Wiley, New York, 1958.
[46] V. Chvatal. Linear Programming. W. H. Freeman and Company, New York,1983.
[47] E. <;mlar. Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, 1975.
[48] C. W. Cobb and P. H. Douglas. A theory of production. American Economic Review, 18(Supp. No. 2):139-165, 1928.
[49] L. Cooper and M. W. Cooper. Introduction to Dynamic Programming. Pergamon Press, New York, 1981.
[50] R. B. Cooper. Introduction to Queueing Theory. CEE Press, Washington, D.C., 1990.
[51] R. M. Corless. Essential Maple. Springer-Verlag, New York, 1995.
[52] D. R. Cox. The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proceedings of Cambridge Philosophical SOCiety, 51 :33-41, 1955.
[53] D. R. Cox and H. D. Miller. The Theory of Stochastic Processes. Chapman and Hall, London, 1965.
[54] D. R. Cox and W. L. Smith. Queues. Chapman and Hall, London, 1961.
[55] T. B. Crabill, D. Gross, and M. J. Magazine. A classified bibliography of research on optimal design and control of queues. Operations Research, 25:219-232, 1977.
[56] M. A. Crane and A. J. Lemoine. An Introduction to the Regenerative Method for Simulation Analysis. Springer-Verlag, New York, 1977.
[57] S. DaruJ. Nonlinear and Dynamic Programming. Springer-Verlag, New York,1975.
[58] G. B. Dantzig. Maximization of a linear function of variables subject to linear inequalities. In T. C. Koopmans, editor, Activity Analysis of Production and Allocation, pages 339-347. John Wiley, New York, 1951.
References 453
[59] G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, Princeton, N.J., 1963.
[60] M. D. Davis. Game Theory: A Nontechnical Introduction. Dover, Mineola, N.Y.,1983.
[61] N. Derzlm, S. P. Sethi, and G. L. Thompson. Dirtributed parameter systems approach to the optimal cattle ranching problem. Optimal Control Applications and Methods, 1:3-10, 1980.
[62] R. L. Disney and P. C. Kiessler. Traffic Processes in Queueing Networks: A Markov Renewal Approach. John Hopkins University Press, Baltimore, MD,1987.
[63] W. Edwards. Dynamic decision theory and probabilistic information processing. Human Factors, 4:59-73, 1962.
[64] R. M. Feldman and C. Valdez-Flores. Applied Probability and Stochastic Processes. PWS Publishing Company, Boston, 1996.
[65] W. Feller. An Introduction to Probability Theory and its Applications, volume II. John Wiley, New York, 2nd edition, 1971 .
[66] G. S. Fishman. Principles of Discrete Event Simulation. Wiley, New York, 1978.
[67] D. A. Gall. A practical multifactor optimization criterion. In A. Lavi and T. P. Vogel, editors, Recent Advances in Optimization Techniques. John Wiley, New York, 1966.
[68] D. P. Gaver and G. L. Thompson. Programming and Probability Models in Operations Research. Brooks/Cole, Monterey, Calif., 1973.
[69] Y. Gerchak and M. Parlar. Yield randomness, cost tradeoffs and diversification in the EOQ model. Naval Research Logistics, 37:341-354,1990.
[70] Y. Gerchak and M. Parlar. Investing in reducing lead-time randomness in continuous-review inventory models. Engineering Costs and Production Economics, 21:191-197,1991.
[71] Y. Gerchak, M. Parlar, and S. S. Sengupta. On manpower planning in the presence of learning. Engineering Costs and Production Economics, 20:295-303,1990.
[72] A. Ghosal, S. G. Loo, and N. Singh. Examples and Exercises in Operations Research. Gordon and Breach, London, 1975.
[73] P. E. Gill, W. Murray, and M. H. Wright. Practical Optimization. Academic Press, New York, 1981.
454 References
[74] R. Goodman. Introduction to Stochastic Models. Benjamin/Cummings, Menlo Park, 1988.
[75] B. S. Gottfried and J. Weisman. Introduction to Optimization Theory. Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
[76] D. Gross and C. M. Harris. Fundamentals of Queueing Theory. John Wiley, New York, 2nd edition, 1985.
[77] R. L. Gue and M. E. Thomas. Mathematical Methods in Operations Research. Macmillan, London, 1968.
[78] O. GOrier and M. Parlar. An inventory problem with two randomly available suppliers. Operations Research, 45(6):1-15, 1997.
