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Joint-replenishment problem under stochastic demands with backorders-lost sales mixtures, controllable lead times, and investment to reduce the major ordering cost

Author

Listed:
  • Marcello Braglia

    (Università di Pisa)

  • Davide Castellano

    (Università di Pisa)

  • Marco Frosolini

    (Università di Pisa)

Abstract

In this paper, we study the periodic-review stochastic Joint-replenishment Problem (JRP), with backorders-lost sales mixtures, controllable lead times, and investment to reduce the major ordering cost. The purpose is to determine a strict cyclic replenishment policy, the length of lead times, and the major ordering cost that minimize the total system cost. We first present an effective heuristic algorithm to approach the problem. However, results illustrate how computationally expensive the algorithm would be for a practical application. Hence, we then propose an efficient and more practically applicable solution procedure. In particular, approximating part of the cost function with its second-order Taylor series expansion, we obtain an expression that resembles the deterministic cost structure. Therefore, the problem can be approached exploiting a standard algorithm suitable for the deterministic JRP. Numerical tests compare the performances of the algorithms developed and show that the approximated approach is actually promising for a practical application.

Suggested Citation

  • Marcello Braglia & Davide Castellano & Marco Frosolini, 2016. "Joint-replenishment problem under stochastic demands with backorders-lost sales mixtures, controllable lead times, and investment to reduce the major ordering cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1108-1120, August.
    • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:8:d:10.1057_jors.2016.13
    DOI: 10.1057/jors.2016.13
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    References listed on IDEAS

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    1. Glock, C. H., 2012. "Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57816, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    6. Glock, Christoph H., 2012. "Lead time reduction strategies in a single-vendor–single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand," International Journal of Production Economics, Elsevier, vol. 136(1), pages 37-44.
    7. Amaya, Ciro Alberto & Carvajal, Jimmy & Castaño, Fabian, 2013. "A heuristic framework based on linear programming to solve the constrained joint replenishment problem (C-JRP)," International Journal of Production Economics, Elsevier, vol. 144(1), pages 243-247.
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    Cited by:

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    2. Cui, Ligang & Deng, Jie & Liu, Rui & Xu, Dongyang & Zhang, Yajun & Xu, Maozeng, 2020. "A stochastic multi-item replenishment and delivery problem with lead-time reduction initiatives and the solving methodologies," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    3. Zhang, Ren-Qian & Yi, Meng & Wang, Qi-Qi & Xiang, Chen, 2018. "Polynomial algorithm of inventory model with complete backordering and correlated demand caused by cross-selling," International Journal of Production Economics, Elsevier, vol. 199(C), pages 193-198.

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