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October  2013, 9(4): 945-965. doi: 10.3934/jimo.2013.9.945

Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity

1. 

Department of Industrial Engineering and Management, National Taipei University of Technology, No.1, Sec. 3, Chung-Shiao E. Rd., Taipei, Taiwan 10643, Taiwan, Taiwan

2. 

Department of Transportation Science, National Taiwan Ocean University, 2 Pei-Ning Road, Keelung, Taiwan 20224, Taiwan

3. 

College of Management, National Taipei University of Technology, No.1, Sec. 3, Chung-Shiao E. Rd., Taipei, Taiwan 10643, Taiwan

Received  September 2011 Revised  November 2012 Published  August 2013

The aim of this paper is to develop an improved inventory model which helps the enterprises to advance their profit increasing and cost reduction in a single vendor-single buyer environment with permissible delay in payments depending on the ordering quantity and imperfect production. Through this study, some numerical examples available in the literature are provided herein to apply the permissible delay in payments depending on the ordering quantity strategy. Furthermore, imperfect products will cause the cost and increase number of lots through the whole model. Therefore, for more closely conforming to the actual inventories and responding to the factors that contribute to inventory costs, our proposed model can be the references to the business applications. Finally, results of this study showed applying the permissible delay in payments can promote the cost reduction; and also showed a longer trade credit term can decrease costs for the complete supply chain.
Citation: Chui-Yu Chiu, Ming-Feng Yang, Chung-Jung Tang, Yi Lin. Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity. Journal of Industrial and Management Optimization, 2013, 9 (4) : 945-965. doi: 10.3934/jimo.2013.9.945
References:
[1]

M. Badell, Empowering financial tradeoff with joint financial and supply chain planning models, Mathematical and Computer Modelling, 46 (2007), 12-23. doi: 10.1016/j.mcm.2006.12.027.

[2]

M. Ben-Daya and M. Hariga, Economic lot scheduling problem with imperfect production processes, Journal of the Operational Research Society, 51 (2000), 875-881.

[3]

C. E. Cheng, An economic order quantity model with demand-dependent unit production cost and imperfect production, IIE Transactions, 23 (1991), 23-28. doi: 10.1080/07408179108963838.

[4]

P. Chu, K.-J. Chung and S.-P. Lan, Economic order quantity of deteriorating items under permissible delay in payments, Computers & Operations Research, 25 (1998), 817-824. doi: 10.1016/S0305-0548(98)00006-9.

[5]

S.-L. Chung, H.-M. Wee and P.-C. Yang, Optimal policy for a closed-loop supply chain inventory system with remanufacturing, Mathematical and Computer Modelling, 48 (2008), 867-881. doi: 10.1016/j.mcm.2007.11.014.

[6]

K.-J. Chung, S. K. Goyal and Y.-F. Huang, The optimal inventory policies under permissible delay in payments depending on the ordering quantity, International Journal of Production Economics, 95 (2005), 203-213. doi: 10.1016/j.ijpe.2003.12.006.

[7]

S. K. Goyal, An integrated inventory model for a single supplier-single customer problem, International Journal of Production Research, 15 (1976), 107-111. doi: 10.1080/00207547708943107.

[8]

S. K. Goyal and L. E. Cardenas-Barron, Note on: Economic production quantity model for items with imperfect quality - a practical approach, International Journal of Production Economics, 77 (2002), 85-87. doi: 10.1016/S0925-5273(01)00203-1.

[9]

D. Ha and S.-L. Kim, Implementation of JIT purchasing: An integrated approach, Production Planning & Control, 8 (1997), 152-157. doi: 10.1080/095372897235415.

[10]

P. A. Hayek and M. K. Salameh, Production lot sizing with the reworking of imperfect quality items produced, Production Planning & Control, 12 (2001), 584-590. doi: 10.1080/095372801750397707.

[11]

C.-K. Huang, An integrated vendor-buyer cooperative inventory model for items with imperfect quality, Production Planning & Control, 13 (2002), 355-361. doi: 10.1080/09537280110112424.

[12]

C.-K. Huang, An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration, International Journal of Production Economics, 91 (2004), 91-98. doi: 10.1016/S0925-5273(03)00220-2.

[13]

H. Hwang and S. W. Shinn, Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments, Computers & Operations Research, 24 (1997), 539-547. doi: 10.1016/S0305-0548(96)00069-X.

[14]

B. Khorrami, "Static and Dynamic Inventory Models Under Inflation, Time Value of Money and Permissible Delay in Payment,'' Master thesis, West Virginia University, 2001.

[15]

I. Konstantaras, K. Skouri and M. Y. Jaber, Inventory models for imperfect quality items with shortages and learning in inspection, Applied Mathematical Modelling, 36 (2012), 5334-5343. doi: 10.1016/j.apm.2011.12.005.

