[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/oprepe/v7y2020ics2214716019301678.html
   My bibliography  Save this article

An approximated solution to the constrained integrated manufacturer-buyer supply problem

Author

Listed:
  • Herbon, Avi
Abstract
In recent decades, the integrated manufacturer-buyer supply chain problem has been widely studied by many scholars, as it provides benefits to both parties in terms of planning flexibility, information sharing and joint costs. The manufacturer produces a production lot of size Q, with variable production rate P ≤ U, where U denotes the maximal production rate (e.g., due to technological restrictions or due to limited machinery and/or manpower capacities). The manufacturer delivers the lot to the buyer in n (integer) smaller shipments, each of size q. An upper bound on the production cycle length is assumed (e.g., to enable the scheduling of maintenance periods or idle windows of time in which workers are not required to work.) In order to solve the problem mathematically, we suggest a sub-optimal nested formulation of the problem that utilizes existing formulas for n*(r) and q*(r) (where r denotes the demand-to-production rate ratio, r = D/P) for the unconstrained problem. The optimal solution of the accurate formulation is obtained through numerical optimization, utilizing the IBM CPLEX solver, and is compared with the proposed sub-optimal method. Among the advantages of the suggested approach are that the solution is analytically derived, it is very simple to implement, and it yields a minimal joint cost that is close to the accurate formulation.

