Finite Production Rate Model With Quality Assurance, Multi-customer and Discontinuous Deliveries

 

Yuan-Shyi Peter Chiu¹, Li-Wen Lin¹, Fan-Yun Pai³, Singa Wang Chiu*²

 

¹ Department of Industrial Engineering Chaoyang University of Technology, Taichung 413, Taiwan.

² Department of Business Administration, Chaoyang University of Technology, Taichung 413, Taiwan.

³ Department and Graduate Institute of Business Administration, National Changhua University of Education, Changhua 500, Taiwan.

 

Abstract

This study is concerned with the replenishment-shipment decision for a multi-customer finite production rate (FPR) model with quality assurance and discontinuous deliveries. We consider that a product is manufactured by a producer and all items are screened for quality control purpose. Nonconforming items will be picked up and categorized as scrap or repairable items. The reworking will be done right after the regular production in each replenishment cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to multi-customer in each cycle. Each customer has its own annual product demand, unit stock holding cost, as well as fixed and variable product delivery costs. Mathematical modeling along with Hessian matrix equations is employed to solve the proposed model. A closed-form optimal replenishment-shipment policy for such a specific integrated FPR model is obtained. A numerical example is provided to show the practical applicability of the obtained results.

Keywords: optimization, finite production rate model, replenishment-shipment policy, multiple customers, discontinuous deliveries, scrap, rework.

 

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References

[1] E.W. Taft, "The most economical production lot," Iron Age, vol. 101, pp. 1410-1412, 1918.         [ Links ]

[2] G. Hadley and T.M. Whitin, "An optimal final inventory model," Management Science, vol. 7, pp. 179-183, 1961.         [ Links ]

[3] W. Shih, "Optimal inventory policies when stock-outs result from defective products," International Journal of Production Research, vol. 18, no. 6, pp. 677-686, 1980.         [ Links ]

[4] M. Henig and Y. Gerchak, "Structure of periodic review policies in the presence of random yield," Operations Research, vol. 38, no. 4, pp. 634-643, 1990.         [ Links ]

[5] T. Boone et al., "The impact of imperfect processes on production run times," Decision Sciences, vol. 31, no. 4, pp.773-785, 2000.         [ Links ]

[6] E. Rubio and J.C. Jáuregui-Correa, "A Wavelet Approach to Estimate The Quality of Ground Parts," J. Appl. Res. Tech., vol. 10, no. 1, pp. 28-37, 2012.         [ Links ]

[7] G.C. Mahata, "An EPQ-based inventory model for exponentially deteriorating items under retailer partial trade credit policy in supply chain," Expert Systems with Applications, vol. 39, no. 3, pp. 3537-3550, 2012.         [ Links ]

[8] S.W. Chiu et al., "Production-shipment policy for EPQ model with quality assurance and an improved delivery schedule," Mathematical and Computer Modelling of Dynamical Systems, vol. 19, no. 4, pp. 344-352, 2013.         [ Links ]

[9] B.J. Yum and E.D. McDowell, "Optimal Inspection Policies in a Serial Production System including scrap, rework and repair: An MILP approach," International Journal of Production Research, vol. 25, no. 10, pp. 1451-1464, 1987.         [ Links ]

[10] A.M. Zargar, "Effect of rework strategies on cycle time," Computers and Industrial Engineering, vol. 29, no. 1-4, pp. 239-243, 1995.         [ Links ]

[11] R.H. Teunter and S.D.P. Flapper, "Lot-sizing for a single-stage single-product production system with rework of perishable production defectives," OR Spectrum, vol. 25, no. 1, pp. 85-96, 2003.         [ Links ]

[12] S.W. Chiu et al., "Note on the mathematical modeling approach used to determine the replenishment policy for the EMQ model with rework and multiple shipments," Applied Mathematics Letters, vol. 25, no. 11, pp. 1964-1968, 2012.         [ Links ]

[13] H.D. Lin and Y.S.P. Chiu, "Note on "replenishment run time problem with machine breakdown and failure in rework"," Expert Systems with Applications, vol. 39, no. 17, pp. 13070-13072, 2012.         [ Links ]

[14] B.R. Sarker and G.R. Parija, "An optimal batch size for a production system operating under a fixed-quantity, periodic delivery policy," Journal of the Operational Research Society, vol. 45, no. 8, pp. 891-900, 1994.         [ Links ]

[15] R.M. Hill, "On an optimal batch size for a production system operating under a fixed-quantity, periodic delivery policy," Journal of the Operational Research Society, vol. 46, no. 2, pp. 271-273, 1995.         [ Links ]

