A Survey of the Stete of the Art in Dynamic Programming

General

• Awate , Prakash G. , “ A Note on ‘Markovian Decision Models for Reject Allowance Problems’ ” Man. Sci.: Theory , 19 , pp. 339 – 339 ( 1972, 5, Jan. ).
   Web of Science ®Google Scholar
• Beebe , J. H. , Beightler , C. S. , and Stark , J. P. , “ Stochastic-Optimization of Production Planning ,” Opns. Res. , 16 , pp. 799 – 799 8 ( 1968, 4, July-Aug. ).
   Google Scholar
• Beesack , Paul R. , “ A Finite Horizon Dynamic Inventory Model with a Stockout Constraint ,” Man. Sci. , 13 , pp. 618 – 630 ( 1967, 9, May ).
   Google Scholar
• Bellman , R. , Dynamic Programming , Princeton University Press ( 1957 ) .
   Google Scholar
• Bellman , R. , “ On a Routing Problem ,” Quar. Appl. Math. , 16 ( 1958 ).
   Google Scholar
• Bellman , R. and Dreyfus , S. , Applied Dynamic Programming , Princeton University Press ( 1962 ) .
   Google Scholar
• Benes , V. E. , “ Programming and Control Problems Arising from Optimal Routing in Telephone Networks ,” The Bell System Technical Journal , 95 , pp. 1373 – 1373 ( 1966,9, Nov. ).
   Google Scholar
• Bickel , Samuel H. , “ Minimum Variance and Optimal Asympotic Portfolios ,” Man. Sci. : Theory, 16 , pp. 221 – 221 ( 1969, 3, Nov. ).
   Google Scholar
• Bierman, Jr. , Harold , and Hausman , Warren H. , “ The Credit Granting Decision ,” Man. Sci.: Application , 16 , pp. B-519-B-532 ( 1970, 8, April ).
   Google Scholar
• Blackwell , D. , “ Discrete Dynamic Programming ,” Annals Math. Stat. , 33 , pp. 719 – 719 ( 1962 ).
   Google Scholar
• Blackwell , D. , “ Discounted Dynamic Programming ,” Annals Math. Stat. , 36 ( 1965 ).
   Google Scholar
• Boltyanskii , V. G. , “ Sufficient Conditions for Optimality and the Justification of the Dynamic Programming Method ,” SZAMJ. Control , 4 , pp. 326 – 326 ( 1966 ).
   Google Scholar
• Boughton , W. C. , “ Optimizing the Gradients of Channels by Dynamic Programming ,” J. of the Institution of Engineers , 38 , pp. 303 – 303 ( 1966,12, Dec. ).
   Google Scholar
• Briskin , Lawrence E. , “ Selecting Delivery Dates in the Tanker Scheduling Problem ,” Man Sci. , 12 , pp. B-224-B-235 ( 1966, 6, Feb. ).
   Google Scholar
• Carter , Phillip L. , Bayesian Approach to Quality Control ,” Man Sci.: Theory , 18 , pp. 647 – 647 ( 1972, 11, July ).
   Web of Science ®Google Scholar
• Collins , D. C. , “ Reduction of Dimensionality in Dynamic Programming via the Method of Diagonal Decomposition ,” J. Math. Analysis and Appl. , 31 , pp. 223 – 223 ( 1970 ).
   Google Scholar
• Collins , D. C. , “ Terminal State Dynamic Programming for Differential Difference Equations ,” J. Math. Analysis and Appl. , 31 , pp. 487 – 487 ( 1970 ).
   Google Scholar
• Cozzolino , John M. , “ Optimal Scheduling for Investment of Excess Cash ,” Decision Sciences , 2 , pp. 265 – 265 ( 1971, 3, July ).
   Google Scholar
• Denardo , Eric V. , “ Contraction Mappings in the Theory Underlying Dynamic Programming ,” SIAM Review , 9 , pp. 165 – 165 ( 1967,2, April ).
   Web of Science ®Google Scholar
• Denardo , E. V. and Mitten, L. G. , “ Elements of Sequential Decision Processes ,” J. Ind. Engr. , 18 , pp. 106 – 106 12 ( 1967 ).
   Web of Science ®Google Scholar
• Derman , Cyrus , Finite State Markovian Decision Processes , Academic Press ( 1970 ) .