[79] G. Hadley. Linear Programming. Addison-Wesley, Reading, Mass., 1962.
[80] G. Hadley. Nonlinear and Dynamic Programming. Addison-Wesley, Reading, Mass., 1964.
[81] G. Hadley and T. M. Whitin. Analysis of Inventory Systems. Prentice-Hall, Englewood Cliffs, N.J., 1963.
[82] B. Harris. Theory of Probability. Addison-Wesley, Reading, Mass., 1966.
[83] F. W. Harris. How many parts to make at once. Factory, The Magazine of Management, 10:135-136, 1913.
[84] A. C. Hax and D. Candea. Production and Inventory Management. Prentice Hall, Englewood Cliffs, N.J., 1984.
[85] K. M. Heal, M. L. Hansen, and K. M. Rickard. Maple V Learning Guide. Springer-Verlag, New York, 1998.
[86] A. Heck. Introduction to Maple. Springer-Verlag, New York, 2nd edition, 1996.
[87] J. M. Henderson and R. E. Quandt. Microeconomic Theory: A Mathematical Approach. McGraw-Hili, New York, 1958.
[88] D. P. Heyman and M. J. Sobel. Stochastic Models in Operations Research, Volume I: Stochastic Processes and Operating Characteristics. McGrawHill, New York, 1982.
[89] D. P. Heyman and M. J. Sobel. Stochastic Models in Operations Research, Volume II: Stochastic Optimization. McGraw-Hili, New York, 1984.
[90] D. P. Heyman and M. 1. Sobel, editors. Stochastic Models. Handbooks in Operations Research and Management Science. North-Holland, Amsterdam, 1990.
References 455
[91] F. B. Hildebrand. Methods of Applied Mathematics. Prentice-Hall, Englewood Cliffs, N.J., 2nd edition, 1965.
[92] F. S. Hillier and G. J. Liebennan. Introduction to Operations Research. Holden-Day, Oakland, Calif., 4th edition, 1986.
[93] C. C. Holt, F. Modigliani, J. F. Muth, and H. A. Simon. Planning Production, Inventories, and Work Force. Prentice-Hall, Englewood Cliffs, N.J., 1960.
[94] I. Horowitz. Decision Making and the Theory of the Firm. Holt, Rinehart and Winston, New York. 1970.
[95] R. A. Howard. Dynamic programming. Management Science, 12:317-348,1966.
[96] J. P.Ignizio. Linear Progamming in Single- and Multiple Objective Systems. Prentice-Hall, Englewood Cliffs, N.J., 1982.
[97] R. B. Israel. Calculus the Maple Way. Addison-Wesley, Don Mills, Ontario, 1996.
[98] J. R. Jackson. Networks of waiting lines. Operations Research, 5:518-521, 1957.
[99] M. I. Kamien and N. L. Schwartz. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. NorthHolland, New York, 1981.
[l00] L. V. Kantorovich. Mathematical Models of Organizing and Planning Production. Leningrad State University, Leningrad, 1939. In RussianEnglish translation appeared in Management Science, 6, pp. 366-422, (1959-60).
[101] E. P. C. Kao. An Introduction to Stochastic Processes. Duxbury, Belmont, Calif., 1997.
[102] S. Karlin and H. M. Taylor. A First Course in Stochastic Processes. Academic Press, San Diego, 2nd edition, 1975.
[103] J. L. Kelly. A new interpretation ofinfonnationrate. Bell System Technical Journal, 35:917-926,1956.
[104] W. D. Kelton, R. P. Sadowski, and D. A. Sadowski. Simulation with Arena. McGraw-Hill, Boston, 1998.
[105] D. G. Kendall. Some problems in the theory of queues. Journal of the Royal Statistical Society, Series B, 13:151-185, 1951.
456 References
[106] D. G. Kendall. Stochastic processes occmring in the theory of queues and their analysis by the method of imbedded Markov chains. Annals of Mathematical Statistics, 24:338-354, 1953.
[107] M. Khouja. The single-period (news-vendor) problem: Literature review and suggestions for future research. Omega, 27:537-553, 1999.
[108] D. E. Kirk. Optimal Control Theory. Prentice-Hall, Englewood Cliffs, New Jersey, 1970.
[109] C. F. Klein and W. A. Gruver. Dynamic optimization in Markovian queueing systems. In E. Roxin and P. T. Liu, editors, Kingston Conference on Differential Games and Control Theory, pages 95-118. Marcel Dekker, New York, 1978.
