New Formulation for an Economic Order Quantity Distribution Policy in Vendor-Managed Inventory Routing Problems

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In vendor managed inventory systems, logistics decisions are centralized at the vendor, allowing inventory storage and transportation costs to be reduced simultaneously. Operation of such systems requires the solution of a complex combinatorial optimization problem, known as the Inventory Routing Problem (IRP), which involves managing client inventory and determining the frequency and size of product deliveries as well as the route taken by the vehicle over a given planning horizon. We present a new formulation based on an economic order quantity distribution policy for the multivehicle inventory routing problem (MIRP). A mathematical programming model with additional practical constraints was used for the MIRP. A new heuristic approach that breaks the MIRP down into the following two sub-problems was also proposed: one dealing with the scheduling of deliveries and the formation of delivery clusters over the planning horizon, and the second sub-problem, which builds the routes for the delivery clusters using classic route construction heuristics and a procedure for intra-route improvements. Adjustments between routes are performed with the aid of a new large neighborhood search (LNS) strategy. Small, medium-sized and large scenarios with different storage and transportation costs were generated using parameters based on data from the literature. Extensive computational tests were carried out to determine the effectiveness of the proposed distribution policy and the heuristic used.

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Advanced Materials Research (Volumes 945-949)

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3219-3236

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June 2014

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© 2014 Trans Tech Publications Ltd. All Rights Reserved

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[1] A. Campbell, L. Clarke, A.J. Kleywegt, M. Savelsbergh, The Inventory Routing Problem, in: T.G. Crainic, G. Laporte (Eds. ), Fleet Management and Logistics, 1998: p.95–113.

DOI: 10.1007/978-1-4615-5755-5_4

Google Scholar

[2] A.J. Kleywegt, V.S. Nori, M.W.P. Savelsbergh, The stochastic inventory routing problem with direct deliveries, Transportation Science. 36 (2002) 94–118.

DOI: 10.1287/trsc.36.1.94.574

Google Scholar

[3] R. Gronhaug, M. Christiansen, G. Desaulniers, J. Desrosiers, A Branch-and-Price Method for a Liquefied Natural Gas Inventory Routing Problem, Transportation Science. 44 (2010) 400–415.

DOI: 10.1287/trsc.1100.0317

Google Scholar

[4] J.G. Rakke, M. Stålhane, C.R. Moe, M. Christiansen, H. Andersson, K. Fagerholt, et al., A rolling horizon heuristic for creating a liquefied natural gas annual delivery program, Transportation Research Part C: Emerging Technologies. 19 (2011).

DOI: 10.1016/j.trc.2010.09.006

Google Scholar

[5] D. Popović, M. Vidović, G. Radivojević, Variable Neighborhood Search heuristic for the Inventory Routing Problem in fuel delivery, Expert Systems with Applications. 39 (2012) 13390–13398.

DOI: 10.1016/j.eswa.2012.05.064

Google Scholar

[6] K. Gumasta, F.T.S. Chan, M.K. Tiwari, An incorporated inventory transport system with two types of customers for multiple perishable goods, International Journal of Production Economics. 139 (2012) 678–686.

DOI: 10.1016/j.ijpe.2012.06.020

Google Scholar

[7] A.H. Hiassat, A. Diabat, A Location Inventory Routing Problem with Perishable Products, in: Proceedings of the 41st International Conference on Computers & Industrial Engineering, Los Angeles - USA, 2010: p.386–391.

Google Scholar

[8] V. Hemmelmayr, K.F. Doerner, R.F. Hartl, M.W.P. Savelsbergh, Delivery strategies for blood products supplies, OR Spectrum. 31 (2008) 707–725.

DOI: 10.1007/s00291-008-0134-7

Google Scholar

[9] M. Christiansen, K. Fagerholt, T. Flatberg, Ø. Haugen, O. Kloster, E.H. Lund, Maritime inventory routing with multiple products: A case study from the cement industry, European Journal of Operational Research. 208 (2011) 86–94.

DOI: 10.1016/j.ejor.2010.08.023

Google Scholar

[10] J. Alegre, M. Laguna, J. Pacheco, Optimizing the periodic pick-up of raw materials for a manufacturer of auto parts, European Journal of Operational Research. 179 (2007) 736–746.

DOI: 10.1016/j.ejor.2005.03.063

Google Scholar

[11] L. Coelho, J. Cordeau, G. Laporte, Consistency in multi-vehicle inventory-routing, Transportation Research Part C: Emerging Techologies 24 (2012) 270–287.

DOI: 10.1016/j.trc.2012.03.007

Google Scholar

[12] Y. Adulyasak, J. Cordeau, R. Jans, Formulations and branch-and-cut algorithms for multi-vehicle production and inventory routing problems, Technical Report - Centre Interuniversitaire de Recherche sur les Réseaux d'Entreprise, la Logistique et le Transport - Montreal, (2012).

DOI: 10.1287/ijoc.2013.0550

Google Scholar

[13] L. Coelho, Flexibility and consistency in inventory-routing, Phd Thesis in Adminstration - H.E.C. - Université de Montréal, (2012).

Google Scholar

[14] C. Archetti, L. Bertazzi, A. Hertz, M.G. Speranza, A Hybrid Heuristic for an Inventory Routing Problem, INFORMS Journal on Computing. 24 (2011) 101–116.

DOI: 10.1287/ijoc.1100.0439

Google Scholar

[15] L. Bertazzi, G. Paletta, M. Speranza, Minimizing the Total Cost in an Integrated Vendor Managed Inventory System, Journal of Heuristics. 11 (2005) 393–419.

DOI: 10.1007/s10732-005-0616-6

Google Scholar

[16] C. Archetti, L. Bertazzi, G. Laporte, M.G. Speranza, A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem, Transportation Science. 41 (2007) 382–391.