   Google Scholar
• Dijkstra , E. W. , “ A Note on Two Problems in Connection with Graphs ,” Numerische Mathematick , 1 ( 1959 ).
   Google Scholar
• Eckles , James E. , “ Optimum Maintenance with Incomplete Information ,” Opns. Res. , 16 , pp. 1058 – 1058 ( 1968, 5, Sept.-Oct. ).
   Web of Science ®Google Scholar
• Elmaghraby , S. E. , “ The Concept of ‘State’ in Discrete Dynamic Programming ,” J. Math. Analysis and Appl. , 43 , pp. 642 – 642 ( 1973 ).
   Google Scholar
• Elmaghraby , Salah E. , and Bawle , Vishwas Y. , “ Optimization of Batch Ordering Under Deterministic Variable Demand ,” Man. Sci.: Theory , 18 , pp. 508 – 508 ( 1972, 9, May ).
   Web of Science ®Google Scholar
• Erlenkotter , Donald , “ Sequencing Expansion Projects ,” Opns. Rer , 21 , pp. 542 – 542 ( 1973,2, March-April ).
   Web of Science ®Google Scholar
• Esogbue , A. O. , and Marks , B. R. , “ Nonserial Dynamic Programming-A Survey ,” Operational Research Quarterly , 25 , pp. 253 – 253 ( 1974 ).
   Google Scholar
• Evans , Richard V. , “ Sales and Restocking Policies in a Single Item Inventory System ,” Man. Sci.: Theory , 14 , pp. 463 – 463 ( 1968,7, March ).
   Web of Science ®Google Scholar
• Evans , Richard V. , “ Optimality of (s, S) Policies when Set-Up Costs Vary ,” Opsearch , 6 , pp. 25 – 25 ( 1969, 1, March ).
   Google Scholar
• Falkner , Charles H. , “ Jointly Optimal Deterministic Inventory and Replacement Policies ,” Man. Sci.: Theory , 16 , pp. 622- 635 ( 1970,9, May ).
   Google Scholar
• Fine , F. S. , and Bankoff , S. G. , “ Second Variational Methods for Optimization of Discrete Systems ,” Industrial & Engineering Chemistry Fundamentals , 6 , pp. 293 – 293 ( 1967, 2, May ).
   Google Scholar
• Florian , Michael , and Klein , Morton , “ Deterministic Production Planning and Concave Costs and Capacity Constraints ,” Man. Sci.: Theory , 18 , pp. 12 – 12 ( 1971, 1, Sept. ).
   Web of Science ®Google Scholar
• Fox , B. L. , “ Finite State Approximations t o Denumerable-State Dynamic Programs ,” J. Math. Analysis and Applications , 34 , pp. 665 – 665 ( 1971 ).
   Web of Science ®Google Scholar
• Fox , B. L. , “ Discretizing Dynamic Programs ,” J. Opt. Theory and Appl. , 11 , pp. 228 – 228 ( 1973 ).
   Google Scholar
• Freimer , Marshall , Rao , Mendu R. , and Weingartner , Martin H. , “ Note on Municipal Bond Coupon Schedules with Limitations on the Number of Coupons ,” Man. Sci. , 19 , pp. 379- 380 ( 1972, 4, Dec. ).
   Google Scholar
• Gilmore , P. C. and Gomory , R. E. , “ Multi-Stage Cutting Stock Problems of Two or More Dimensions ,” Opns. Res. , 13 , pp. 94 – 94 ( 1965 ).
   Web of Science ®Google Scholar
• Glassey , C. R. , “ Minimum Change-Over Scheduling of Several Products on One Machine ,” Opns. Res. , 16 , pp. 342 – 342 ( 1968, 2, March-April ).
   Web of Science ®Google Scholar
• Gomory , R. E. , “ On the Relation Between Integer and Non- Integer Solutions t o Linear Programs ,” Proc. Nut. Acad. Sci. , 53 , 260–265.
   PubMedGoogle Scholar
• Greenberg , H. J. , “ Dynamic Programming with Linear Uncertainty ,” Opns, Res. , 16 , pp. 1100 – 1100 ( 1968, 6, Nov.-Dec. ).
   Google Scholar
• Grinold , Richard C. , “ A Generalized Discrete Dynamic Programming Model ,” Man. Sci. , 20 , pp. 1092 – 1092 ( 1974, 7, March ).