[16]

H. L. Lee and M. J. Rosenblatt, Simultaneous determination of production cycle and inspection schedules in a production systems, Management Science, 33 (1987), 1125-1136. doi: 10.1287/mnsc.33.9.1125.

[17]

J.-J. Liao, An inventory control system under deferrable delivery conditions, Mathematical and Computer Modelling, 47 (2008), 247-258. doi: 10.1016/j.mcm.2007.02.021.

[18]

J. Lin, H. Feng and M. Wang, A replenishment policy with defective products, backlog and delay of payments, Journal of Industrial and Management Optimization, 5 (2009), 867-880. doi: 10.3934/jimo.2009.5.867.

[19]

A. K. Maity, K. Maiti, S. Mondal and M. Maiti, A Chebyshev approximation for solving the optimal production inventory problem of deteriorating multi-item, Mathematical and Computer Modelling, 45 (2007), 149-161. doi: 10.1016/j.mcm.2006.04.011.

[20]

L. Y. Ouyang, C. H. Ho and C. H. Su, Optimal strategy for the integrated vendor-buyer inventory model with adjustable production rate and trade credit, International Journal of Information and Management Sciences, 16 (2005), 19-37.

[21]

E. L. Porteus, Optimal lot sizing process quality improvement and setup cost reduction, Operations Research, 34 (1986), 137-144. doi: 10.1287/opre.34.1.137.

[22]

M. J. Rosenblatt and H. L. Lee, Economic production cycles with imperfect production processes, IIE Transactions, 18 (1986), 48-55. doi: 10.1080/07408178608975329.

[23]

A. Roy, M. K. Maiti, S. Kar and M. Maiti, Two storage inventory model with fuzzy deterioration over a random planning horizon, Mathematical and Computer Modelling, 46 (2007), 1419-1433. doi: 10.1016/j.mcm.2007.02.017.

[24]

M. K. Salameh and M. Y. Jaber, Economic production quantity model for items with imperfect quality, International Journal of Production Economics, 64 (2000), 59-64. doi: 10.1016/S0925-5273(99)00044-4.

[25]

B. Sarkar, An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production, Applied Mathematics and Computation, 218 (2012), 8295-8308. doi: 10.1016/j.amc.2012.01.053.

[26]

R. L. Schwaller, EOQ under inspection costs, Product Investment Management, 29 (1988), 22-24.

[27]

S. W. Shinn, Determining optimal retail price and lot size under day-terms supplier credit, Computers & Industrial Engineering, 33 (1997), 717-720. doi: 10.1016/S0360-8352(97)00230-1.

[28]

M.-J. Yao, S.-C. Chen and Y.-J. Chang, A common cycle approach for solving the economic lot and inspection scheduling problem, Journal of Industrial and Management Optimization, 8 (2012), 141-162. doi: 10.3934/jimo.2012.8.141.

[29]

X. Zhang and Y. Gerchak, Joint lot sizing and inspection policy in an EOQ model with random yield, IIE Transactions, 22 (1990), 41-47. doi: 10.1080/07408179008964156.

show all references

References:
[1]

M. Badell, Empowering financial tradeoff with joint financial and supply chain planning models, Mathematical and Computer Modelling, 46 (2007), 12-23. doi: 10.1016/j.mcm.2006.12.027.

[2]

M. Ben-Daya and M. Hariga, Economic lot scheduling problem with imperfect production processes, Journal of the Operational Research Society, 51 (2000), 875-881.

[3]

C. E. Cheng, An economic order quantity model with demand-dependent unit production cost and imperfect production, IIE Transactions, 23 (1991), 23-28. doi: 10.1080/07408179108963838.

[4]

P. Chu, K.-J. Chung and S.-P. Lan, Economic order quantity of deteriorating items under permissible delay in payments, Computers & Operations Research, 25 (1998), 817-824. doi: 10.1016/S0305-0548(98)00006-9.

[5]

S.-L. Chung, H.-M. Wee and P.-C. Yang, Optimal policy for a closed-loop supply chain inventory system with remanufacturing, Mathematical and Computer Modelling, 48 (2008), 867-881. doi: 10.1016/j.mcm.2007.11.014.

[6]

K.-J. Chung, S. K. Goyal and Y.-F. Huang, The optimal inventory policies under permissible delay in payments depending on the ordering quantity, International Journal of Production Economics, 95 (2005), 203-213. doi: 10.1016/j.ijpe.2003.12.006.

[7]

S. K. Goyal, An integrated inventory model for a single supplier-single customer problem, International Journal of Production Research, 15 (1976), 107-111. doi: 10.1080/00207547708943107.

