Decomposing inventory routing problems with approximate value functions

Naval Research Logistics

Volumn 57, Issue 8, 2010, Pages 718-727

  Toriello, Alejandro ^a   Nemhauser, George ^b   Savelsbergh, Martin ^c  

^a University of Southern California ^*  (United States)

^b Georgia Institute of Technology   (United States)

^c CSIRO   (Australia)

Author keywords

Approximate dynamic program; Inventory routing; Mixed integer program

Indexed keywords

APPROXIMATE VALUE FUNCTION; COMPUTATIONAL EXPERIMENT; COMPUTATIONAL TIME; DYNAMIC PROGRAMMING TECHNIQUES; DYNAMIC PROGRAMS; INVENTORY ROUTING; INVENTORY ROUTING PROBLEMS; MIXED-INTEGER PROGRAMS; MULTI-PERIOD; PIECE-WISE LINEAR FUNCTIONS; SOLUTION QUALITY; SUB-PROBLEMS; TIME DECOMPOSITIONS; VALUE FUNCTIONS;

DYNAMIC PROGRAMMING; PIECEWISE LINEAR TECHNIQUES;

INTEGER PROGRAMMING;

EID: 78649281028     PISSN: 0894069X     EISSN: 15206750     Source Type: Journal    
DOI: 10.1002/nav.20433     Document Type: Article

References (32)

1. D. Adelman, Price-directed replenishment of subsets: Methodology and its application to inventory routing, Manuf Serv Operat Manage 5 (2003), 348 - 371.
2. D. Adelman, A price-directed approach to stochastic inventory/routing, Operat Res 52 (2004), 499 - 514.
3. D. P. Bertsekas, J. N. Tsitsiklis, Neuro-dynamic programming, Athena Scientific, 1996.
4. C. E. Blair, R. G. Jeroslow, The value function of an integer program, Math Program 23 (1982), 237 - 273.
5. A. Campbell, L. Clarke, A. Kleywegt, M. Savelsbergh, The inventory routing problem, Fleet management and logistics, chapter 4, T. G. Crainic, G. Laporte, (Editors), Springer, 1998, pp. 95 - 114.
6. A. M. Campbell, M. W. P. Savelsbergh, A decomposition approach for the inventory-routing problem, Trans Sci 38 (2004), 488 - 502.
7. M. Christiansen, Decomposition of a combined inventory and time constrained ship routing problem, Trans Sci 33 (1999), 3 - 16.
8. M. Christiansen, B. Nygreen, A method for solving ship routing problems with inventory constraints, Ann Operat Res 81 (1998), 357 - 378.
9. M. Christiansen, B. Nygreen, Modelling path flows for a combined ship routing and inventory management problem, Ann Operat Res 82 (1998), 391 - 412.
10. J.-F. Cordeau, G. Laporte, M. W. P. Savelsbergh, D. Vigo, Vehicle routing, Handbook in operations research and management science: transportation, C. Barnhart, G. Laporte, (Editors), Elsevier, 2007, volume 14, chapter 6, pp. 367 - 428.
11. G. Desaulniers, J. Desrosiers, M. M. Solomon, (Editors), Column Generation, Springer, Berlin, 2005.
12. A. Drexl, A. Kimms, Lot sizing and scheduling-Survey and extensions, Eur J of Oper Res 99 (1997), 221 - 235.
13. F. G. Engineer, Shortest path based column generation for integer programming, Ph.D. thesis, Georgia Institute of Technology, 2009.
14. M. Hewitt, G. L. Nemhauser, M. W. P. Savelsbergh, Combining exact and heuristic approaches for the capacitated fixed charge network flow problem, INFORMS J Comput 22 (2010), 314 - 325.
15. D. Klabjan, D. Adelman, An infinite-dimensional linear programming algorithm for deterministic semi-markov decision processes on borel spaces, Math Operat Res 32 (2007), 528 - 550.
16. A. Kleywegt, V. Nori, M. W. P. Savelsbergh, The stochastic inventory routing problem with direct deliveries, Trans Sci 36 (2002), 94 - 118.
17. A. Kleywegt, V. Nori, M. W. P. Savelsbergh, Dynamic programming approximations for a stochastic inventory routing problem, Trans Sci 38 (2004), 42 - 70.
18. F. A. Longstaff, E. S. Schwartz, Valuing American options by simulation: a simple least-squares approach, Rev Financ Stud 14 (2001), 113 - 147.
19. A. Magnani, S. Boyd, Convex piecewise-linear fitting, Optim Eng 10 (2009), 1 - 17.
20. J. O. McClain, Dynamics of exponential smoothing with trend and seasonal terms, Manage Sci 20 (1974), 1300 - 1304.
21. S. Michel, F. Vanderbeck, A column generation based tactical planning method for inventory routing, INRIA Bordeaux Sud-Ouest, team RealOpt, 2008. Available at.
22. A. Minkoff, A Markov decision model and decomposition heuristic for dynamic vehicle dispatching, Oper Res 41 (1993), 77 - 90.
23. N. H. Moin, S. Salhi, Inventory routing problems: a logistical overview, J Oper Res Soc 58 (2007), 1185 - 1194.
24. N. Nananukul, Lot-sizing and inventory routing for a production- distribution supply chain, The University of Texas at Austin, 2008.
25. G. Nemhauser, L. Wolsey, Integer and combinatorial optimization, Wiley, 1999.
26. Y. Pochet, L. Wolsey, Production planning by mixed integer programming, Springer, 2006.
27. W. B. Powell, Approximate dynamic programming: Solving the curses of dimensionality, Wiley, 2007.
28. M. W. P. Savelsbergh, J.-H. Song, Inventory routing with continuous moves, Comput Oper Res 34 (2007), 1744 - 1763.
29. M. W. P. Savelsbergh, J.-H. Song, An optimization algorithm for the inventory routing problem with continuous moves, Comput Oper Res 35 (2008), 2266 - 2282.
30. L. Schenk, D. Klabjan, Intramarket optimization for express package carriers, Transp Sci 42 (2008), 530 - 545.
31. L. Schenk, D. Klabjan, Intra market optimization for express package carriers with station to station travel and proportional sorting, Comput Oper Res 37 (2010), 1749 - 1761.
32. H. Topaloglu, W. Powell, An algorithm for approximating piecewise linear concave functions from sample gradients, Oper Res Lett 31 (2003), 66 - 76.