[110] L. Kleinrock. Queueing Systems, Volume J: Theory. John Wiley, New York,1975.
[Ill] G. Klimek and M. Klimek. Discovering Curves and Surfaces with Maple. Springer-Verlag, New York, 1997.
[112] P. J. Kolesar, K. L. Rider, T. B. Crabill, and W. E. Walker. A queueinglinear programming approach to scheduling police patrol cars. OperatiOns Research, 23:1045-1062,1975.
[113] B. O. Koopman. Air-terminal queues under time-dependent conditions. Operations Research, 6:1089-1114,1972.
[114] H. W. Kuhn and A. W. Tucker. Nonlinear programming. In J. Neyman, editor, Proceedings of 2nd Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, 1951. University of California Press.
[115] P. J. M. Laarhoven and E. H. L. Aarts. Simulated Annealing: Theory and Applications. Kluwer Academic, Boston, 1987.
[116] M. S. Lane, A. H. Mansour, and 1. L. Harpell. Operations research techniques: A longitudinal update 1973-1988. Interfaces, 23(2):63-68, 1993.
[117] R. E. Larson and 1. L. Casti. Principles of Dynamic Programming. Part I: Basic Analytic and Computational Methods. Marcel Dekker, New York, 1978.
[118] A. M. Law and W. D. Kelton. Simulation Modeling and Analysis. McGraw-Hili, New York, 1982.
[119] H. Lee and C. A. Yano. Production control for multi-stage systems with variable yield losses. Operations Research, 36:269-278, 1988.
References 457
[120] H. L. Lee and S. Nahmias. Single-product, single-location models. In S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin, editors, Logistics of Production and Inventory, pages 3-55. North-Holland, Amsterdam, 1993.
[121] B. Leonardz. To Stop or Not to Stop: Some Elementary Optimal Stopping Problems with Economic interpretations. Almqvist and Wtksell, Stockholm,1974.
[122] D. V. Lindley. The theory of queues with a single server. Proceedings of Cambridge Philosophical Society, 48:277-289,1952.
[123] S. A. Lippman and J. J. McCall. The economics of job search: A survey. Part I. Economic Inquiry, 14:155-189, 1976.
[124] S. A. Lippman and J. J. McCall. The economics of job search: A survey. Part II. Economic Inquiry, 14:347-368, 1976.
[125] J. D. C. Little. A proof for the queueing formula L = ..tW. Operations Research,9:383-387, 1961.
[126] R. F. Love, J. G. Morris, and G. o. Wesolowsky. Facilities Location: Models and Methods. North-Holland, New York, 1988.
[127] D. G. Luenberger. Linear and Nonlinear Programming. Addison-Wesley, Reading, Mass., 1984.
[128] D. G. Luenberger. Investment Science. Oxford University Press, New York,I998.
[129] J. Medhi. Recent Developments in Bulk Queueing Models. Wiley Eastern Limited, New Delhi, 1984.
[130] J. Medhi. Stochastic Models in Queuing Theory. Academic Press, New York,I991.
[131] J. Medhi. Stochastic Processes. John Wiley, New York, 1994.
[t 32] M. B. Monagan, K. O. Geddes, G. Labahn, and S. Vorkoetter. Maple V Programming Guide. Springer-Verlag, New York, 1996.
[133] J. Mossin. Optimal multi-period portfolio policies. Journal of Business, 41:215-229,1968.
[134] S. Nahmias. Inventory models. In A. Holzman J. Belzer and A. Kent, editors, The Encyclopedia of Computer Sciences and Technology, volume 9, pages 447-483. Marcel Dekker, New York, 1978.
[135] S. Nahmias. Production and Operations Analysis. Irwin, Homewood, III., 2nd edition, 1993.
458 References
[136] S. N. Neft~i. An Introduction to Financial Derivatives. Academic Press, San Diego, 1996.
[137] R. Nelson. Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling. Springer-Verlag, New York,I995.
[138] G. L. Nemhauser. Introduction to Dynamic Programming. John Wiley, New York, 1966.
[139] Operations Research Center, MIT. Notes on Operations Research 1959. The Technology Press, Cambridge, Massachusetts, 1959.
[140] M. Parlar. A decomposition technique for an optimal control problem with "PQDZ" cost and bounded controls. IEEE Transactions on Automatic Control, AC-27(4):947-951, 1982.
