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A Multi-Product Dynamic Lot-Size Model with Individual and Joint Set-up Costs

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  • Edward P. C. Kao

    (University of Houston, Houston, Texas)

Abstract

This paper considers a multi-product dynamic lot-size problem. In addition to a separate set-up cost for each product ordered, a joint set-up cost is incurred when one or more products are ordered. We present a dynamic programming formulation for finding the optimal ordering policy that calls for a smaller state space than that proposed by Zangwill. As a convenient substitute, we also introduce a very simple heuristic procedure and two of its variants. For the two-product problem we report computational experience for evaluating the performance of these procedures.

Suggested Citation

  • Edward P. C. Kao, 1979. "A Multi-Product Dynamic Lot-Size Model with Individual and Joint Set-up Costs," Operations Research, INFORMS, vol. 27(2), pages 279-289, April.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:2:p:279-289
    DOI: 10.1287/opre.27.2.279
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    Cited by:

    1. Danny Segev, 2014. "An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 432-444, May.
    2. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Monalisha Pattnaik & Padmabati Gahan, 2021. "Preservation effort effects on retailers and manufacturers in integrated multi-deteriorating item discrete supply chain model," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 276-329, June.
    4. E P Robinson & A Narayanan & L-L Gao, 2007. "Effective heuristics for the dynamic demand joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 808-815, June.
    5. Robinson, Powell & Narayanan, Arunachalam & Sahin, Funda, 2009. "Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms," Omega, Elsevier, vol. 37(1), pages 3-15, February.
    6. Tsao, Yu-Chung & Sheen, Gwo-Ji, 2012. "A multi-item supply chain with credit periods and weight freight cost discounts," International Journal of Production Economics, Elsevier, vol. 135(1), pages 106-115.
    7. Fuying Jing & Zirui Lan, 2017. "Forecast horizon of multi-item dynamic lot size model with perishable inventory," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-15, November.
    8. Narayanan, Arunachalam & Robinson, Powell, 2010. "Efficient and effective heuristics for the coordinated capacitated lot-size problem," European Journal of Operational Research, Elsevier, vol. 203(3), pages 583-592, June.
    9. Rizk, Nafee & Martel, Alain & Ramudhin, Amar, 2006. "A Lagrangean relaxation algorithm for multi-item lot-sizing problems with joint piecewise linear resource costs," International Journal of Production Economics, Elsevier, vol. 102(2), pages 344-357, August.
    10. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2006. "Primal-Dual Algorithms for Deterministic Inventory Problems," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 267-284, May.
    11. Chung, Chia-Shin & Hum, Sin-Hoon & Kirca, Omer, 1996. "The coordinated replenishment dynamic lot-sizing problem with quantity discounts," European Journal of Operational Research, Elsevier, vol. 94(1), pages 122-133, October.
    12. Martel, Alain & Diaby, Moustapha & Boctor, Fayez, 1995. "Multiple items procurement under stochastic nonstationary demands," European Journal of Operational Research, Elsevier, vol. 87(1), pages 74-92, November.
    13. J-M Chen & T-H Chen, 2005. "Effects of joint replenishment and channel coordination for managing multiple deteriorating products in a supply chain," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1224-1234, October.
    14. Lu, Liang & Qi, Xiangtong, 2011. "Dynamic lot sizing for multiple products with a new joint replenishment model," European Journal of Operational Research, Elsevier, vol. 212(1), pages 74-80, July.

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