Approximation algorithms for inventory problems with submodular or routing costs

Mathematical Programming

Volumn 160, Issue 1-2, 2016, Pages 225-244

  Nagarajan, Viswanath ^a   Shi, Cong ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Approximation algorithms; Inventory management; Inventory routing problem; Joint replenishment problem; Submodular function

Indexed keywords

COSTS; INVENTORY CONTROL; OPTIMIZATION; POLYNOMIAL APPROXIMATION; ROUTING ALGORITHMS; SALES;

FACTOR APPROXIMATION ALGORITHMS; FINITE PLANNING HORIZON; INVENTORY MANAGEMENT; INVENTORY OPTIMIZATION; INVENTORY ROUTING PROBLEMS; JOINT REPLENISHMENT PROBLEM; LOGARITHMIC APPROXIMATION; SUBMODULAR FUNCTIONS;

APPROXIMATION ALGORITHMS;

EID: 84990848856     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-016-0981-y     Document Type: Article

References (33)

1. Aksoy, Y., Erenguc, S.S.: Multi-item inventory models with co-ordinated replenishments: a survey. Int. J. Oper. Prod. Manag. 8(1), 63–73 (1993)
2. Anily, S., Federgruen, A.: One warehouse multiple retailer systems with vehicle routing costs. Manag. Sci. 36(1), 92–114 (1990)
3. Anily, S., Federgruen, A.: Two-echelon distribution systems with vehicle routing costs and central inventories. Oper. Res. 41(1), 37–47 (1993)
4. Arkin, E., Joneja, D., Roundy, R.: Computational complexity of uncapacitated multi-echelon production planning problems. Oper. Res. Lett. 8(2), 61–66 (1989)
5. Bertazzi, L.: Analysis of direct shipping policies in an inventory-routing problem with discrete shipping times. Manag. Sci. 54(4), 748–762 (2008)
6. Bienkowski, M., Byrka, J., Chrobak, M., Jez, L., Sgall, J.: Better approximation bounds for the joint replenishment problem (2013). arXiv preprint arXiv:1307.2531
7. Burns, L.D., Hall, R.W., Blumenfeld, D.E., Daganzo, C.F.: Distribution strategies that minimize transportation and inventory costs. Oper. Res. 33(3), 469–490 (1985)
8. Campbell, A.M., Savelsbergh, M.W.P.: A decomposition approach for the inventory-routing problem. Transp. Sci. 38(4), 488–502 (2004)
9. Chan, L.M.A., Federgruen, A., Simchi-Levi, D.: Probabilistic analyses and practical algorithms for inventory-routing models. Oper. Res. 46(1), 96–106 (1998)
10. Cheung, M., Elmachtoub, A., Levi, R., Shmoys, D.B.: The submodular joint replenishment problem. Math. Program. (2015). doi:10.1007/s10107-015-0920-3
11. Chien, T.W., Balakrishnan, A., Wong, R.T.: An integrated inventory allocation and vehicle routing problem. Transp. Sci. 23(2), 67–76 (1989)
12. Coelho, L.C., Cordeau, J.-F., Laporte, G.: Thirty years of inventory routing. Transp. Sci. 48(1), 1–19 (2014)
13. Federgruen, A., Zheng, Y.S.: The joint replenishment problem with general joint cost structures. Oper. Res. 40(2), 384–403 (1992)
14. Federgruen, A., Zipkin, P.: A combined vehicle routing and inventory allocation problem. Oper. Res. 32(5), 1019–1037 (1984)
15. Feige, U.: A threshold of ln N for approximating set cover. J. ACM 45(4), 634–652 (1998)
16. Feige, U.: On maximizing welfare when utility functions are subadditive. In: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing. STOC ’06, ACM, New York, NY, USA, pp. 41–50 (2006)
17. Fukunaga, T., Nikzad, A., Ravi, R.: Deliver or hold: approximation algorithms for the periodic inventory routing problem. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2014, September 4–6, 2014, Barcelona, Spain, pp. 209–225 (2014)
18. Garg, N.: Saving an epsilon: a 2-approximation for the k-mst problem in graphs. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing. STOC ’05, ACM, New York, NY, USA, pp. 396–402 (2005)
19. Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. J. ACM 50(6), 795–824 (2003)
20. Jansen, K.: Approximate strong separation with application in fractional graph coloring and preemptive scheduling. Theor. Comput. Sci. 302(1–3), 239–256 (2003)
21. Joneja, D.: The joint replenishment problem: new heuristics and worst case performance bounds. Oper. Res. 38(4), 711–723 (1990)
22. Levi, R., Roundy, R., Shmoys, D., Sviridenko, M.: A constant approximation algorithm for the one-warehouse multiretailer problem. Manag. Sci. 54(4), 763 (2008)
23. Levi, R., Roundy, R.O., Shmoys, D.B.: Primal-dual algorithms for deterministic inventory problems. Math. Oper. Res. 31(2), 267–284 (2006)
24. Nonner, T., Sviridenko, M.: An efficient polynomial-time approximation scheme for the joint replenishment problem. In: Goemans, M., Correa, J. (eds.) Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, vol 7801, pp. 314–323. Springer, Heidelberg (2013)
25. Queyranne, M.: A polynomial-time, submodular extension to roundy’s 98% effective heuristic for production/inventory. In: Proceedings of the 1986 IEEE International Conference on Robotics and Automation, vol. 3. IEEE, pp. 1640–1640 (1986)
26. Schrijver, A.: Combinatorial Optimization. Springer, Berlin, Heidelberg (2003)
27. Shmoys, D.B., Williamson, D.P.: Analyzing the held-karp tsp bound: a monotonicity property with application. Inf. Process. Lett. 35(6), 281–285 (1990)
28. Teo, C.-P., Bertsimas, D.: Multistage lot sizing problems via randomized rounding. Oper. Res. 49(4), 599–608 (2001)
29. Vaidya, P.M.: An algorithm for linear programming which requires O(((m+n)n 2 + (m+n) 1.5 n)L) arithmetic operations. Math. Program. 47, 175–201 (1990)
30. Vaidya, P.M.: A new algorithm for minimizing convex functions over convex sets. Math. Program. 73, 291–341 (1996)
31. Viswanathan, S., Mathur, K.: Integrating routing and inventory decisions in one-warehouse multiretailer multiproduct distribution systems. Manag. Sci. 43(3), 294–312 (1997)
32. Wagner, H.M., Whitin, T.M.: Dynamic version of the economic lot size model. Manag. Sci. 5(1), 89–96 (1958)
33. Wolsey, L.A.: Heuristic analysis, linear programming and branch and bound. Math. Program. Stud. 13, 121–134 (1980)