[141] M. Parlar. Optimal dynamic service rate control in time dependent MlM/S/N queues. International Journal of Systems Science, 15( 1): 107-118,1984.
[142] M. Parlar. EXPIM: A knowledge-based expert system for produc-tion/inventory modelling. International Journal of Production Research, 27(1):101-118,1989.
[143] M. Parlar. Probabilistic analysis of renewal cycles: An application to a non-Markovian inventory problem with multiple objectives. Operations Research, 48(2), 2000.
[144] M. Parlar and Y. Gerchak. Control of a production system with variable yield and random demand. Computers and Operations Research, 16(4):315-324, 1989.
[145] M. Parlar and R. Rempala. Stochastic inventory problem with piecewise quadratic holding cost function containing a cost-free interval. Journal of Optimization Theory and Applications, 75(1): 133-153, 1992.
[146] M. Parlar and R. G. Vickson. An optimal control problem with piecewisequadratic cost functional containing a "dead-zone". Optimal Control Applications and Methods, 1 :361-372, 1980.
[147] M. Parlar and Z. K. Weng. Designing a firm's coordinated manufacturing and supply decisions with short product life-cycles. Management Science, 43(10):1329-1344,1997.
[148] A. L. Peressini, F. E. Sullivan, and J. J. UbI. The Mathematics of Nonlinear Programming. Springer-Verlag, New York, 1988.
References 459
[149] S. R. Pliska. Management and optimization of queueing systems. In S. Ozekici, editor, Queueing Theory and Applications, pages 168-187. Hemisphere Publishing Corporation, New York, 1990.
[150] E. L. Porteus. Numerical comparisons of inventory policies for periodic review systems. Operations Research, 33( I): 134--152, January/February 1985.
[151] E. L. Porteus. Stochastic inventory theory. In Heyman and Sobel [90], pages 605-652.
[152] N. U. Prabhu. Stochastic Processes. Macmillan, New York, 1965.
[153] A. A. B. Pritsker, J. J. O'Reilly, and D. K. LaVal. Simulation with VISual SLAM and AweSim. John Wiley, New York, 1997.
[154] D. Redfern and E. Chandler. Maple O.D.E. Book. Springer-Verlag, New York,1996.
[155] S. M. Roberts and J. S. Shipman. Two-Point Boundary Value Problems: Shooting Methods. American Elsevier, New York, 1972.
[156] S. Ross. Applied Probability Models with Optimization Applications. Holden Day, San Francisco, Calif., 1970.
[157] S. Ross. Stochastic Processes. John Wiley, New York, 1983.
[158] S. Ross. Introduction to Probability Models. Academic Press, Orlando, Fla., 3rd edition, 1985.
[159] S. M. Ross. Introduction to Stochastic Dynamic Programming. Academic Press, New York, 1983.
[160] S. M. Ross. A Course in Simulation. Macmillan, New York, 1991.
[161] T. L. Saaty. Mathematical Methods of Operations Research. McGrawHill, New York, 1959.
(162] A. P. Sage and C. C. White. Optimum Systems Control. Prentice Hall, Englewood Cliffs, N.J., 2nd edition, 1977.
[163] i. ~ahin. Regenerative Inventory Systems: Operating Characteristics and Optimization. Springer-Verlag, New York, 1990.
[164] M. Sasieni, A. Yaspan, and L. Friedman. Operations Research: Methods and Problems. John Wiley, New York, 1959.
(165] M. Vos Savant. The Power of Logical Thinking. St. Martin's Griffin, New York,I996.
460 References
[166] H. Scarf. The optimality of (S, s) policies in the dynamic inventory problem. In K. J. Arrow, S. Karlin, and P. Suppes, editors, Mathematical Methods in the Social Sciences. Stanford University Press, Stanford, Calif., 1960.
[167] J. W. Schmidt and R. P. Davis. Foundations of Analysis in Operations Research. Academic Press, New York, 1981.
[168] L. B. Schwarz, editor. Multi-Level Production/Inventory Control Systems: Theory and Practice. Studies in the Management Sciences, Volume 16. North-Holland, Amsterdam, 1981.
[169] S. P. Sethi and G. L. Thompson. Optimal Control Theory: Applications to Management Science. Martinus NijhoffPublishing, Boston, 1981.
[I70] M. Shaked and J. G. Shantikumar. Reliability and maintainability. In Heyman and Sobel [90], pages 653-713.