DOI: 10.1287/trsc.1060.0188

Google Scholar

[17] O. Solyali, H. Sural, A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem, Transportation Science. 45 (2011) 335–345.

DOI: 10.1287/trsc.1100.0354

Google Scholar

[18] L.C. Coelho, J. -F. Cordeau, G. Laporte, The inventory-routing problem with transshipment, Computers & Operations Research. 39 (2012) 2537–2548.

DOI: 10.1016/j.cor.2011.12.020

Google Scholar

[19] B. Raa, E. -H. Aghezzaf, A practical solution approach for the cyclic inventory routing problem, European Journal of Operational Research. 192 (2009) 429–441.

DOI: 10.1016/j.ejor.2007.09.032

Google Scholar

[20] R. Birger, A. El-Houssaine, Designing distribution patterns for long-term inventory routing with constant demand rates, International Journal of Production Economics. 112 (2008) 255–263.

DOI: 10.1016/j.ijpe.2006.08.023

Google Scholar

[21] S. -C. Liu, W. -T. Lee, A heuristic method for the inventory routing problem with time windows, Expert Systems with Applications. 38 (2011) 13223–13231.

DOI: 10.1016/j.eswa.2011.04.138

Google Scholar

[22] S. Sindhuchao, H.E. Romeijn, E. Akçali, R. Boondiskulchok, An Integrated Inventory-Routing System for Multi-item Joint Replenishment with Limited Vehicle Capacity, Journal of Global Optimization. 32 (2005) 93–118.

DOI: 10.1007/s10898-004-5908-0

Google Scholar

[23] L.B. Schwarz, Building Intuition: Insights From Basic Operations Management Models and Principles., Springer US, Boston, MA, (2008).

Google Scholar

[24] P.F. Wanke, Product, operation, and demand relationships between manufacturers and retailers, Transportation Research Part E: Logistics and Transportation Review. 48 (2012) 340–354.

DOI: 10.1016/j.tre.2011.07.010

Google Scholar

[25] P.C. Pop, I. Kara, A.H. Marc, New mathematical models of the generalized vehicle routing problem and extensions, Applied Mathematical Modelling. 36 (2012) 97–107.

DOI: 10.1016/j.apm.2011.05.037

Google Scholar

[26] N. Nananukul, Clustering model and algorithm for production inventory and distribution problem, Applied Mathematical Modelling. Article in Press (2013).

DOI: 10.1016/j.apm.2013.05.029

Google Scholar

[27] J. a. Díaz, E. Fernández, Hybrid scatter search and path relinking for the capacitated p-median problem, European Journal of Operational Research. 169 (2006) 570–585.

DOI: 10.1016/j.ejor.2004.08.016

Google Scholar

[28] D. J. Rosenkrantz, R. E. Stearns, P. M. Lewis, An Analysis of Several Heuristics for the Traveling Salesman Problem. SIAM Journal on Computing, v. 6, n. 3, pp.563-581, (1977).

DOI: 10.1137/0206041

Google Scholar

[29] M.T.A. Steiner, L.V. da Silva, D.B. da Costa, C. Carnieri, A.C.L. da Silva, O Problema do Roteamento no Transporte Escolar, Pesquisa Operacional. 20 (2000) 83–99.

DOI: 10.1590/s0101-74382000000100009

Google Scholar

[30] M. Boudia, C. Prins, A memetic algorithm with dynamic population management for an integrated production–distribution problem, European Journal of Operational Research. 195 (2009) 703–715.

DOI: 10.1016/j.ejor.2007.07.034

Google Scholar

[31] S. -C. Liu, A. -Z. Chen, Variable neighborhood search for the inventory routing and scheduling problem in a supply chain, Expert Systems with Applications. 39 (2012) 4149–4159.

DOI: 10.1016/j.eswa.2011.09.120

Google Scholar

[32] N. Shukla, a. K. Choudhary, P.K.S. Prakash, K.J. Fernandes, M.K. Tiwari, Algorithm portfolios for logistics optimization considering stochastic demands and mobility allowance, International Journal of Production Economics. 141 (2013) 146–166.

DOI: 10.1016/j.ijpe.2012.07.007

Google Scholar

[33] P. Shaw, Using constraint programming and local search methods to solve ve- hicle routing problems. In CP-98 (Fourth InternationalConference on Princi- ples and Practice of Constraint Programming), volume 1520 of Lecture Notes in Computer Science, pages 417–431, (1998).

DOI: 10.1007/3-540-49481-2_30

Google Scholar

[34] V. Goel, K.C. Furman, J. -H. Song, A.S. El-Bakry, Large neighborhood search for LNG inventory routing, Journal of Heuristics. 18 (2012) 821–848.

DOI: 10.1007/s10732-012-9206-6

Google Scholar

[35] Y. Adulyasak, J.F. Cordeau, R. Jans, Optimization-Based Adaptive Large Neighborhood Search for the Production Routing Problem, Transportation Science. 1655 (2012) 1–26.

DOI: 10.1287/trsc.1120.0443

Google Scholar

[36] V. Schmid, K.F. Doerner, G. Laporte, Rich routing problems arising in supply chain management, European Journal of Operational Research. 224 (2013) 435–448.

DOI: 10.1016/j.ejor.2012.08.014

Google Scholar

[37] D. Pisinger, S. Ropke, Large neighborhood search, Handbook of Metaheuristics. (2010) 1–22.

Google Scholar

[38] S. Lin, B. W. Kernighan, An Effective Heuristic Algorithm for the Traveling Salesman Problem. Operations Research, v. 21, pp.498-516, (1973).

DOI: 10.1287/opre.21.2.498

Google Scholar