   Google Scholar
• Hahn , Susan G. , “ On the Optimal Cutting of Defective Sheets ,” Opns. Res. , 16 , pp. 1100 – 1100 114 ( 1968, 6, Nov.-Dec. ).
   Web of Science ®Google Scholar
• Hastings , N. A. J. , “ Some Notes on Dynamic Programming and Replacement ,” Operat. Res. Quart. , 19 , pp. 453 – 453 ( 1968,4, Dec. ).
   Google Scholar
• Hausman , Warren H. , and Thomas , Joseph L. , “ Inventory Control with Probabilistic Demand and Periodic Withdrawals ,” Man. Sci.: Theory , 18 , pp. 265 – 265 ( 1972,5, Jan. ).
   Google Scholar
• Held , M. , and Karp , R. M. , “ A Dynamic Programming Approach to Sequencing Problems ,” J. SIAM , 10 , pp. 196- 210 ( 1962 ).
   Google Scholar
• Howard , R. A. , Dynamic Programmingand Markov Processes , Technology Press and John Wiley and Sons ( 1960 ) .
   Google Scholar
• Howard , R. A. , Dynamic Probabilistic Systems , 2 , John Wiley and Sons ( 1970 ).
   Google Scholar
• Hordijk , Arie , and Tijms , Henk , “ Convergence Results and Approximations for Optimal (s, S) Policies ,” Man. Sci. , 20 , pp. 1432 – 1432 ( 1974, 11, July ).
   Google Scholar
• Hyman , Warren , and Gordon , Larry , “ Commercial Airline Scheduling Technique ,” Transportation Research , 2 , pp. 23- 29 ( 1968, 1, March ).
   Google Scholar
• Ingall , Edward , “ Optimal Continuous Review Policies for Two Product Inventory Systems with Joint Setup Costs ,” Man. Sci.: Theory , 15 , pp. 278 – 278 ( 1969,5, Jan. ).
   Google Scholar
• Jaquette , David L. , “ A Discrete-Time Population-Control Model with Setup Cost ,” Opns. Res. , 22 , pp. 298 – 298 ( 1974, 2, March-April ).
   Google Scholar
• Jensen , Paul A. , “ Optimization of Series-Parallel-Series Networks ,” Opns. Res. , 18 , pp. 471 – 471 ( 1970, 3, May-June ).
   Web of Science ®Google Scholar
• Jensen , Paul A. , “ Optimum Network Partitioning ,” Opns. Res. , 19 , pp. 916 – 916 ( 1971, 3, May-June ).
   Google Scholar
• Johnson , Ellis L. , Optimality and Computation of (s, S) Policies in the Multi-Item Infinite Horizon Inventory Problem ,” Man. Sci. , 13 , pp. 475 – 475 ( 1967, 7, March ).
   Google Scholar
• Karp , R. M. and Held , M. , “ Finite-State Processes and Dynamic Programming ,” SIAMJ. Appl. Math. , 15 , 3 ( 1967 ).
   Google Scholar
• Larson , R. E. , State Increment Dynamic Programming , American Elsevier, N. Y. ( 1968 ) .
   Google Scholar
• Luss , Hanan , and Kander , Zvi , “ Inspection Policies when Duration of Checking is Non-Negligible ,” Operat. Res. Quart. , 25 , pp. 299 – 299 ( 1974, 2, June ).
   Google Scholar
• MacQueen , J. , “ A Test for Suboptimal Actions in Markovian Decision Problems ,” Opns. Res. , 15 , pp. 559 – 559 ( 1967, 3, May-June ).
   Google Scholar
• Magazine , M. , Optimal Policies for Queueing Systems with Periodic Review , Ph.D. Thesis, University of Florida ( 1969 ) .
   Google Scholar
• Meyer , C. F. , and Newett , R. J. , “ Dynamic Programming for Feedlot Optimization ,” Man. Sci.: Application , 16 , pp. B-410-B-426 ( 1970,6, Feb. ).
   Google Scholar
• Mitten , L. G. , “ Composition Principles for the Synthesis of Optimal Multi-stage Processes ,” Operations Research , 12 ( 1964 ).
   Google Scholar
• Mitten , L. G. , “ Preference Order Dynamic Programming ,” Man. Sci. , 21 , pp. 43 – 43 ( 1974, 1, September ).