[171] C. Shannon. A mathematical theory of communication. Bell System Technical Journal, 27:379--423, 1948.
[172] W. Shih. Optimal inventory policies when stockout results from defective products. International Journal of Production Research, 18:677--{)86, 1980.
[173] E. A. Silver. Establishing the reorder quantity when the amount received is uncertain. INFOR, 14:32-29, 1976.
[174] E. A. Silver. Operations research in inventory management: A review and critique. Operations Research, 29:628--{)45, 1981.
[175] E. A. Silver and R. Peterson. Decision Systems for Inventory Management and Production Planning. John Wiley, New York, 2nd edition. 1985.
[176] J. Singh. Operations Research. Penguin, Hannondsworth, England, 1968.
[177] B. D. Sivazlian and L. E. Stanfel. Analysis of Systems in Operations Research. Prentice-Hall, Englewood Cliffs, 1975.
[178] J. S. Smart. The Sonnets of Milton. Maclehose, Jackson. Glasgow, 1921.
[I79] M. J. Sobel. Optimal average cost policy for a queue with start-up and shut-down costs. Operations Research, 17:145-162, 1969.
[180] S. Stidham. L = A W: A discounted analogue and a new proof. Operations Research, 20:1115-1126,1972.
[181] D. Stirzaker. Elementary Probability. Cambridge University Press, Cambridge, 1994.
References 461
[182] H. A. Taha. Operations Research: An Introduction. Macmillan, New York, 1987.
[183] L. Takacs. Stochastic Processes. Methuen, London, 1966.
[184] H. M. Taylor. Optimal replacement under additive damage and other failure models. Naval Research Logistics Quarterly, 22:1-18,1975.
[185] R. J. Tersine. Principles of Inventory and Materials Management. North Holland, New York, 3rd edition, 1988.
[186] H. C. Tijms. Stochastic Modeling and Analysis. John Wiley, Chichester, 1986.
[187] H. C. Tijms. Stochastic Models: An Algorithmic Approach. John Wiley, Chichester, 1994.
[188] A. F. Veinott. Optimal policy for a multi-product, dynamic nonstationary inventory problem. Management Science, 12:206-222, 1965.
[189] R. G. Vickson. Lecture notes in MS 635, 1993. Department of Management Sciences, University of Waterloo.
[190] H. M. Wagner. Principles of Operations Research with Applications to Managerial Decisions. Prentice-Hall, Englewood Cliffs, N.J., 1969.
[191] H. M. Wagner and T. M. Whitin. Dynamic version of the economic lot size model. Management Science, 5:89-96, 1958.
[192] A. Waldo Sequential Analysis. John Wiley, New York, 1947. Republished by Dover in 1973.
[193] Z. K. Weng and M. Parlar. Integrating early sales with production decisions: Analysis and insights. liE 7ransactions on Scheduling and logistics, 31(11):1051-1060,1999.
[194] P. Wilmott. Derivatives: The Theory and Practice of Financial Engineering. John Wiley, Chichester, 1998.
[195] R. H. Wilson. A scientific routine for stock control. Harvard Business Review, 13:116-128, 1934.
[196] R. Wolff. Stochastic Modeling and the Theory of Queues. Prentice-Hall, Englewood Cliffs, N.J., 1989.
[197] C. A. Yano and H. L. Lee. Lot sizing with random yields: A review. 0perations Research, 43:311-334,1995.
[198] S. Zionts. Linear and Integer Programming. Prentice-Hall, Englewood Cliffs, N.J., 1974.
462 References
[199] P. H. Zipkin. Foundations of Inventory Management. McGraw-Hili, Boston, 2000.