Suggested Citation

  • Herbon, Avi, 2020. "An approximated solution to the constrained integrated manufacturer-buyer supply problem," Operations Research Perspectives, Elsevier, vol. 7(C).
    • Handle: RePEc:eee:oprepe:v:7:y:2020:i:c:s2214716019301678
    DOI: 10.1016/j.orp.2020.100140
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2214716019301678
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.orp.2020.100140?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Goyal, Suresh K. & Gupta, Yash P., 1989. "Integrated inventory models: The buyer-vendor coordination," European Journal of Operational Research, Elsevier, vol. 41(3), pages 261-269, August.
    2. Hoque, M.A., 2013. "A vendor–buyer integrated production–inventory model with normal distribution of lead time," International Journal of Production Economics, Elsevier, vol. 144(2), pages 409-417.
    3. Glock, Christoph H., 2012. "Coordination of a production network with a single buyer and multiple vendors," International Journal of Production Economics, Elsevier, vol. 135(2), pages 771-780.
    4. David, Israel & Eben-Chaime, Moshe, 2008. "How accurate is the integrated vendor-buyer continuous model?," International Journal of Production Economics, Elsevier, vol. 114(2), pages 805-810, August.
    5. AlDurgam, Mohammad & Adegbola, Kehinde & Glock, Christoph H., 2017. "A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate," International Journal of Production Economics, Elsevier, vol. 191(C), pages 335-350.
    6. Marchi, B. & Ries, J.M. & Zanoni, S. & Glock, C.H., 2016. "A joint economic lot size model with financial collaboration and uncertain investment opportunity," International Journal of Production Economics, Elsevier, vol. 176(C), pages 170-182.
    7. AlDurgham, M. & Adegbola, K. & Glock, C. H., 2017. "A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 87594, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    8. David, Israel & Eben-Chaime, Moshe, 2003. "How far should JIT vendor-buyer relationships go?," International Journal of Production Economics, Elsevier, vol. 81(1), pages 361-368, January.
    9. S. Thomas McCormick & Michael L. Pinedo & Scott Shenker & Barry Wolf, 1989. "Sequencing in an Assembly Line with Blocking to Minimize Cycle Time," Operations Research, INFORMS, vol. 37(6), pages 925-935, December.
    10. Glock, C. H. & Kim, T., 2012. "A joint economic lot sizemodel with returnable transport items," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 59079, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    11. Glock, C. H., 2012. "Coordination of a production network with a single buyer and multiple vendors," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57812, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    12. Wakhid Ahmad Jauhari & I. Nyoman Pujawan, 2014. "Joint economic lot size (JELS) model for single-vendor single-buyer with variable production rate and partial backorder," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 20(1), pages 91-108.
    13. Marchi, B. & Ries, J. M. & Zanoni, S. & Glock, C. H., 2016. "A joint economic lot size model with financial collaboration and uncertain investment opportunity," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 79714, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    14. Sajadieh, Mohsen S. & Larsen, Christian, 2015. "A coordinated manufacturer-retailer model under stochastic demand and production rate," International Journal of Production Economics, Elsevier, vol. 168(C), pages 64-70.
    15. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-528, June.
    16. Sana, Shib Sankar, 2010. "An economic production lot size model in an imperfect production system," European Journal of Operational Research, Elsevier, vol. 201(1), pages 158-170, February.
    17. Glock, C. H., 2012. "The joint economic lot size problem: a review," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57811, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    18. Wahab, M.I.M. & Mamun, S.M.H. & Ongkunaruk, P., 2011. "EOQ models for a coordinated two-level international supply chain considering imperfect items and environmental impact," International Journal of Production Economics, Elsevier, vol. 134(1), pages 151-158, November.
    19. Hau L. Lee & Meir J. Rosenblatt, 1987. "Simultaneous Determination of Production Cycle and Inspection Schedules in a Production System," Management Science, INFORMS, vol. 33(9), pages 1125-1136, September.
    20. Hajji, Adnene & Gharbi, Ali & Kenne, Jean-Pierre & Pellerin, Robert, 2011. "Production control and replenishment strategy with multiple suppliers," European Journal of Operational Research, Elsevier, vol. 208(1), pages 67-74, January.
    21. Paul J. Schweitzer & Abraham Seidmann, 1991. "Optimizing Processing Rates for Flexible Manufacturing Systems," Management Science, INFORMS, vol. 37(4), pages 454-466, April.
    22. Glock, Christoph H., 2012. "The joint economic lot size problem: A review," International Journal of Production Economics, Elsevier, vol. 135(2), pages 671-686.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Herbon, Avi, 2021. "An integrated manufacturer-buyer chain with bounded production cycle length," Operations Research Perspectives, Elsevier, vol. 8(C).
    2. Herbon, Avi & David, Israel, 2023. "Optimal manufacturer's cost sharing ratio, shipping policy and production rate – A two-echelon supply chain," Operations Research Perspectives, Elsevier, vol. 10(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Glock, Christoph H. & Grosse, Eric H., 2021. "The impact of controllable production rates on the performance of inventory systems: A systematic review of the literature," European Journal of Operational Research, Elsevier, vol. 288(3), pages 703-720.
    2. Herbon, Avi, 2021. "An integrated manufacturer-buyer chain with bounded production cycle length," Operations Research Perspectives, Elsevier, vol. 8(C).
    3. Hwang, Juhwen & Wan, Yat-wah, 2013. "A supplier–retailer supply chain with intermediate storage for batch ordering," International Journal of Production Economics, Elsevier, vol. 142(2), pages 343-352.
    4. Chan, Chi Kin & Fang, Fei & Langevin, André, 2018. "Single-vendor multi-buyer supply chain coordination with stochastic demand," International Journal of Production Economics, Elsevier, vol. 206(C), pages 110-133.
    5. Faranak Emtehani & Nasim Nahavandi & Farimah Mokhatab Rafiei, 2021. "A joint inventory–finance model for coordinating a capital-constrained supply chain with financing limitations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-39, December.
    6. Dhahri, Akrem & Gharbi, Ali & Ouhimmou, Mustapha, 2022. "Integrated production-delivery control policy for an unreliable manufacturing system and multiple retailers," International Journal of Production Economics, Elsevier, vol. 245(C).
    7. Tiwari, Sunil & Kazemi, Nima & Modak, Nikunja Mohan & Cárdenas-Barrón, Leopoldo Eduardo & Sarkar, Sumon, 2020. "The effect of human errors on an integrated stochastic supply chain model with setup cost reduction and backorder price discount," International Journal of Production Economics, Elsevier, vol. 226(C).
    8. Herbon, Avi & David, Israel, 2023. "Optimal manufacturer's cost sharing ratio, shipping policy and production rate – A two-echelon supply chain," Operations Research Perspectives, Elsevier, vol. 10(C).
    9. Beatrice Marchi & Simone Zanoni & Mohamad Y. Jaber, 2020. "Improving Supply Chain Profit through Reverse Factoring: A New Multi-Suppliers Single-Vendor Joint Economic Lot Size Model," IJFS, MDPI, vol. 8(2), pages 1-16, April.
    10. Sarker, Bhaba R. & Rochanaluk, Ratkrit & Yi, Huizhi & Egbelu, Pius J., 2014. "An operational policy for a three-stage distributive supply chain system with retailers’ backorders," International Journal of Production Economics, Elsevier, vol. 156(C), pages 332-345.
    11. Lin, Feng & Jia, Tao & Wu, Feng & Yang, Zhen, 2019. "Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 219-234.
    12. Asif Iqbal Malik & Biswajit Sarkar, 2020. "Coordination Supply Chain Management Under Flexible Manufacturing, Stochastic Leadtime Demand, and Mixture of Inventory," Mathematics, MDPI, vol. 8(6), pages 1-32, June.
    13. Beck, Fabian G. & Glock, Christoph H. & Kim, Taebok, 2017. "Coordination of a production network with a single buyer and multiple vendors with geometrically increasing batch shipments," International Journal of Production Economics, Elsevier, vol. 193(C), pages 633-646.
    14. Glock, Christoph H. & Grosse, Eric H. & Ries, Jörg M., 2017. "Reprint of “Decision support models for supplier development: Systematic literature review and research agenda”," International Journal of Production Economics, Elsevier, vol. 194(C), pages 246-260.
    15. Hauck, Zsuzsanna & Rabta, Boualem & Reiner, Gerald, 2023. "Coordinating quality decisions in a two-stage supply chain under buyer dominance," International Journal of Production Economics, Elsevier, vol. 264(C).
    16. Castellano, Davide & Gallo, Mosè & Grassi, Andrea & Santillo, Liberatina C., 2019. "The effect of GHG emissions on production, inventory replenishment and routing decisions in a single vendor-multiple buyers supply chain," International Journal of Production Economics, Elsevier, vol. 218(C), pages 30-42.
    17. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Lot sizing and lead time decisions in production/inventory systems," International Journal of Production Economics, Elsevier, vol. 155(C), pages 351-360.
    18. Pal, Brojeswar & Sana, Shib Sankar & Chaudhuri, Kripasindhu, 2014. "Joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles," International Journal of Production Economics, Elsevier, vol. 155(C), pages 229-238.
    19. Daryanto, Yosef & Wee, Hui Ming & Astanti, Ririn Diar, 2019. "Three-echelon supply chain model considering carbon emission and item deterioration," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 368-383.
    20. Ali Ekici & Baṣak Altan & Okan Örsan Özener, 2016. "Pricing decisions in a strategic single retailer/dual suppliers setting under order size constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 54(7), pages 1887-1898, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:oprepe:v:7:y:2020:i:c:s2214716019301678. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/operations-research-perspectives .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.