   Web of Science ®Google Scholar
• Morin , T. L. and Esogbue , A. O. , “ The Imbedded State Space Approach to Reducing Dimensionality in Dynamic Programs of Higher Dimensions ,” J. Math. Analysis and Appl. , 148 , pp. 801 – 801 ( 1974 ).
   Google Scholar
• Morton , Thomas E. , “ On the Asymptotic Convergence Rate of Cost Differences for Markovian Decision Processes ,” Opns. Res. , 19 , pp. 244 – 244 ( 1971, 1, Jan.-Feb. ).
   Web of Science ®Google Scholar
• Nemhauser , G. , Introduction t o Dynamic Programming , John Wiley and Sons ( 1966 ) .
   Google Scholar
• Nemhauser , George L. , “ Scheduling Local and Express Service ,” Trans. Sci. , 3 , pp. 164 – 164 ( 1969, 2, May ).
   Google Scholar
• Nemhauser , George L., and Ullman, Z. , “ Discrete Dynamic Programming and Capital Allocation ,” Man Sci.: Theory , 15 , pp. 494 – 494 ( 1969,9, May ).
   Web of Science ®Google Scholar
• Nemhauser , George L. , and P. Lu Yu , “ A Problem in Bulk Service Scheduling ,” Opns. Res. , 20 , pp. 813 – 813 ( 1972, 4, July-Aug. ).
   Web of Science ®Google Scholar
• Odoni , A. , “ On Finding the Maximal Gain for Markovian Decision Processes ,” Opns. Res. , 17 , pp. 857 – 857 ( 1969, 5, Sept.-Oct. ).
   Web of Science ®Google Scholar
• Peterson , E. R. , “ A Dynamic Programming Model for the Expansion of Electric Power Systems ,” Man. Sci. , 10 , pp. 656 – 656 ( 1973,4, Dec. ).
   Google Scholar
• Petrovic , Radivoj , “ Optimization of Resource Allocation in Project Planning ,” Opns. Res. , 16 , pp. 559 – 559 ( 1968, 3, May-June ).
   Web of Science ®Google Scholar
• Pontryagin , L. S. , Boltyanskii , V. G. , Gamkrelidze , R. V. , and Mishchenko , E. F. , The Mathematical Theory of Optimal Processes , (Translated by K. N. Trirogoff) Interscience, New York ( 1957 ) .
   Google Scholar
• Porteus , E. L. , “ Some Bounds for Discounted Sequential Decision Progress ,” Man. Sci. , 18 , pp. 7 – 7 ( 1971 ).
   Web of Science ®Google Scholar
• Prochan , F. and Bray , T. A. , “ Optimal Redundancy under Multiple Constraints ,” Opns. Res. , 13 , pp. 800 – 800 ( 1965 ).
   Google Scholar
• Powell , Bruce A. , “ Optimal Elevator Banking under Heavy Up-Traffic ,” Trans. Sci. , 5 , pp. 109 – 109 ( 1971, 2, May ).
   Google Scholar
• Pyle, III , E. B. , Douglas , B. , Ebright , G. W. , Westlake , W. J. , and Bender , A. D . , “ Scientific Manpower Allocation to New Drug Screening Programs ,” Man. Sci. , 19 , pp. 1433 – 1433 ( 1973, 12, Aug. ).
   Google Scholar
• Rao , Vithala R. , and Thomas , Joseph L. , “ Dynamic Models for Sales Promotion Policies ,” Operat. Res. Quart. , 24 , pp. 403 – 403 ( 1973, 3, Sept. ).
   Google Scholar
• Roman , Ronald J. , “ Mine-Mill Production Scheduling by Dynamic Programming ,” Operat. Res. Quart. , 22 , pp. 319- 328 ( 1971,4, Dec. ).
   Google Scholar
• Ross , S. H. , Applied Probability Models with Optimization Applications , Holden-Day, San Francisco ( 1970 ) .
   Google Scholar
• Rosseel , Marc , “ Comments on a Paper by Romesh Saigal: ‘A Constrained Shortest Route Problem’ ” Opns. Res. , 16 , pp. 1232 – 1232 ( 1968, 6, Nov.-Dec. ).