Index
->,8 :,6 :=,8 ;,6
%1,369 %2,369
adaptive random search optimization using, 441
advertising policies, 127 algsubs, 217 all values, 41, 342, 368 alternating renewal process, 265 arrays, II assign, 11,369 assume, 8, 307 augment, 59
balance equations, 319 basic solution, 105 basic solution set, 105 basis,63 basis matrix, 105 birth and death process, 306, 377
bivariate normal plot of density, 25
Chapman-Kolmogorov equations, 276 charpoly,62 Cholesky factorization, 164 Cobb-Douglas production function,
179 coeff,217 collect, 13 combine,7 complementary slackness, 171 constraint qualification, 174 continuous-time Markov chain, 306
balance equations, 319 exponential matrix, 313 infinitesimal generator, 306 Kolmogorov differential equa-
tions, 308 limiting probabilities, 318
contourplot,22 convert, II convex function, 68, ISS convex set, 101, 154 convexity
464 Index
relation to Hessian, 160 cycle length, 425
D,45 definite, 67, 159 derivatives, 45 describe, 17 det, 56 diagonalization, 61 diff,45 difference equation
nonlinear, 229 differential equation, 15
analytic solution, 69 infolevel,31 numerical solution, 22 partial,77 savings account, 69 system
in optimal control, 73 Lancaster's, 72 numerical solution, 74
Van der Pol's numerical solution, 70
Digits, 277 display, 101 dsol ve, 23, 72, 76, 241, 395 dual,139 dual price, 131 duality, 136
economic interpretation, 138 in game theory, 143 main results, 140
dynamic inventory model dynamic programming formu
lation, 361 optimal base-stock policy, 362 optimality of (s, S) policy, 366
dynamic programming backward recursion, 195 continuous time, 211 cost-to-go (value) function, 196 decision, 194 discount factor, 211, 213 forward recursion, 195
policy, 194 stage, 194 state, 193 transformation, 194
dynamic simulation inventory model
random yield, 436
eigenvalUes, 61, 159 eigenvectors, 61 eigenvectors, 62 elementary renewal theorem, 261 empirical,91 EOQ model, 335
planned backorders, 338 equation
analytic solution, 14 difference (recurrence), 79 numerical solution, 16 solution of cubic, 38 solution of quadratic, 38
equations differential-difference, 244 homogeneous linear system, 60 linear system, 58 nonlinear system, 41
eval,8 evalf,16
int, 433 evalm, 12,55 expand,6 exponential,313 exponential matrix, 313 exporting to
FORTRAN,32 LaTeX, 32
extrema, 68 extreme point, 101
factor, 6 feasible points, 105 Fibonacci sequence, 79 finance, 33 fit, 64 fsolve, 17,40, 170
futurevalue,29
G/G/l simulation, 438
gambling model, 225 geneqns,58 generating function, 81, 85,296,302
as opposed to z-transfonn, 85 numerical inversion, 87
genfunc,298,302,388 genmatrix,107 grad,156 gradient, 67 gradient vector, 156 graphics
three-dimensional, 24 two-dimensional, 20
Hamilton-Jacobi-Bellman equation, 213
hazard rate, 240 Hessian, 66, 156 hessian, 157 histogram, 18
ifactor, 16 ilp,146 implicitdiff,48 implici tplot, 22 implied backorder costs, 343 indefinite, 157 inequal, 101 inequality
solution, 39 infeasible basic solution, 106 infinite series, 54 infolevel, 113 infolevel,30 integer programming, 145 integral, 50
multiple, 53 integration
infolevel,30 interface, 29 intersect, 10
inttrans, 242, 258 inventory, 331
Index 465
classification, 332 reasons for keeping, 332
inventory cost holding, 334 penalty, 335 procurement, 334
inventory model backorder cost function, 161 backorders, 24 constrained multi-item, 41 continuous-review, 49 lost sales, 46 periodic review, 274, 277 periodic-review
stationary distribution, 279 quantity discounts, 27 random yield
simulation, 436 stochastic, 14
inverse, 56 invlaplace,81 is,68 iso-profit lines, 103 isolate, 359
Jackson network, 398 Jacobian, 67, 95
key renewal theorem, 264 Kolmogorov differential equations
backward, 310 forward, 313
Kolmogorov-Smimov test, 426 Kuhn-Tucker conditions, 171
geometric interpretation, 173
I'Hopital's rule, 296 Lagrange multipliers, 171
economic interpretation, 181 Lagrangian dual, 186 Lagrangian function, 176 laplace, 82 Laplace transfonn, 81
466 Index
numerical inversion, 83 least squares, 64 leastsquare,64 Leibniz's rule, 47, 358 limit, 44 limiting (steady-state) probabilities,
278 linalg, 55, 302 linear programming, 19
degeneracy, 119 graphical solution, 100 infeasibility, 118 mixed constraints, 116 number of iterations, 107 simplex, 104 transportation model, 121 unbounded solution, 119
