Dynamic Programming Approximations for a Stochastic Inventory Routing Problem

References

• Anily S., Federgruen A. One warehouse multiple retailer systems with vehicle routing costs. Management Sci. (1990) 36:92–114Link, Google Scholar
• Anily S., Federgruen A. Rejoinder to comments on one warehouse multiple retailer systems with vehicle routing costs. Management Sci. (1991) 37:1497–1499Link, Google Scholar
• Anily S., Federgruen A. Two-echelon distribution systems with vehicle routing costs and central inventories. Oper. Res. (1993) 41:37–47Link, Google Scholar
• Bard J. F., Huang L., Jaillet P., Dror M. A decomposition approach to the inventory routing problem with satellite facilities. Transportation Sci. (1998) 32:189–203Link, Google Scholar
• Barnes-Schuster D., Bassok Y. Direct shipping and the dynamic single-depot/multi-retailer inventory system. Eur. J. Oper. Res. (1997) 101:509–518Crossref, Google Scholar
• Bassok Y., Ernst R. Dynamic allocations for multi-product distribution. Transportation Sci. (1995) 29:256–266Link, Google Scholar
• Bell W., Dalberto L., Fisher M., Greenfield A., Jaikumar R., Kedia P., Mack R., Prutzman P. Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces (1983) 13:4–23Link, Google Scholar
• Bellman R., Dreyfus S. Functional approximations and dynamic programming. Math. Tables Other Aids Comput. (1959) 13:247–251Crossref, Google Scholar
• Bellman R., Kalaba R., Kotkin B. Polynomial approximation —A new computational technique in dynamic programming: Allocation processes. Math. Comput. (1963) 17:155–161Google Scholar
• Bertazzi L., Paletta G., Speranza M. G. Deterministic order-up-to level policies in an inventory routing problem. Transportation Sci. (2002) 36:119–132Link, Google Scholar
• Bertsekas D. P. Convergence of discretization procedures in dynamic programming. IEEE Trans. Auto. Control (1975) AC-20:415–419Crossref, Google Scholar
• Bertsekas D. P. Dynamic Programming and Optimal Control (1995) (Athena Scientific, Belmont MA) Google Scholar
• Bertsekas D. P., Shreve S. E.Stochastic Optimal Control: The Discrete Time Case (1978) (Academic Press, New York) Google Scholar
• Bertsekas D. P., Tsitsiklis J. N.Neuro-Dynamic Programming (1996) (Athena Scientific, New York) Google Scholar
• Bramel J., Simchi-Levi D. A location based heuristic for general routing problems. Oper. Res. (1995) 43:649–660Link, Google Scholar
• Burns L. D., Hall R. W., Blumenfeld D. E., Daganzo C. F. Distribution strategies that minimize transportation and inventory costs. Oper. Res. (1985) 33:469–490Link, Google Scholar
• Çetinkaya S., Lee C. Y. Stock replenishment and shipment scheduling for vendor managed inventory systems. Management Sci. (2000) 46:217–232Link, Google Scholar
• Chan L. M. A., Federgruen A., Simchi-Levi D. Probabilistic analysis and practical algorithms for inventory-routing models. Oper. Res. (1998) 46:96–106Link, Google Scholar
• Chang C. S. Discrete-sample curve fitting using Chebyshev polynomials and the approximate determination of optimal trajectories via dynamic programming. IEEE Trans. Auto. Control (1966) AC-11:116–118Crossref, Google Scholar
• Chen V. C. P., Ruppert D., Shoemaker C. A. Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming. Oper. Res. (1999) 47:38–53Link, Google Scholar
• Chien T. W., Balakrishnan A., Wong R. T. An integrated inventory allocation and vehicle routing problem. Transportation Sci. (1989) 23:67–76Link, Google Scholar
• Chow C. S., Tsitsiklis J. N. An optimal one-way multigrid algorithm for discrete-time stochastic control. IEEE Trans. Auto. Control (1991) AC-36:898–914Crossref, Google Scholar
• Christiansen M. Decomposition of a combined inventory and time constrained ship routing problem. Transportation Sci. (1999) 33:3–16Link, Google Scholar
• Christiansen M., Nygreen B. A method for solving ship routing problems with inventory constraints. Ann. Oper. Res. (1998a) 81:357–378Crossref, Google Scholar
• Christiansen M., Nygreen B. Modelling path flows for a combined ship routing and inventory management problem. Ann. Oper. Res. (1998b) 82:391–412Crossref, Google Scholar
• Collins D. C. Reduction of dimensionality in dynamic programming via the method of diagonal decomposition. J. Math. Anal. Appl. (1970) 31:223–234Crossref, Google Scholar