[8]

S. K. Goyal and L. E. Cardenas-Barron, Note on: Economic production quantity model for items with imperfect quality - a practical approach, International Journal of Production Economics, 77 (2002), 85-87. doi: 10.1016/S0925-5273(01)00203-1.

[9]

D. Ha and S.-L. Kim, Implementation of JIT purchasing: An integrated approach, Production Planning & Control, 8 (1997), 152-157. doi: 10.1080/095372897235415.

[10]

P. A. Hayek and M. K. Salameh, Production lot sizing with the reworking of imperfect quality items produced, Production Planning & Control, 12 (2001), 584-590. doi: 10.1080/095372801750397707.

[11]

C.-K. Huang, An integrated vendor-buyer cooperative inventory model for items with imperfect quality, Production Planning & Control, 13 (2002), 355-361. doi: 10.1080/09537280110112424.

[12]

C.-K. Huang, An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration, International Journal of Production Economics, 91 (2004), 91-98. doi: 10.1016/S0925-5273(03)00220-2.

[13]

H. Hwang and S. W. Shinn, Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments, Computers & Operations Research, 24 (1997), 539-547. doi: 10.1016/S0305-0548(96)00069-X.

[14]

B. Khorrami, "Static and Dynamic Inventory Models Under Inflation, Time Value of Money and Permissible Delay in Payment,'' Master thesis, West Virginia University, 2001.

[15]

I. Konstantaras, K. Skouri and M. Y. Jaber, Inventory models for imperfect quality items with shortages and learning in inspection, Applied Mathematical Modelling, 36 (2012), 5334-5343. doi: 10.1016/j.apm.2011.12.005.

[16]

H. L. Lee and M. J. Rosenblatt, Simultaneous determination of production cycle and inspection schedules in a production systems, Management Science, 33 (1987), 1125-1136. doi: 10.1287/mnsc.33.9.1125.

[17]

J.-J. Liao, An inventory control system under deferrable delivery conditions, Mathematical and Computer Modelling, 47 (2008), 247-258. doi: 10.1016/j.mcm.2007.02.021.

[18]

J. Lin, H. Feng and M. Wang, A replenishment policy with defective products, backlog and delay of payments, Journal of Industrial and Management Optimization, 5 (2009), 867-880. doi: 10.3934/jimo.2009.5.867.

[19]

A. K. Maity, K. Maiti, S. Mondal and M. Maiti, A Chebyshev approximation for solving the optimal production inventory problem of deteriorating multi-item, Mathematical and Computer Modelling, 45 (2007), 149-161. doi: 10.1016/j.mcm.2006.04.011.

[20]

L. Y. Ouyang, C. H. Ho and C. H. Su, Optimal strategy for the integrated vendor-buyer inventory model with adjustable production rate and trade credit, International Journal of Information and Management Sciences, 16 (2005), 19-37.

[21]

E. L. Porteus, Optimal lot sizing process quality improvement and setup cost reduction, Operations Research, 34 (1986), 137-144. doi: 10.1287/opre.34.1.137.

[22]

M. J. Rosenblatt and H. L. Lee, Economic production cycles with imperfect production processes, IIE Transactions, 18 (1986), 48-55. doi: 10.1080/07408178608975329.

[23]

A. Roy, M. K. Maiti, S. Kar and M. Maiti, Two storage inventory model with fuzzy deterioration over a random planning horizon, Mathematical and Computer Modelling, 46 (2007), 1419-1433. doi: 10.1016/j.mcm.2007.02.017.

[24]

M. K. Salameh and M. Y. Jaber, Economic production quantity model for items with imperfect quality, International Journal of Production Economics, 64 (2000), 59-64. doi: 10.1016/S0925-5273(99)00044-4.

[25]

B. Sarkar, An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production, Applied Mathematics and Computation, 218 (2012), 8295-8308. doi: 10.1016/j.amc.2012.01.053.

[26]

R. L. Schwaller, EOQ under inspection costs, Product Investment Management, 29 (1988), 22-24.

[27]

S. W. Shinn, Determining optimal retail price and lot size under day-terms supplier credit, Computers & Industrial Engineering, 33 (1997), 717-720. doi: 10.1016/S0360-8352(97)00230-1.

[28]

M.-J. Yao, S.-C. Chen and Y.-J. Chang, A common cycle approach for solving the economic lot and inspection scheduling problem, Journal of Industrial and Management Optimization, 8 (2012), 141-162. doi: 10.3934/jimo.2012.8.141.

[29]

X. Zhang and Y. Gerchak, Joint lot sizing and inspection policy in an EOQ model with random yield, IIE Transactions, 22 (1990), 41-47. doi: 10.1080/07408179008964156.

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