Computational Optimization of Manufacturing Batch Size and Shipment for an Integrated EPQ Model with Scrap

Yuan-Shyi Peter Chiu, Hong-Dar Lin, Ming-Hon Hwang, Nong Pan
DOI: 10.4236/ajcm.2011.13023                

Abstract

This paper employs mathematical modeling and algebraic approach to derive the optimal manufacturing batch size and number of shipment for a vendor-buyer integrated economic production quantity (EPQ) model with scrap. Unlike the conventional method by using differential calculus to determine replenishment lot size and optimal number of shipments for such an integrated system, this paper proposes a straightforward algebraic approach to replace the use of calculus on the total cost function for solving the optimal production- shipment policies. A simpler form for computing long-run average cost for such a vendor- buyer integrated EPQ problem is also provided.

Keywords

Computational Optimization, Manufacturing Batch Size, Shipments, EPQ Model, Random Scrap Rate, Algebraic Approach

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	E. W. Taft, “The Most Economical Production Lot,” Iron Age, Vol. 101, 1918, pp. 1410-1412.
[2]	S. K. Goyal, “Integrated Inventory Model for a Single Supplier-Single Customer Prob-lem,” International Journal of Production Research, Vol. 15, No. 1, 1977, pp. 107-111.
[3]	L. B. Schwarz, B. L. Deuer-meyer and R. D. Badinelli, “Fill-Rate Optimization in a One-Warehouse N-Identical Retailer Distribution System,” Management Science, Vol. 31, No. 4, 1985, pp. 488-498.
[4]	L. Lu, “A One-Vendor Multi-Buyer Integrated Inventory Model,” European Journal of Operational Research, Vol. 81, No. 2, 1995, pp. 312-323.
[5]	R. A. Sarker and L. R. Khan, “Optimal Batch Size for a Production System Operating under Periodic Delivery Policy,” Computers and Industrial Engineering, Vol. 37, No. 4, 1999, pp. 711-730.
[6]	S. Viswanathan and R. Piplani, “Coordinating Supply Chain Inventories through Common Replenishment Epochs,” European Journal of Operational Research, Vol. 129, No. 2, 2001, pp. 277-286.
[7]	M. Eben-Chaime, “The Effect of Discreteness in Vendor- Buyer Relationships,” IIE Transactions, Vol. 36, No. 6, 2004, pp. 583-589.
[8]	R. M. Hill and M. Omar, “Another Look at the Single- Vendor Single-Buyer Integrated Production-Inventory Problem,” International Journal of Production Research, Vol. 44, No. 4, 2006, pp. 791-800.
[9]	Y.-S. P. Chiu, S. W. Chiu, C.-Y. Li, and C.-K. Ting, “Incorporating Multi-Delivery Policy and Quality Assurance into Economic Production Lot Size Problem,” Journal of Scientific & Indus-trial Research, Vol. 68, No. 6, 2009, pp. 505-512.
[10]	M. J. Rosenblatt and H. L. Lee, “Economic Production Cycles with Imperfect Production Processes,” IIE Transactions, Vol. 18, No. 1, 1986, pp. 48-55.
[11]	K. Moinzadeh and P. Aggarwal, “Analysis of a Production/Inventory System Subject to Ran-dom Disruptions,” Management Science, Vol. 43, No. 11, 1997, pp. 1577- 1588.
[12]	A. Chelbi and N. Rezg, “Analysis of a Production/In- Ventory System with Randomly Failing Production Unit Subjected to a Minimum Required Availability Level,” International Journal of Production Economics, Vol. 99, 2006, pp. 131-143.
[13]	S. W. Chiu, Y.-S. P. Chiu and C.-C. Shih, “Determining Expedited Time and Cost of the End Product with Defective Component Parts Using Critical Path Method (CPM) and Time-Costing Method,” Journal of Scien-tific & Industrial Research, Vol. 65, No. 9, 2006, pp. 695-701.
[14]	J. Li, D. E. Blumenfeld and S. P. Marin, “Pro-duction System Design for Quality Robustness,” IIE Transactions, Vol. 40, No. 3, 2008, pp. 162-176.
[15]	K-Y. C. Yu and D. L. Bricker, “Analysis of a Markov Chain Model of a Multi-stage Manufacturing System with Inspection, Rejection, and Rework,” IIE Transactions, Vol. 25, No. 1, 1993, pp. 109-112.
[16]	A. M. M. Jamal, B. R. Sarker and S. Mondal, “Optimal Manufacturing Batch Size with Rework Process at a Single-Stage Production System,” Computers & Industrial Engineering, Vol. 47, No. 2, 2004, pp. 77-89.
[17]	S. W. Chiu and Y.-S. P. Chiu, “Mathematical Modeling for Production System with Backlogging and Failure in Repair,” Journal of Scientific & Industrial Research, Vol. 65, 2006, pp. 499-506.
[18]	S. W. Chiu, “Production Run Time Problem with Machine Breakdowns under AR Control Policy and Re-work,” Journal of Scientific & Industrial Research, Vol. 66, No. 12, 2007, pp. 979-988
[19]	S. W. Chiu, K.-K. Chen and H.-H. Chang, “Mathematical Method for Expediting Scrap-or-Rework Decision Making in EPQ Model with Failure in Repair,” Mathematical and Computational Applications, Vol. 13, No. 3, 2008, pp. 137-145.
[20]	S. W. Chiu, “Robust Planning in Optimization for Production System Subject to Random Machine Breakdown and Failure in Rework,” Computers & Operations Research, Vol. 37, No. 5, 2010, pp. 899-908.
[21]	R. W. Grubbstr?m and A. Erdem, “The EOQ with Backlogging Derived without Derivatives,” International Journal of Production Economics, Vol. 59, No. 1-3, 1999, pp. 529-530.
[22]	S. W. Chiu, “Production Lot Size Problem with Failure in Repair and Backlogging Derived without Deriva-tives,” European Journal of Operational Research, Vol. 188, No. 2, 2008, pp. 610-615.
[23]	S. W. Chiu, C.-B. Cheng, M.-F. Wu and J.-C. Yang, “An Algebraic Approach for Determining Optimal Lot Size for EPQ Model with Rework Process,” Mathematical and Computational Applications, Vol. 2010, No. 3, 2010, pp. 364-370.
[24]	S. W. Chiu, H.-D. Lin, C.-B. Cheng and C.-L. Chung, “Optimal Production-Shipment Decisions for the Finite Production Rate Model with Scrap,” International Journal for Engineering Modelling, Vol. 22, No. 1-4, 2009, pp. 15-24.