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Solving the forward-reserve allocation problem in warehouse order picking systems

Author

Listed:
  • J Gu

    (Nestle USA)

  • M Goetschalckx

    (School of Industrial and Systems Engineering, Georgia Institute of Technology)

  • L F McGinnis

    (School of Industrial and Systems Engineering, Georgia Institute of Technology)

Abstract

Many warehouses store at least some goods in two areas, a reserve area that is efficient for storage and a forward area that is efficient for order picking. The forward-reserve allocation problem determines the set of Stock-Keeping Units and their space allocations in the forward area to maximize the forward area's benefit by trading off the relevant costs of order picking and internal replenishment. The mathematical model of this decision resembles the classical knapsack problem with the additional complexity that it has a discontinuous nonlinear cost function. A simple greedy heuristic has been proposed in the literature to solve this problem. This paper proposes an alternative branch-and-bound algorithm that can quickly solve the problem to optimality. Heuristic and optimal solutions are numerically compared using problem instances based on real warehouse data. Results suggest that the heuristic solutions are very close to the optimal ones in terms of both the objective value and the forward assignment.

Suggested Citation

  • J Gu & M Goetschalckx & L F McGinnis, 2010. "Solving the forward-reserve allocation problem in warehouse order picking systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(6), pages 1013-1021, June.
    • Handle: RePEc:pal:jorsoc:v:61:y:2010:i:6:d:10.1057_jors.2009.39
    DOI: 10.1057/jors.2009.39
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    References listed on IDEAS

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    1. AGHEZZAF, El-Houssaine, 2005. "Capacity planning and warehouse location in supply chains with uncertain demands," LIDAM Reprints CORE 1808, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Ahmet B. Keha & Ismael R. de Farias & George L. Nemhauser, 2006. "A Branch-and-Cut Algorithm Without Binary Variables for Nonconvex Piecewise Linear Optimization," Operations Research, INFORMS, vol. 54(5), pages 847-858, October.
    3. E Aghezzaf, 2005. "Capacity planning and warehouse location in supply chains with uncertain demands," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 453-462, April.
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    Cited by:

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    2. Dragan Djurdjević & Nenad Bjelić & Dražen Popović & Milan Andrejić, 2022. "A Combined Dynamic Programming and Simulation Approach to the Sizing of the Low-Level Order-Picking Area," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    3. de Vries, Harwin & Carrasco-Gallego, Ruth & Farenhorst-Yuan, Taoying & Dekker, Rommert, 2014. "Prioritizing replenishments of the piece picking area," European Journal of Operational Research, Elsevier, vol. 236(1), pages 126-134.
    4. Simon Emde, 2017. "Scheduling the replenishment of just-in-time supermarkets in assembly plants," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 321-345, January.
    5. Leung, Eric K.H. & Lee, Carmen Kar Hang & Ouyang, Zhiyuan, 2022. "From traditional warehouses to Physical Internet hubs: A digital twin-based inbound synchronization framework for PI-order management," International Journal of Production Economics, Elsevier, vol. 244(C).
    6. AERTS, Babiche & CORNELISSENS, Trijntje & SÖRENSEN, Kenneth, 2022. "The internal warehouse replenishment problem: the importance of storage and replenishment policies," Working Papers 2022007, University of Antwerp, Faculty of Business and Economics.
    7. Zheng Wang & Jiuh‐Biing Sheu & Chung‐Piaw Teo & Guiqin Xue, 2022. "Robot Scheduling for Mobile‐Rack Warehouses: Human–Robot Coordinated Order Picking Systems," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 98-116, January.
    8. Walter, Rico & Boysen, Nils & Scholl, Armin, 2013. "The discrete forward–reserve problem – Allocating space, selecting products, and area sizing in forward order picking," European Journal of Operational Research, Elsevier, vol. 229(3), pages 585-594.
    9. Jiang, Min & Leung, K.H. & Lyu, Zhongyuan & Huang, George Q., 2020. "Picking-replenishment synchronization for robotic forward-reserve warehouses," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    10. Jiang, Min & Huang, George Q., 2022. "Intralogistics synchronization in robotic forward-reserve warehouses for e-commerce last-mile delivery," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    11. Lam, H.Y. & Ho, G.T.S. & Mo, Daniel Y. & Tang, Valerie, 2023. "Responsive pick face replenishment strategy for stock allocation to fulfil e-commerce order," International Journal of Production Economics, Elsevier, vol. 264(C).
    12. Çelik, Melih & Archetti, Claudia & Süral, Haldun, 2022. "Inventory routing in a warehouse: The storage replenishment routing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1117-1132.

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