The Stochastic Inventory Routing Problem with Direct Deliveries

Vendor managed inventory replenishment is a business practice in which vendors monitor their customers' inventories, and decide when and how much inventory should be replenished. The inventory routing problem addresses the coordination of inventory management and transportation. The ability to solve the inventory routing problem contributes to the realization of the potential savings in inventory and transportation costs brought about by vendor managed inventory replenishment. The inventory routing problem is hard, especially if a large number of customers is involved. We formulate the inventory routing problem as a Markov decision process, and we propose approximation methods to find good solutions with reasonable computational effort. Computational results are presented for the inventory routing problem with direct deliveries.

[1]  Francesca Fumero,et al.  Synchronized Development of Production, Inventory, and Distribution Schedules , 1999, Transp. Sci..

[2]  Oded Berman,et al.  Deliveries in an Inventory/Routing Problem Using Stochastic Dynamic Programming , 2001, Transp. Sci..

[3]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[4]  D. Bertsekas.  Convergence of discretization procedures in dynamic programming , 1975 .

[5]  Moshe Dror,et al.  CASH FLOW OPTIMIZATION IN DELIVERY SCHEDULING , 1996 .

[6]  Teodor Gabriel Crainic,et al.  Fleet management and logistics , 1998 .

[7]  John N. Tsitsiklis,et al.  Analysis of temporal-difference learning with function approximation , 1996, NIPS 1996.

[8]  David F. Pyke,et al.  Performance characteristics of stochastic integrated production-distribution systems , 1993 .

[9]  Moshe Dror,et al.  Stochastic Inventory Routing: Route Design with Stockouts and Route Failures , 1989, Transp. Sci..

[10]  Julian Benjamin,et al.  An Analysis of Inventory and Transportation Costs in a Constrained Network , 1989, Transp. Sci..

[11]  D. Blumenfeld,et al.  Analyzing trade-offs between transportation, inventory and production costs on freight networks , 1985 .

[12]  David F. Pyke,et al.  Multiproduct integrated production—distribution systems☆ , 1994 .

[13]  Benjamin Van Roy,et al.  A neuro-dynamic programming approach to retailer inventory management , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[14]  M. Savelsbergh,et al.  The Inventory Routing Problem , 1998 .

[15]  Moshe Dror,et al.  A Decomposition Approach to the Inventory Routing Problem with Satellite Facilities , 1998, Transp. Sci..

[16]  Moshe Dror,et al.  A computational comparison of algorithms for the inventory routing problem , 1985 .

[17]  H. Kushner.  Numerical Methods for Stochastic Control Problems in Continuous Time , 2000 .

[18]  Richard T. Wong,et al.  An Integrated Inventory Allocation and Vehicle Routing Problem , 1989, Transp. Sci..

[19]  Bruce L. Golden,et al.  Analysis of a large scale vehicle routing problem with an inventory component , 1984 .

[20]  Moshe Dror,et al.  A branch and cut algorithm for the VRP with satellite facilities , 1998 .

[21]  Marielle Christiansen,et al.  Decomposition of a Combined Inventory and Time Constrained Ship Routing Problem , 1999, Transp. Sci..

[22]  A. Ruszczynski,et al.  A method of aggregate stochastic subgradients with on-line stepsize rules for convex stochastic programming problems , 1986 .

[23]  Andrzej Ruszczyński,et al.  On convergence of the stochastic subgradient method with on-line stepsize rules , 1986 .

[24]  Alan S. Minkoff.  A Markov Decision Model and Decomposition Heuristic for Dynamic Vehicle Dispatching , 1993, Oper. Res..

[25]  Randolph W. Hall,et al.  Distribution Strategies that Minimize Transportation and Inventory Costs , 1985, Oper. Res..

[26]  Lap Mui Ann Chan,et al.  Probabilistic Analyses and Practical Algorithms for Inventory-Routing Models , 1998, Oper. Res..

[27]  Douglas J. Thomas,et al.  Coordinated supply chain management , 1996 .

[28]  Yehuda Bassok,et al.  Direct shipping and the dynamic single-depot/multi-retailer inventory system , 1997 .

[29]  Marshall L. Fisher,et al.  Coordination of production and distribution planning , 1994 .

[30]  B. Nelson,et al.  Using common random numbers for indifference-zone selection and multiple comparisons in simulation , 1995 .

[31]  M. Savelsbergh,et al.  The Stochastic Inventory Routing Problem , 2000 .

[32]  David Simchi-Levi,et al.  Analysis of vehicle routing and inventory-routing problems , 1995 .

[33]  Louis M. Dalberto,et al.  Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer , 1983 .

[34]  John M. Blatt,et al.  Numerical quadrature in n dimensions , 1963, Comput. J..

[35]  R. C. Bose,et al.  Orthogonal Arrays of Strength two and three , 1952 .

[36]  Awi Federgruen,et al.  A Combined Vehicle Routing and Inventory Allocation Problem , 1984, Oper. Res..

[37]  T. Chien,et al.  Determining profit-maximizing production/shipping policies in a one-to-one direct shipping, stochastic demand environment , 1993 .

[38]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[39]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .

[40]  Chung-Yee Lee,et al.  Stock Replenishment and Shipment Scheduling for Vendor-Managed Inventory Systems , 2000 .

[41]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[42]  J. Tsitsiklis,et al.  An optimal one-way multigrid algorithm for discrete-time stochastic control , 1991 .

[43]  Awi Federgruen,et al.  Two-Echelon Distribution Systems with Vehicle Routing Costs and Central Inventories , 1993, Oper. Res..

[44]  Marielle Christiansen,et al.  Modelling path flows for a combined ship routingand inventory management problem , 1998, Ann. Oper. Res..

[45]  Alexander H. G. Rinnooy Kan,et al.  Bounds and Heuristics for Capacitated Routing Problems , 1985, Math. Oper. Res..

[46]  Steven Nahmias,et al.  Optimizing inventory levels in a two-echelon retailer system with partial lost sales , 1994 .

[47]  Yehuda Bassok,et al.  Dynamic Allocations for Multi-Product Distribution , 1995, Transp. Sci..

[48]  Lawrence M. Wein,et al.  Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem , 1999, Transp. Sci..

[49]  Moshe Dror,et al.  Inventory/routing: Reduction from an annual to a short-period problem , 1987 .

[50]  Hau L. Lee,et al.  Strategic Analysis of Integrated Production-Distribution Systems: Models and Methods , 1988, Oper. Res..

[51]  Awi Federgruen,et al.  One warehouse multiple retailer systems with vehicle routing costs , 1990 .

[52]  D. Blumenfeld,et al.  Synchronizing production and transportation schedules , 1991 .

[53]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[54]  Guillermo Gallego,et al.  On the effectiveness of direct shipping strategy for the one-warehouse multi-retailer R -systems , 1990 .

[55]  E. Fainberg,et al.  On Homogeneous Markov Models with Continuous Time and Finite or Countable State Space , 1979 .

[56]  Marielle Christiansen,et al.  A method for solving ship routing problemswith inventory constraints , 1998, Ann. Oper. Res..