Annals of Operations Research

, Volume 257, Issue 1–2, pp 613–639 | Cite as

Diversity of payment contracts in a decentralized assembly system



Conventional wisdom views that in an assembly system, suppliers have to accept a unified payment contract when transacting with a manufacturer. However, in practice, the implementation of a payment contract is clearly more dependent on the channel power of the supplier in the supply chain. This paper considers an assembly system consisting of two suppliers with different channel powers, and identifies three payment contracts, namely, on-delivery payment, on-agreed-time payment, and ready-to-assemble payment. We investigate the equilibrium delivery and timing decisions of firms under three different cases distinguished by the combinations of different payment contracts in the system. Based on both theoretical and quantitative analyses, three major results are obtained. First, the delivery times of suppliers are cost-driven and time-related. Second, the buffer time of the manufacturer can balance the production lead times of the supplier. Third, the supply chain achieves the lowest cost when the core supplier chooses an on-agreed-time payment contract, and the general supplier adopts a ready-to-assemble payment contract.


Assembly system Payment contracts Comparative analysis Game theory 



This work was partially supported by Youth Foundation for Humanities and Social Sciences of Ministry of Education of China [14YJC630041]; China Postdoctoral Science special Foundation [2014T70741]; National Natural Science Foundation of China [71402126], [71102174], [71372019], [71371147], [71471057] and [71231007]; Beijing Higher Education Young Elite Teacher Project [YETP1173]; Specialized Research Fund for Doctoral Program of Higher Education of China [20111101120019]; Beijing Philosophy and Social Science Foundation of China [11JGC106].