   Google Scholar
• Rothstein , Marvin , “ An Ailine Overbooking Model ,” Trans. Sci. , 5 , pp. 180 – 180 ( 1971, 2, May ).
   Google Scholar
• Rutenberg , David P. , “ Design Commonality to Reduce Multi-Item Inventory: Optimal Depth of a Product Line ,” Opns. Res. , 19 , pp. 491 – 491 ( 1971, 2, March-April ).
   Web of Science ®Google Scholar
• Schweitzer , Paul J. , “ Multiple Policy Improvements in Undiscounted Markov Renewal Programming ,” Opns. Res. , 19 , pp. 784 – 784 ( 1971, 3, May-June ).
   Web of Science ®Google Scholar
• Shapiro , Jeremy F. , “ Dynamic Programming Algorithm for the Integer Programming Problem-1 : The Integer Programming Problem Viewed as a Knapsack Type Problem ,” Opns. Res. , 16 , pp. 103 – 103 ( 1968,1, Jan.-Feb. ).
   Google Scholar
• Shapiro , Jeremy F. , “ Turnpike Theorems for Integer Programming Problems ,” Opns. Res. , 18 , pp. 432 – 432 ( 1970, 3, May-June ).
   Google Scholar
• Sreedharan , V. P. , and Wein , H. H. , “ A Stochastic, Multi-stage, Multiproduct Investment Model ,” SIAM J. Appl. Math. , 15 , pp. 347 – 347 ( 1967, 2, March ).
   Google Scholar
• Veinott, Jr. , Arthur F. , “ On Finding Optimal Policies in Discrete Dynamic Programming with No Discounting ,” Ann. Math;l. Stat. , 37 , pp. 1284 – 1284 ( 1966 ).
   Google Scholar
• Veinott, Jr. , Arthur F. , “ Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems ,” Opns. Res. , 17 , pp. 262 – 262 ( 1969, 2, March- April ).
   Google Scholar
• Weingartner , H. M. , “ Capital Budgeting of Interrelated Problems: Survey and Synthesis ,” Man. Sci. , 12 , pp. 485 – 485 ( 1966 ).
   Google Scholar
• Weingartner , H. Martin , “ Municipal Bond Coupon Schedules with Limitations on the Number of Coupons ,” Man. Sci. , 19 , pp. 369 – 369 ( 1972,4, Dec. ).
   Google Scholar
• White , D. M. , “ Dynamic Programming and Probabilistic Con- straints ,” Opns. Res. , 22 , pp. 654 – 654 ( 1974, 3, May-June ).
   Google Scholar
• Wilkinson , Cliff , and Gupta , Shiv. K. , “ Allocating Promo- tional Effort to Competing Activities: A Dynamic Programming Approach ,” Proceedings of the Fifth International Conference on Operational Research , pp. 41 9-432 ( June, 1969 ).
   Google Scholar
• Wolsey , Laurence A. , “ Generalized Dynamic Programming Methods in Integer Programming ,” Math. Prog. , 4 , pp. 222- 232 ( 1973,2, April ).
   Google Scholar
• Wong , Peter J. , and Luenberger , David G. , “ Reducing the Memory Requirements ,” Opns. Res. , 16 , pp. 115 – 115 ( 1968, 6, Nov.-Dec. ).
   Google Scholar
• Wong , Peter , “ An Approach to Reducing the Computing Time for Dynamic Programming ,” Opns. Res. , 18 , pp. 181- 185 ( 1970, 1, Jan.-Feb. ).
   Google Scholar
• Wong , Peter , “ A New Decomposition Procedure for Dynamic Programming ,” Opns. Res. , 18 , pp. 119 – 119 ( 1970, 1, Jan.- Feb. ).
   Google Scholar
• Woodman , R. D. , “ Replacement Policies for Components that Deteriorate ,” Operat. Res. Quart. , 18 , pp. 267 – 267 ( 1967, 3, Sept. ).
   Google Scholar
• Young , Dennis R. , “ Scheduling a Fixed-Schedule, Common Carrier Passenger Transportation System ,” Trans. Sci , 4 , pp. 243 – 243 ( 1970, 3, Aug. ).
   Google Scholar
• Zacks , S. , “ A Two-Echelon Multi-Station Inventory Model for Navy Applications ,” Naval Research Logistics Quarterly , 17 , pp. 79 – 79 ( 1970,1, March ).
   Google Scholar