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The benefit of VMI strategies in a stochastic multi-product serial two echelon system. (English) Zbl 1175.90024
Summary: We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.

##### MSC:
 90B05 Inventory, storage, reservoirs 90C15 Stochastic programming
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##### References:
 [1] Dong, Y.; Xu, K.; Dresner, M., Environmental determinants of VMI adoption: an explorative analysis, Transportation research part E, 43, 355-369, (2007) [2] Kuk, G., Effectiveness of vendor-managed inventory in the electronics industry: determinants and outcomes, Information and management, 41, 645-654, (2004) [3] Waller, M.; Johnson, ME.; Davis, T., Vendor managed inventory in the retail supply chain, Journal of business logistics, 20, 1, 183-203, (1999) [4] Dong, Y.; Xu, K., A supply chain model of vendor managed inventory, Transportation research part E, 38, 75-95, (2002) [5] Braglia, M.; Zavanella, L., Modelling an industrial strategy for inventory management in supply chains: the ‘consignment stock’ case, International journal of production research, 41, 3793-3808, (2003) · Zbl 1059.90047 [6] Valentini, G.; Zavanella, L., The consignment stock of inventories: industrial case and performance analysis, International journal of production economics, 81-82, 215-224, (2003) [7] Bertazzi, L.; Paletta, G.; Speranza, MG., Minimizing the total cost in an integrated vendor-managed inventory system, Journal of heuristics, 11, 393-419, (2005) · Zbl 1122.90303 [8] Broekmeulen RACM, van Donselaar KH, Fransoo JC, van Woensel T. Excess shelf space in retail stores: an analytical model and empirical assessment. BETA Working paper; 2004 p. 109. [9] Hassini, E., Storage space allocation to maximize inter-replenishment times, Computers and operations research, 32, 3191-3207, (2005) [10] Petersen, C.G., The impact of routing and storage policies on warehouse efficiency, International journal of operations and production management, 19, 10, 1053-1064, (1999) [11] de Koster, R.; Le-Duc, T.; Roodbergen, HJ., Design and control of warehouse order picking, European journal of operational research, 182, 481-501, (2007) · Zbl 1121.90385 [12] Aksoy, Y.; Erenguc, S.S., Multi-item inventory models with coordinated replenishments: a survey, International journal of operations and productions management, 8, 63-73, (1988) [13] Khouja, M.; Goyal, S., A review of the joint replenishment problem literature: 1989-2005, European journal of operational research, 186, 1-16, (2008) · Zbl 1138.90322 [14] Chen, J.; Chen, T., The multi-item replenishment problem in a two-echelon supply chain: the effect of centralization versus decentralization, Computers and operations research, 32, 3191-3207, (2005) · Zbl 1178.90012 [15] Ben-Daya, M.; Darwish, M.; Ertogal, K., The joint economic lotsizing problem: review and extensions, European journal of operational research, 185, 726-742, (2008) · Zbl 1137.90305 [16] Clark, A.J.; Scarf, H., Optimal policies for a multi-echelon inventory problem, Management science, 6, 457-490, (1960) [17] van Houtum, G.J.; Scheller-Wolf, A.; Jinxin, Y., Optimal control of serial inventory systems with fixed replenishment intervals, Operations research, 55, 674-687, (2007) · Zbl 1167.90356 [18] Chen, F.; Zheng, Y.S., Lower bounds for multi-echelon stochastic inventory systems, Management science, 40, 1426-1443, (1994) · Zbl 0823.90034 [19] Shang, K.H.; Song, J.S., Serial supply chains with economies of scale: bounds and approximations, Operations research, 55, 843-853, (2007) · Zbl 1167.90354 [20] Chen, F.; Zheng, YS., Evaluating echelon stock $$(R, \mathit{nQ})$$ policies in serial production/inventory systems with stochastic demand, Management science, 40, 1262-1275, (1994) · Zbl 0822.90043 [21] Shang, KH., Note: a simple heuristic for serial inventory systems with fixed order costs, Operations research, 56, 1039-1043, (2008) · Zbl 1167.90353 [22] Parker, R.P.; Kapuscinski, R., Optimal policies for a capacitated two-echelon inventory system, Operations research, 52, 739-755, (2004) · Zbl 1165.90334 [23] Chen, F., 94% effective policies for a two-stage serial inventory system with stochastic demand, Management science, 45, 1679-1696, (1999) · Zbl 1231.90018 [24] Feng, K.; Rao, US., Echelon-stock $$(R, \mathit{nT})$$ control in two-stage serial stochastic inventory systems, Operations research letters, 35, 95-104, (2007) · Zbl 1145.90003 [25] Hsiao, Y., Integrated logistic and inventory model for two-stage supply chain controlled by the reorder and shipping points with sharing information, International journal of production economics, 115, 229-235, (2008) [26] Ben-Daya, M.; Hariga, M., Integrated single vendor single buyer model with stochastic demand and variable lead time, International journal of production economics, 92, 75-80, (2004) [27] Hsiao, Y., A note on integrated single vendor single buyer model with stochastic demand and variable leadtime, International journal of production economics, 114, 294-297, (2008) [28] Pan, J.C.; Yang, J., A study of an integrated inventory with controllable lead time, International journal of production research, 40, 1263-1273, (2002) · Zbl 1027.90024 [29] Ouyang, L.; Wu, K.; Ho, C., Integrated vendor – buyer cooperative models with stochastic demand in controllable leadtime, International journal of production economics, 92, 255-266, (2004) [30] Hoque, MA., An alternative model for integrated vendor – buyer inventory under controllable lead time and its heuristic solution, International journal of system science, 38, 501-509, (2007) · Zbl 1149.90009 [31] Ouyang, L.; Wu, K.; Ho, C., The single-vendor single-buyer integrated inventory problem with quality improvement and lead time reduction—minimax distribution-free approach, International journal of production economics, 92, 255-266, (2004) [32] Daganzo, CF., Logistics systems analysis, (1999), Springer Berlin, Heidelberg, New York [33] Angerer A. The impact of automatic store replenishment systems on retail. Dissertation, University of St. Gallen, Graduate School of Business Administration, Economics, Law and Social Sciences (HSG); 2005. [34] Cachon, G., Managing a Retailer’s shelf space, inventory, and transportation, Manufacturing and service operations, 3, 3, 211-229, (2001) [35] Huntjens RMG, Tandpasta bij shampoo $$\ldots$$ of toch maar apart (in Dutch). MSC thesis, Technische Universiteit Eindhoven, Eindhoven; 2008. [36] Law, AM.; Kelton, WD., Simulation modeling and analysis, (2000), McGraw-Hill Boston
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