• Collins D. C., Angel E. S. The diagonal decomposition technique applied to the dynamic programming solution of elliptic partial differential equations. J. Math. Anal. Appl. (1971) 33:467–481Crossref, Google Scholar
• Collins D. C., Lew A. A dimensional approximation in dynamic programming by structural decomposition. J. Math. Anal. Appl. (1970) 30:375–384Crossref, Google Scholar
• Cook W., Rohe A. Computing minimum-weight perfect matchings. (1998) . PreprintGoogle Scholar
• Courtois P. J. Decomposability: Queueing and Computer System Applications (1977) (Academic Press, New York) Google Scholar
• Courtois P. J., Semal P., Iazeolla G., Courtois P. J., Hordijk A. Error bounds for the analysis by decomposition of non-negative matrices. Mathematical Computer Performance and Reliability (1984) (Elsevier Science Publishers B.V., Amsterdam, The Netherlands) 209–224Chapter 2.2Google Scholar
• Daniel J. W. Splines and efficiency in dynamic programming. J. Math. Anal. Appl. (1976) 54:402–407Crossref, Google Scholar
• De Farias D. P., Van Roy B. On the existence of fixed points for approximate value iteration and temporal-difference learning. J. Optim. Theory Appl. (2000) 105:589–608Crossref, Google Scholar
• Dror M., Ball M. Inventory/routing: Reduction from an annual to a short period problem. Naval Res. Logist. Quart. (1987) 34:891–905Crossref, Google Scholar
• Dror M., Levy L. Vehicle routing improvement algorithms: Comparison of a “greedy” and a matching implementation for inventory routing. Comput. Oper. Res. (1986) 13:33–45Crossref, Google Scholar
• Dror M., Ball M., Golden B. A computational comparison of algorithms for the inventory routing problem. Ann. Oper. Res. (1985) 4:3–23Crossref, Google Scholar
• Edmonds J. Maximum matching and a polyhedron with 0,1-vertices. J. Res. National Bureau Standards (1965a) 69B:125–130Crossref, Google Scholar
• Edmonds J. Paths trees and flowers. Canadian J. Math. (1965b) 17:449–467Crossref, Google Scholar
• Federgruen A., Zipkin P. A combined vehicle routing and inventory allocation problem. Oper. Res. (1984) 32:1019–1037Link, Google Scholar
• Fox B. L. Discretizing dynamic programs. J. Optim. Theory Appl. (1973) 11:228–234Crossref, Google Scholar
• Gabow H. N. Data structures for weighted matching and nearest common ancestors with linking. Proc. 1st Annual ACM-SIAM Sympos (1990) (Society for Industrial and Applied Mathematics, Philadelphia, PA) 434–443Discrete AlgorithmsGoogle Scholar
• Gallego G., Simchi-Levi D. On the effectiveness of direct shipping strategy for the one-warehouse multi-retailer Rsystems. Management Sci. (1990) 36:240–243Link, Google Scholar
• Gaur V., Fisher M. L. An optimization algorithm for the joint vehicle routing and inventory control problem and its implementation at a large supermarket chain. (2002) . PreprintGoogle Scholar
• Golden B., Assad A., Dahl R. Analysis of a large scale vehicle routing problem with an inventory component. Large Scale Systems (1984) 7:181–190Google Scholar
• Haurie A., L'Ecuyer P. Approximation and bounds in discrete event dynamic programming. IEEE Trans. Auto. Control (1986) AC-31:227–235Crossref, Google Scholar
• Herer Y., Roundy R. Heuristics for a one-warehouse multiretailer distribution problem with performance bounds. Oper. Res. (1997) 45:102–115Link, Google Scholar
• Hinderer K. Estimates for finite-stage dynamic programs. J. Math. Anal. Appl. (1976) 55:207–238Crossref, Google Scholar
• Hinderer K, Puterman M.L. On approximate solutions of finite-stage dynamic programs. Dynamic Programmming and its Applications (1978) (Academic Press, New York) 289–317Google Scholar
• Hinderer K., Hübner G., Tijms H.C., Wessels J. On exact and approximate solutions of unstructured finite-stage dynamic programs. Markov Decision Theory: Proc. Adv. Sem. Markov Decision Theory (1977) (Amsterdam, The Netherlands)57–76September 13–17, 1976Google Scholar
• Kleywegt A. J., Nori V. S., Savelsbergh M. W. P. The stochastic inventory routing problem with direct deliveries. Transportation Sci. (2002) 36:94–118Link, Google Scholar
• Kushner H. J. Numerical methods for continuous control problems in continuous time. SIAM J. Control Optim. (1990) 28:999–1048Crossref, Google Scholar
• Kushner H. J., Dupuis P.Numerical Methods for Stochastic Control Problems in Continuous Time (1992) (Springer-Verlag, New York) Crossref, Google Scholar
