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A Simultaneous Inventory Control and Facility Location Model with Stochastic Capacity Constraints

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  • Pablo Miranda
  • Rodrigo Garrido

Abstract

Traditionally, logistics analysts divide decisions levels into strategic, tactical and operational. Often these levels are considered separately for modeling purposes. The latter may conduce to make non-optimal decisions, since in reality there is interaction between the different levels. In this research, a cross-level model is derived to analyze decisions about inventory control and facility location, specially suited to urban settings, where the storage space is scarce and the vehicles’ capacity is usually restricted. Both conditions, on the one hand make the problem difficult to solve optimally but on the other hand make it more realistic and useful in practice. This paper presents a simultaneous nonlinear-mixed-integer model of inventory control and facility location decisions, which considers two novel capacity constraints. The first constraint states a maximum lot size for the incoming orders to each warehouse, and the second constraint is a stochastic bound to inventory capacity. This model is NP-Hard and presents nonlinear terms in the objective function and a nonlinear constraint. A heuristic solution approach is introduced, based on Lagrangian relaxation and the subgradient method. Numerical experiments were designed and applied. The solution procedure presented good performance in terms of the objective function. One of the key conclusions of the proposed modeling approach is the fact that a reduction of the inventory capacity does not necessarily imply an increase in the number of installed warehouses. In fact, reducing the order size allows the optimal allocation of customers (those with higher variances) into different warehouses, reducing the total system’s cost. Copyright Springer Science + Business Media, LLC 2006

Suggested Citation

  • Pablo Miranda & Rodrigo Garrido, 2006. "A Simultaneous Inventory Control and Facility Location Model with Stochastic Capacity Constraints," Networks and Spatial Economics, Springer, vol. 6(1), pages 39-53, March.
    • Handle: RePEc:kap:netspa:v:6:y:2006:i:1:p:39-53
    DOI: 10.1007/s11067-006-7684-5
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    References listed on IDEAS

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    1. Nozick, Linda K. & Turnquist, Mark A., 1998. "Integrating inventory impacts into a fixed-charge model for locating distribution centers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 34(3), pages 173-186, September.
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    4. Miranda, Pablo A. & Garrido, Rodrigo A., 2004. "Incorporating inventory control decisions into a strategic distribution network design model with stochastic demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 40(3), pages 183-207, May.
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    1. Aaron Guerrero Campanur & Elias Olivares-Benitez & Pablo A. Miranda & Rodolfo Eleazar Perez-Loaiza & Jose Humberto Ablanedo-Rosas, 2018. "Design of a Logistics Nonlinear System for a Complex, Multiechelon, Supply Chain Network with Uncertain Demands," Complexity, Hindawi, vol. 2018, pages 1-16, November.
    2. Jianing Zhi & Burcu B. Keskin, 2018. "A Multi-Product Production/Distribution System Design Problem with Direct Shipments and Lateral Transshipments," Networks and Spatial Economics, Springer, vol. 18(4), pages 937-972, December.
    3. Shu, Jia & Li, Zhengyi & Shen, Houcai & Wu, Ting & Zhong, Weijun, 2012. "A logistics network design model with vendor managed inventory," International Journal of Production Economics, Elsevier, vol. 135(2), pages 754-761.
    4. Tapia-Ubeda, Francisco J. & Miranda, Pablo A. & Macchi, Marco, 2018. "A Generalized Benders Decomposition based algorithm for an inventory location problem with stochastic inventory capacity constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 806-817.
    5. Ali Diabat & Jean-Philippe Richard & Craig Codrington, 2013. "A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design," Annals of Operations Research, Springer, vol. 203(1), pages 55-80, March.
    6. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2015. "A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 238-255.
    7. Ali Diabat & Jean-Philippe Richard, 2015. "An integrated supply chain problem: a nested lagrangian relaxation approach," Annals of Operations Research, Springer, vol. 229(1), pages 303-323, June.
    8. Mehrdad Shahabi & Shirin Akbarinasaji & Avinash Unnikrishnan & Rachel James, 2013. "Integrated Inventory Control and Facility Location Decisions in a Multi-Echelon Supply Chain Network with Hubs," Networks and Spatial Economics, Springer, vol. 13(4), pages 497-514, December.
    9. Francisco Silva & Lucia Gao, 2013. "A Joint Replenishment Inventory-Location Model," Networks and Spatial Economics, Springer, vol. 13(1), pages 107-122, March.
    10. Puntipa Punyim & Ampol Karoonsoontawong & Avinash Unnikrishnan & Chi Xie, 2018. "Tabu Search Heuristic for Joint Location-Inventory Problem with Stochastic Inventory Capacity and Practicality Constraints," Networks and Spatial Economics, Springer, vol. 18(1), pages 51-84, March.
    11. Wu, Xin & Nie, Lei & Xu, Meng & Zhao, Lili, 2019. "Distribution planning problem for a high-speed rail catering service considering time-varying demands and pedestrian congestion: A lot-sizing-based model and decomposition algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 61-89.
    12. Shuangyan Li & Xialian Li & Dezhi Zhang & Lingyun Zhou, 2017. "Joint Optimization of Distribution Network Design and Two-Echelon Inventory Control with Stochastic Demand and CO2 Emission Tax Charges," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-22, January.
    13. Miranda, Pablo A. & Garrido, Rodrigo A., 2009. "Inventory service-level optimization within distribution network design problem," International Journal of Production Economics, Elsevier, vol. 122(1), pages 276-285, November.
    14. Zhalechian, M. & Tavakkoli-Moghaddam, R. & Zahiri, B. & Mohammadi, M., 2016. "Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 182-214.
    15. Shahabi, Mehrdad & Tafreshian, Amirmahdi & Unnikrishnan, Avinash & Boyles, Stephen D., 2018. "Joint production–inventory–location problem with multi-variate normal demand," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 60-78.
    16. Shahabi, Mehrdad & Unnikrishnan, Avinash & Jafari-Shirazi, Ehsan & Boyles, Stephen D., 2014. "A three level location-inventory problem with correlated demand," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 1-18.

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