linear system homogeneous, 60 solution, II
linear-quadratic control, 187,201 infinite stage, 207 relation to nonlinear program-
ming,204 linsol ve, 58 lists, to location problem, 163, 169
M(t)/M(t)/S/N dynamic service rate control, 406
M/Ek/ I,299 M/ M/l, 298, 378
controlled arrivals, 404 M/M/I/I
transient solution, 390 M/M/l/K,382 M/M/c,383 M/M/oo
transient solution, 391 M/M/oo,78 makeproc,79 map, 12 Maple
books on, 6 help facility, 5
Internet resources, xiii knowledge base, xi Release 5.1 and 6, xiii users, xi
Markov chain, 61, 272 aperiodic, 288 communicating states, 287 equivalence class, 288 ergodic, 290 first passage time probability, 288 imbedded, 293 irreducible, 288 machine maintenance, 283 Markovian property, 273 mean recurrence time, 290 null recurrent, 290 pathological case, 286 period of a state, 288 positive recurrent, 290 reachable states, 287 recurrent state, 288 transient behavior, 301 transient state, 288
matrix multiplication, 55 matrix operations, 55 matrixDE,311 Milton's sonnets, 375 minus, 280 mixed-congruential method, 424 Monte Carlo simulation, 432
numerical evaluation of definite integrals, 432
multiply, 129 MX /M/I,387 myopic solution, 227
negative definite, 157 negative semidefinite, 157 nonbasic variables, 105 nonhomogeneous Poisson process, 247 nonlinear programming, 153
duality theorem, 186 NONNEGATIVE, 126 nops,11 normal,7
odetest, 69, 72 op, 10,30 open-loop decision, 220 operations research
definition, 2 journals, 2 origins, 1 without mathematics, 37
optimal stopping, 228 infinite stage, 230
option pricing blackscholes,34
orientation in plot3d, 26
output=listprocedure, 410
partial differential equation, 77 partial fraction expansion, 82 pdsolve,77 piecewise, 27, 222, 347, 409 piecewise-quadratic cost, 189 plot,249 plot3d, 25, 282 Poisson process, 243,308
compound, 252 nonhomogeneous, 247
Pollaczek-Khinchine formula, 298 Pontryagin's principle, 408 portfolio selection, 154, 171 positive definite, 157 positive definiteness, 67 positive semidefinite, 157 principal minor, 158 principle of optimality, 195 probabilistic inventory model
continuous review with backorders
approximate formulation, 349 exact formulation, 354
one period (newsvendor), 358 yield randomness, 367
probability conditional, 277 unconditional, 277
programming, 32
Index 467
Pushkin, 273
quadratic form, 157 quantity discounts, 346 queueing networks, 394 queueing notation, 376 queueing system
optimization, 401
random, 420 uniform, 426
random variable beta, 231 binomial, 418
moment generating function, 55
simulation, 420 Cauchy, 94 continuous
pdf, cdf, icdf, 89 discrete
pf, dcdf, idcdf, 89 Erlang, 242
density, 246, 299 exponential, 14,52,238
memory less property, 239 geometric, 55 normal, 16, 89
mean and variance, 92 Poisson, 90 triangular, 28 uniform, 423 unit normal, 52 Weibull, 241
plot of density, 20 random variate generation, 18
exponential, 429 inverse transform method, 430 random, 430
random vector joint density, 95
random walk, 272 randvector, 129 rank,58 renewal density, 259
468 Index
renewal equation, 262 renewal function, 259 renewal process, 256 renewal reward theorem, 268
use in inventory models, 335 rgf _encode, 85 rgf _expand, 85 rgf _expand, 303 rsolve, 79, 229, 383 Runge-Kutta method, 395
saddle-point conditions, 186 select, 437 sensitivity analysis
adding a new decision variable, 135
change in objective function, 134 change in RHS values, 131
serial queue with blocking, 394 sets, 10 simplex, 19
final table, 115 simplex, 113
not useful in integer programming,145
simplify, 7, 370 simulation, 417
number of runs, 421 programs, 418 runlength,421
slack variable, 104 solve, 16,171,181 sprint, 315 stagecoach problem, 197 statevalf,89 static simulation
car and goats problem, 434 s ta ts, 17, 64,426
distributions, 430 statsplots,18 stochastic matrix, 272 stochastic process, 237 strong law oflarge numbers, 433 student, 248 subs,8
successive approximations, 207 sum, 170,385
tallyinto, 18 time~ependentarrivalrate, 75 transform, 18 transportation queueing process, 402 type=nurneric, 23, 70, 76
unapply,8, 10,304,355 union, 10,280
work force planning model, 219
zero-sum game solution using linear program
ming, 124 ztrans,85