  1. Chu, H., Wang, J., Jin, Y., & Suo, H. S. (2006). Decentralized inventory control in a two-component assembly system. International Journal of Production Economics, 102(2), 255–264.CrossRefGoogle Scholar
  2. Gerchak, Y., Wang, Y., & Yano, C. A. (1994). Lot sizing in assembly systems with random component yields. IIE Transactions, 26(2), 19–24.CrossRefGoogle Scholar
  3. Granot, D., & Yin, S. (2008). Competition and cooperation in decentralized push and pull assembly systems. Management Science, 54(4), 733–747.CrossRefGoogle Scholar
  4. Guan, X., Li, G., & Yin, Z. (2014). The implication of time-based payment contract in the decentralized assembly system. Annals of Operation Research. doi: 10.1007/s10479-014-1579-5.
  5. Guan, X., & Liu, M. Q. (2013). Coordination in the decentralized assembly system with dual supply modes. Discrete Dynamics in Nature and Society, 1–9. doi: 10.1155/2013/381987.
  6. Güler, M. G. (2015). Coordinating decentralized assembly systems with random yield and random demand. International Journal of Production Research, 53(3), 886–896.CrossRefGoogle Scholar
  7. Güler, M. G., & Bilgic, T. (2009). On coordinating an assembly system under random yield and random demand. European Journal of Operational Research, 196(1), 342–350.CrossRefGoogle Scholar
  8. Gurnani, H., & Gerchak, Y. (2007). Coordination in decentralized assembly systems with uncertain component yields. European Journal of Operational Research, 176(3), 1559–1576.CrossRefGoogle Scholar
  9. Haibatolah, S., Ahmad, M., & Mehdi, H. (2013). Determining the periodicity and planned lead time in serial-production systems with dependent demand and uncertain lead time. Uncertain Supply Chain Management, 1(2), 87–98.Google Scholar
  10. Hayya, J. C., Harrison, T. P., & James He, X. (2011). The impact of stochastic lead time reduction on inventory cost under order crossover. European Journal of Operational Research, 211(2), 274–281.CrossRefGoogle Scholar
  11. He, Y., & Wang, S. Y. (2012). Analysis of production-inventory system for deteriorating items with demand disruption. International Journal of Production Research, 50(16), 4580–4592.CrossRefGoogle Scholar
  12. Hnaien, F., Delorme, X., & Dolgui, A. (2010). Multi-objective optimization for inventory control in two-level assembly systems under uncertainty of lead times. Computers & Operations Research, 37(11), 1835–1843.CrossRefGoogle Scholar
  13. Hoa, J. W., & Fang, C. C. (2013). Production capacity planning for multiple products under uncertain demand conditions. International Journal of Production Economics, 141(2), 593–604.CrossRefGoogle Scholar
  14. Hoque, M. (2013). A vendor–buyer integrated production-inventory model with normal distribution of lead time. International Journal of Production Economics, 144(2), 409–417.Google Scholar
  15. Inderfurth, K., & Kiesmüller, G.P. (2015). Exact and heuristic linear-inflation policies for an inventory model with random yield and arbitrary lead times. European Journal of OperationalResearch, 245(1), 109–120.Google Scholar
  16. Jiang, L., & Wang, Y. Z. (2010). Supplier Competition in decentralized assembly systems with price-sensitive and uncertain demand. Manufacturing & Service Operations Management, 12(1), 93–101.CrossRefGoogle Scholar
  17. Karmarkar, U. S. (1993). Manufacturing lead times, order release and capacity loading. Handbooks in Operations Research and Management Science, 4, 287–329.CrossRefGoogle Scholar
  18. Kelle, P., Transchel, S., & Minner, S. (2009). Buyer–supplier cooperation and negotiation support with random yield consideration. International Journal of Production Economics, 118(1), 152–159.CrossRefGoogle Scholar
  19. Kutzner, S. C., & Kiesmüller, G. P. (2013). Optimal control of an inventory-production system with state-dependent random yield. European Journal of Operational Research, 227(3), 444–452.CrossRefGoogle Scholar
  20. Kwon, H. D., Lippman, S. A., Cardle, K. M., & Tang, C. S. (2010). Project management contracts with delayed payments. Manufacturing & Service Operations Management, 12(4), 692–707.CrossRefGoogle Scholar
  21. Li, G., Gao, T., Ma, S. H., & Wang, Z. H. (2011). Supply collaboration in supply chain under uncertain delivery time and BOM pay-on-produce mode. Computer Integrated Manufacturing Systems, 17(2), 369–379. (in Chinese).Google Scholar
  22. Li, G., Liu, M. Q., Wang, Z. H., & Peng, B. Z. (2013). Supply coordination based on bonus policy in assembly under uncertain delivery time. Chinese Journal of Mechanical Engineering, 26(2), 293–393.CrossRefGoogle Scholar
  23. Li, G., Zhang, X., & Ma, S. H. (2010). Supply coordination model of two-suppliers and one-manufacturer system based on different delivery policies. Chinese Journal of Management Science, 18(5), 66–75. (in Chinese).Google Scholar
  24. Ma, S. H., Yin, Z., & Guan, X. (2013). The role of spot market in a decentralized supply chain under random yield. International Journal of Production Research, 51(21), 6410–6434.CrossRefGoogle Scholar
  25. Roya, A., Sana, S. S., & Chaudhuri, K. (2012). Optimal replenishment order for uncertain demand in three layer supply chain. Economic Modelling, 29(6), 2274–2282.CrossRefGoogle Scholar
  26. Shanthikumar, J. G., & Sumita, U. (1988). Approximations for the time spent in a dynamic job shop with applications to due date assignment. International Journal of Production Research, 26(8), 1329–1352.CrossRefGoogle Scholar
  27. Song, J. S., & Zipkin, P. (2003). Supply chain operations: Assemble-to-order systems. In S. Graves & R. D. Kok (Eds.), Hand books in operations research and management science (Vol. 11). Amsterdam: North Holland.Google Scholar
  28. Song, J. S., & Yao, D. D. (2002). Performance analysis and optimization of assemble to order with random leadtimes. Operations Research, 50(5), 889–903.CrossRefGoogle Scholar
  29. Tang, R., & Grubbstrom, W. (2003). The detailed coordination problem in a two-level supply chain with stochastic leadtimes. International Journal of Production Economic, 81–82, 415–429.CrossRefGoogle Scholar
  30. Thomas, W., & Heinrich, K. (2013). Analysis of a multi-component periodic review inventory system in an assembly environment. OR Spectrum, 35(1), 107–126.CrossRefGoogle Scholar
  31. Wang, Y., & Gerchak, Y. (2003). Capacity games in assembly systems with uncertain demand. Manufacturing & Service Operations Management, 5(3), 252–267.CrossRefGoogle Scholar
  32. Yano, C. A. (1987). Stochastic lead times in two-level assembly systems. IIE Transactions, 19(4), 371–378.CrossRefGoogle Scholar
  33. Yano, C. A., & Lee, H. L. (1995). Lot sizing with random yields: A review. Operations Research, 43(2), 331–334.CrossRefGoogle Scholar
  34. Zhang, J. L., & Chen, J. (2013). Supplier selection and procurement decisions with uncertain demand, fixed selection costs and quantity discounts. Computers & Operations Research., 40(11), 2703–2710.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Management and EconomicsBeijing Institute of TechnologyBeijingChina
  2. 2.Business SchoolHunan UniversityChangshaChina
  3. 3.Economics and Management SchoolWuhan UniversityWuhanChina

Personalised recommendations