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Analysis and evaluation of an assemble-to-order system with batch ordering policy and compound Poisson demand. (English) Zbl 1176.90189
Summary: We consider a multi-product and multi-component Assemble-to-Order (ATO) system where the external demand follows compound Poisson processes and component inventories are controlled by continuous-time batch ordering policies. The replenishment lead-times of components are stochastic, sequential and exogenous. Each element of the bill of material (BOM) matrix can be any non-negative integer. Components are committed to demand on a first-come-first-serve basis. We derive exact expressions for key performance metrics under either the assumption that each demand must be satisfied in full (non-split orders), or the assumption that each unit of demand can be satisfied separately (split orders). We also develop an efficient sampling method to estimate these metrics, e.g., the expected delivery lead-times and the order-based fill-rates. Based on the analysis and a numerical study of an example motivated by a real world application, we characterize the impact of the component interaction on system performance, demonstrate the efficiency of the numerical method and quantify the impact of order splitting.

90B30 Production models
Full Text: DOI
[1] Agrawal, N.; Cohen, M.A., Optimal material control in an assembly system with component commonality, Naval research logistics, 48, 409-429, (2001) · Zbl 1005.90002
[2] Axsater, S., Supply chain operations: serial and distribution inventory systems, ()
[3] Benjaafar, S.; Elhafsi, M., Production and inventory control of a single product assemble-to-order systems with multiple customer classes, Management science, 52, 1896-1912, (2006) · Zbl 1232.90019
[4] Chen, F., Optimal policies for multi-echelon inventory problems with batch ordering, Operations research, 48, 376-389, (2000) · Zbl 1106.90302
[5] Cheng, F.; Ettl, M.; Lin, G.; Yao, D.D., Inventory-service optimization in configure-to-order systems, Manufacturing & service operations management, 4, 114-132, (2002)
[6] De Kok, Ton G., 2003. Evaluation and optimization of strongly ideal assemble-to-order systems. Working Paper, Technische Universiteit Eindhoven. The Netherlands. · Zbl 1149.90310
[7] Diks, E.B.; de Kok, A.G.; Lagodimos, A.G., Multi-echelon systems: A service measure perspective, European journal of operational research, 95, 241-263, (1996) · Zbl 0944.90501
[8] Elhafsi, M., Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes, European journal of operational research, 194, 1, 127-142, (2009) · Zbl 1158.90002
[9] Ernst, R.; Pyke, D.F., Component part stocking policies, Naval research logistics, 39, 509-529, (1992) · Zbl 0825.90340
[10] Hausman, W.H.; Lee, H.L.; Zhang, A.X., Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies, European journal of operational research, 109, 646-659, (1998) · Zbl 0936.90004
[11] Lu, Y., Estimation of average backorder for an assemble-to-order system with random batch demands through extreme statistics, Naval research logistics, 54, 33-45, (2007) · Zbl 1124.90003
[12] Lu, Y., Performance analysis for assemble-to-order systems with general renewal arrivals and random batch demands, European journal of operational research, 185, 635-647, (2008) · Zbl 1137.90317
[13] Lu, Y.; Song, J.S., Order-based cost optimization in assemble-to-order systems, Operations research, 53, 151-169, (2005) · Zbl 1165.90330
[14] Lu, Y.; Song, J.S.; Yao, D.D., Order fill rate, lead-time variability and advance demand information in an assemble-to-order system, Operations research, 51, 292-308, (2003) · Zbl 1163.90465
[15] Plambeck, E.L., 2005. Near optimal control of an assemble-to-order system with leadtime constraints and fixed shipping costs for components. Working Paper, Graduate School of Business, Stanford University. Stanford.
[16] Rosling, K., Optimal inventory policies for assembly systems under random demand, Operations research, 37, 565-579, (1989) · Zbl 0677.90025
[17] Sigman, K., Lecture notes on \(\mathit{GI} / M / 1\) queue, (2001), Columbia University New York, NY
[18] Simchi-Levi, D.; Zhao, Y., Safety stock positioning in supply chains with stochastic lead-times, Manufacturing & service operations management, 7, 295-318, (2005)
[19] Song, J.S., On the order fill rate in a multi-item, base-stock inventory system, Operations research, 46, 831-845, (1998) · Zbl 0987.90011
[20] Song, J.S., A note on assemble-to-order systems with batch ordering, Management sciences, 46, 739-943, (2000) · Zbl 1231.90062
[21] Song, J.S., Order-based backorders and their implications in multi-item inventory systems, Management science, 48, 499-516, (2002) · Zbl 1232.90092
[22] Song, J.S.; Zipkin, P., Supply chain operations: assemble-to-order systems, ()
[23] Svoronos, A.; Zipkin, P., Evaluation of one-for-one replenishment policies for multiechelon inventory systems, Management science, 37, 68-83, (1991)
[24] Tong, Y.L., Probability inequalities in multivariate distributions, (1980), Academic Press New York · Zbl 0455.60003
[25] Xu, S.H., Dependence analysis of assemble-to-order systems, (), (chapter 11)
[26] Zhang, A.X., Demand fulfillment rates in an assemble-to-order system with multiple products and dependent demands, Production and operations management, 6, 309-323, (1997)
[27] Zhao, Y., Evaluation and optimization of installation base-stock policies in supply chains with compound Poisson processes, Operations research, 56, 437-452, (2008) · Zbl 1167.90367
[28] Zhao, Y.; Simchi-Levi, D., Performance analysis and evaluation of assemble-to-order systems with stochastic sequential lead-times, Operations research, 54, 706-724, (2006) · Zbl 1167.90368
[29] Zipkin, P., Evaluation of base-stock policies in multiechelon inventory systems with compound-Poisson demands, Naval research logistics, 38, 397-412, (1991) · Zbl 0727.90022
[30] Zipkin, P., Foundations of inventory management, (2000), McGraw Hill Boston · Zbl 1370.90005
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