• Larson R. Transporting sludge to the 106 mile site: An inventory/ routing model for fleet sizing and logistics system design. Transportation Sci. (1988) 22:186–198Link, Google Scholar
• Meyn S. P., Tweedie R. L.Markov Chains and Stochastic Stability (1993) (Springer-Verlag, London, U.K.) Crossref, Google Scholar
• Minkoff A. S. A Markov decision model and decomposition heuristic for dynamic vehicle dispatching. Oper. Res. (1993) 41:77–90Link, Google Scholar
• Morin T, Puterman M.L. Computational advances in dynamic programming. Dynamic Programmming and its Applications (1978) (Academic Press, New York) 53–90Google Scholar
• Nelson B. L., Matejcik F. J. Using common random numbers for indifference-zone selection and multiple comparisons in simulation. Management Sci. (1995) 41:1935–1945Link, Google Scholar
• Powell W. B., Carvalho T. A. Dynamic control of logistics queueing networks for large-scale fleet management. Transportation Sci. (1998) 32:90–109Link, Google Scholar
• Puterman M. L. Markov Decision Processes (1994) (John Wiley & Sons, Inc., New York) Crossref, Google Scholar
• Reiman M. I., Rubio R., Wein L. M. Heavy traffic analysis of the dynamic stochastic inventory-routing problem. Transportation Sci. (1999) 33:361–380Link, Google Scholar
• Rogers D. F., Plante R. D., Wong R. T., Evans J. R. Aggregation and disaggregation techniques and methodology in optimization. Oper. Res. (1991) 39:553–582Link, Google Scholar
• Schweitzer P. J., Seidman A. Generalized polynomial approximations in Markovian decision processes. J. Math. Anal. Appl. (1985) 110:568–582Crossref, Google Scholar
• Secomandi N. Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands. Comput. Oper. Res. (2000) 27:1201–1225Crossref, Google Scholar
• Stewart G. W, Iazeolla G., Courtois P. J., Hordijk A. On the structure of nearly uncoupled Markov chains. Mathematical Computer Performance and Reliability (1984) (Elsevier Science Publishers B.V., Amsterdam, The Netherlands) 287–302Chapter 2.7Google Scholar
• Sutton R. S., Barto A. G.Reinforcement Learning: An Introduction (1998) (MIT Press, Cambridge, MA) Google Scholar
• Topkis D. M. Optimal ordering and rationing policies in a nonstationary dynamic inventory model with n demand classes. Management Sci. (1968) 15:160–176Link, Google Scholar
• Trudeau P., Dror M. Stochastic inventory routing: Route design with stockouts and route failures. Transportation Sci. (1992) 26:171–184Link, Google Scholar
• Tsitsiklis J. N., Van Roy B. Feature-based methods for large-scale dynamic programming. Machine Learning (1996) 22:59–94Crossref, Google Scholar
• Tsitsiklis J. N., Van Roy B. Average cost temporal-difference learning. Automatica (1999a) 35:1799–1808Crossref, Google Scholar
• Tsitsiklis J. N., Van Roy B. Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional derivatives. IEEE Trans. Auto. Control (1999b) 44:1840–1851Crossref, Google Scholar
• Van Roy B., Tsitsiklis J. N. Stable linear approximations to dynamic programming for stochastic control problems with local transitions. Advances in Neural Information Processing Systems (1996) Vol. 8(MIT Press, Cambridge, MA) 1045–1051Google Scholar
• Van Roy B., Bertsekas D. P., Lee Y., Tsitsiklis J. N. A neurodynamic programming approach to retailer inventory management. Proc. IEEE Conf. Decision Control (1997) (IEEE, New York) 4052–4058Google Scholar
• Viswanathan S., Mathur K. Integrating routing and inventory decisions in one-warehouse multiretailer multiproduct distribution systems. Management Sci. (1997) 43:294–312Link, Google Scholar
• Webb R., Larson R. Period and phase of customer replenishment: A new approach to the strategic inventory/routing problem. Eur. J. Oper. Res. (1995) 85:132–148Crossref, Google Scholar
• Whitt W. Approximations of dynamic programs. I. Math. Oper. Res. (1978) 3:231–243Link, Google Scholar
• Whitt W. A-priori bounds for approximations of Markov programs. J. Math. Anal. Appl. (1979a) 71:297–302Crossref, Google Scholar
• Whitt W. Approximations of dynamic programs II. Math. Oper. Res. (1979b) 4:179–185Link, Google Scholar
• Wong P. J. An approach to reducing the computing time for dynamic programming. Oper. Res. (1970a) 18:181–185Link, Google Scholar
• Wong P. J. A new decomposition procedure for dynamic programming. Oper. Res. (1970b) 18:119–131Link, Google Scholar