在多階物流存貨管理中，兩相鄰階段中批量的傳遞，可牽涉到供應鍊各階段的整備、傳輸、存貨持有的成本問題。其中次批量的大小決定了很重要的成本因素。在此篇論文中，我們提出了一個單一非間斷的生產批量，在每個階段中一次整備，其中在每個相鄰的兩階段中，部分批量可以先傳送給下一生產階段讓下一階段先做。次批量大小遵循著兩相鄰階的生產批量比率的幾何分配，且跨階段次批量大小可以不同。我們將用提出批量分割方法，決定每一階的最佳次批量數；再利用上界線和下界線遞迴緊縮候選法來加以選出最佳成本。

This paper studies the multi-stage logistics and inventory problem in a serial supply chain in which a uniform lot size is produced uninterruptedly with a single setup at each stage. Partial lots, or sub-batches, can be transported to the next stage upon completion. Unequal sub-batch sizes at each stage follow geometric series and the numbers of sub-batches across stages are allowed to be different. Optimization algorithms that determine the economic lot size, the optimal sub-batch sizes and the number of sub-batches for each stage are subsequently developed. The polynomial-time algorithm incorporates the optimality properties derived in the paper to construct the solution ranges and find the lower and upper bounds of the solution accordingly.

[1].Szendrovits A. Z., 1975, “Manufacturing cycle time determination for a multi-stage economic production quantity model”, Management Science, 22, 298-308.
[2].Szendrovits A. Z. and Drezner Z., 1980, “Optimizing Multi-Stage Production with Constant Lot Size and Varying Numbers of Batches”, Omega, 8, 623-629.
[3].Vercellis C., 1999, “Multi-plant production planning in capacitated self-configuring two-stage serial systems”, European Journal of Operational Research, 119, 451-460.
[4].Quinn J., 1997, “What’s the buzz? Supply chain management”, Logistics Management, 36, 43.
[5].Cachon G. P. and Zipkin P. H., 1999, “Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain”, Management Science, 45, 936-953.
[6].Ratliff H.D., 1995, “Logistics management: Integrate your way to an improved bottom line”, IIE Solutions, 27, 31.
[7].Lee H. and Whang S., 1999, “Decentralized Multi-Echelon Supply Chains: Incentives and Information”, Management Science, 45, 633-640.
[8].Yung K. L., Tang J., Andrew W. H. Ip, and Wang D., 2006, “Heuristics for Joint Decisions in Production, Transportation, and Order Quantity”, Transportation Science, 40, 99-116.
[9].Hoque M. A. and Kingsman B. G., 2006, “Synchronization in common cycle lot size scheduling for a multi-product serial supply chain”, International Journal of Production Economics, 103, 316-331.
[10].Rahman M. A. A. and Sarker B. R., 2007, “Supply chain models for an assembly system with preprocessing of raw materials”, European Journal of Operational Research, 181, 733-752.
[11].Spekman R. E., Kamauff J. W. and Salmond D. J., 1994, “At Last Purchasing is Becoming Strategic”, Long Range Planning, 27, 76-84.
[12].Handfield R. B., Nichols E. L., 1999, Introduction to Supply Chain Management, Prentice Hall, Englewood Cliffs, NJ.
[13].Ganeshan R., 1999, “Managing supply chain inventories: A multiple retailer, one warehouse, multiple supplier model”, International Journal of Production Economics, 59, 341-354.
[14].Bogaschewsky R. W., Buscher U. D., and Lindner G., 2001, “Optimizing multi-stage production with constant lot size and varying number of unequal sized batches”, Omega, 29, 183-191.
[15].Goyal S. K., 1976, “Note on: Manufacturing cycle time determination for a multi-stage economic production quantity model”, Management Science, 23, 332-333.
[16].Goyal S. K., 1978, “Economic batch quantity in a multi-stage production system”, International Journal Production Research, 16, 267-273.
[17].Goyal S. K., 1978, “Determination of optimum production quantity for a two-stage production system”, Operations Research Quarterly, 28, 865-870.
[18].Goyal S. K. and Szendrovits A. Z., 1986, “A constant lot size model with equal and unequal sized batch shipments between production stages”, Engineering Costs and Production Economics, 10, 203-210.
[19].Wang S. and Sarker B. R., 2005, “An assembly-type supply chain system controlled by kanbans under a just-in-time delivery policy”, European Journal of Operational Research, 162, 153-172.