[16] D.J. Thomas and S.T. Hackman, "A committed delivery strategy with fixed frequency and quantity," European Journal of Operational Research, vol. 148, no. 2, pp. 363-373, 2003.         [ Links ]

[17] T.J. Lee et al., "On improving replenishment lot size of an integrated manufacturing system with discontinuous issuing policy and imperfect rework," American Journal of Industrial and Business Management, vol. 1, no. 1, pp. 20-29, 2011.         [ Links ]

[18] Y.S.P. Chiu et al., "Determination of production-shipment policy using a two- phase algebraic approach," Maejo Int. J. of Science and Technology, vol. 6, no. 1, pp. 119-129, 2012.         [ Links ]

[19] S.W. Chiu et al., "Optimizing replenishment policy in an EPQ-based inventory model with nonconforming items and breakdown," Economic Modelling, vol. 35, pp. 330-337.         [ Links ]

[20] Y.S. P. Chiu et al., "Reexamine "Combining an alternative multi-delivery policy into economic production lot size problem with partial rework" using alternative approach," J. Appl. Res. Tech., vol. 11, no. 3, pp. 317323, 2013.         [ Links ]

[21] L.B. Schwarz, A simple continuous review deterministic one-warehouse N-retailer inventory problem, Management Science, vol. 19, pp. 555-566, 1973.         [ Links ]

[22] A. Banerjee and S. Banerjee, "Coordinated order-less inventory replenishment for a vendor and multiple buyers," Int. J. Tech. Manage, vol. 7, pp. 328-336, 1992.         [ Links ]

[23] L. Lu, "A one-vendor multi-buyer integrated inventory model," European Journal of Operational Research, vol. 81, no. 2, pp. 312-323, 1995.         [ Links ]

[24] Y.Y. Woo et al., "An integrated inventory model for a single vendor and multiple buyers with ordering cost reduction," International Journal of Production Economics, vol. 73, no. 3, pp. 203-215, 2001.         [ Links ]

[25] M.J. Yao and C.-C. Chiou, "On a replenishment coordination model in an integrated supply chain with one vendor and multiple buyers," European Journal of Operational Research, vol. 159, pp. 406-419, 2004.         [ Links ]

[26] M.F. Yang and M.-C. Lo, "Considering single-vendor and multiple-buyers integrated supply chain inventory model with lead time reduction," Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 225, no. 5, pp. 747-759, 2011.         [ Links ]

[27] M.A. Hoque, "Synchronization in the single-manufacturer multi-buyer integrated inventory supply chain," European Journal of Operational Research, vol. 188, no. 3, pp. 811-825, 2008.         [ Links ]

[28] B.R. Sarker and A. Diponegoro, "Optimal production plans and shipment schedules in a supply- chain system with multiple suppliers and multiple buyers," European Journal of Operational Research, vol. 194, no. 3, pp. 753-773, 2009.         [ Links ]

[29] K.K. Chen et al., "Alternative approach for solving replenishment lot size problem with discontinuous issuing policy and rework," Expert Systems with Applications, vol. 39, no. 2, pp. 2232-2235, 2012.         [ Links ]

[30] J. Rojas-Arce et al., "The methodology for strategic plan implementation," J. Appl. Res. Tech., vol. 10, no. 2, pp. 248-261, 2012.         [ Links ]

[31] J.C. Cuevas-Tello et al., "Parallel Approach for Time Series Analysis with General Regression Neural Networks," J. Appl. Res. Tech., vol. 10, no. 2, pp. 162179, 2012.         [ Links ]

[32] Y.S.P. Chiu et al., "Optimal common cycle time for a multi-item production system with discontinuous delivery policy and failure in rework," Journal of Scientific & Industrial Research, vol. 72, no. 7, pp. 435-440, 2013.         [ Links ]

[33] S.W. Chiu et al., "Determining production-shipment policy for a vendor-buyer integrated system with rework and an amending multi-delivery schedule. Economic Modelling, vol. 33, pp. 668-675, 2013.         [ Links ]

[34] Y.C. Lin, "Mixed-integer constrained optimization based on memetic algorithm," J. Appl. Res. Tech., vol. 11, no. 2, pp. 242-250, 2013.         [ Links ]

[35] Y.S. P. Chiu et al., "Joint determination of rotation cycle time and number of shipments for a multi-item EPQ model with random defective rate," Economic Modelling, vol. 35, pp. 112-117, 2013.         [ Links ]

[36] R.L. Rardin, Optimization in Operations Research, Int. Ed., Prentice-Hall, New Jersey, 1998.         [ Links ]