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July  2016, 12(3): 1091-1119. doi: 10.3934/jimo.2016.12.1091

An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity

Mohsen Lashgari 1, , Ata Allah Taleizadeh 1, and  Shib Sankar Sana 2,

1. 

School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
2. 

Department of Mathematics, Bhangar Mahavidyalaya, Bhangar-743502, South 24 Parganas, India

Received  November 2014 Revised  May 2015 Published  September 2015

The paper deals with an inventory control problem for perishable items where two level credit periods depend on the order quantity over the finite time horizon. We assume that the supplier offers delay in payment on outstanding cost of purchasing goods to the retailer when purchasing amount is more than a fixed large amount. Moreover, the retailer offers a delay period to the customers for payment of their purchasing goods. In the inventory system, shortage is permitted and it is completely backordered.The net present value of the retailer's cost function, including costs of ordering, inventory holding, shortage, purchasing and other opportunities, is optimized. Then, an algorithm is proposed to determine the optimal values of order quantity, shortage quantity, number of cycles and the total cost of the system. Finally, a numerical example with sensitivity analysis of the key parameters is illustrated to show the applicability of the proposed model.
Keywords: inflation, time value of money, Inventory, order quantity, trade credits, shortage..
Mathematics Subject Classification: 90B0.
Citation: Mohsen Lashgari, Ata Allah Taleizadeh, Shib Sankar Sana. An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1091-1119. doi: 10.3934/jimo.2016.12.1091
References:
[1]

S. P. Aggarwal and C. K. Jaggi, Ordering policies of deteriorating items under permissible delay in payments,, Journal of the Operational Research Society, 46 (1995), 658.   Google Scholar

[2]

M. Bakker, J. Riezebos and R. H. Teunter, Review of inventory systems with deterioration since 2001,, European journal of Operational Research, 221 (2012), 275.  doi: 10.1016/j.ejor.2012.03.004.  Google Scholar

[3]

C. T. Chang, L. Y. Ouyang and Y. T. Teng, An EOQ model for deteriorating items under supplier credits linked to ordering quantity,, Applied Mathematical Modelling, 27 (2003), 983.  doi: 10.1016/S0307-904X(03)00131-8.  Google Scholar

[4]

C. T. Chang, An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity,, Int. J. Prod.Econ., 88 (2004), 307.  doi: 10.1016/S0925-5273(03)00192-0.  Google Scholar

[5]

C. T. Chang, S. J. Wu and L. C. Chen, Optimal payment time with deteriorating items under inflation and permissible delay in payment,, International Journal of system Science, 40 (2009), 985.  doi: 10.1080/00207720902974561.  Google Scholar

[6]

J. M. Chen, An inventory model for deteriorating items with time-proportional demand and shortages under inflation and time discounting,, Int. J. Prod.Econ., 55 (1998), 21.  doi: 10.1016/S0925-5273(98)00011-5.  Google Scholar

[7]

C. Y. Chiu, M. F. Yang, C. Jung and Y. Lin, Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity,, Journal of Industrial and Management Optimization, 9 (2013), 945.  doi: 10.3934/jimo.2013.9.945.  Google Scholar

[8]

K. J. Chung, An EOQ model with defective items and partially permissible delay in payments linked to order quantity derived analytically in the supply chain management,, Appl. Math. Model., 37 (2013), 2317.  doi: 10.1016/j.apm.2012.05.014.  Google Scholar

[9]

K. J. Chung and P. S. Ting, The inventory model under supplier's partial trade credit policy in a supply chain system,, Journal of Industrial and Management Optimization, 11 (2015), 1175.  doi: 10.3934/jimo.2015.11.1175.  Google Scholar

[10]

M. Ghoreishi, A. Mirzazadeh, G. W. Weber, A. Turkey and I. Nakhai-Kamalabadi, Joint pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation- and selling price-dependent demand and customer returns,, Journal of Industrial and Management Optimization, 11 (2015), 933.  doi: 10.3934/jimo.2015.11.933.  Google Scholar

[11]

S. K. Goyal, EOQ under conditions of permissible delay in payments,, Journal of the Operational Research Society, 36 (1985), 335.   Google Scholar

[12]

Y. F. Huang, Optimal retailer's ordering polices in the EOQ model under trade credit financing,, Journal of Operational Research, 176 (2003), 911.   Google Scholar

[13]

A. Jamal, B. Sarker and S. Wang, Optimal payment time for a retailer under permitted delay of payment by the wholesaler,, Int. J. Prod.Econ., 66 (2000), 59.  doi: 10.1016/S0925-5273(99)00108-5.  Google Scholar

[14]

N. Khanlarzade, B. YousefiYegane, I. NakhaiKamalabadi and H. Farughid, Inventory control with deteriorating items: A state-of-the-art literature review,, International Journal of Industrial Engineering Computations, 5 (2014), 179.  doi: 10.5267/j.ijiec.2013.11.003.  Google Scholar

[15]

R. Li, H. Lan and J. R. Mawhinney, A review on deteriorating inventory study,, Journal of Service Science and Management, 3 (2010), 117.  doi: 10.4236/jssm.2010.31015.  Google Scholar

[16]

H. Liao and Y. Chen, Optimal payment time for retailers' inventory system,, International Journal of System Science, 34 (2003), 245.  doi: 10.1080/0020772031000158546.  Google Scholar

[17]

L. Y. Ouyang, C. T. Yang, Y. T. Chan and L. E. Cárdenas-Barrón, A comprehensive extension of the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity,, Applied Mathematics and Computation, 224 (2013), 268.  doi: 10.1016/j.amc.2013.08.062.  Google Scholar

[18]

B. Pal, S. S. Sana and K. S. Chaudhuri, Three stage trade credit policy in a three-layer supply chain: A production inventory model,, International Journal of Systems Science, 45 (2014), 1844.  doi: 10.1080/00207721.2012.757383.  Google Scholar

[19]

J. Ray and K. S. Chaudhuri, An EOQ model with stock-dependent demand, shortage, inflation and time discounting,, Int. J. Prod. Econ., 53 (1997), 171.  doi: 10.1016/S0925-5273(97)00112-6.  Google Scholar

[20]

S. Sana, An economic order quantity model for nonconforming quality products,, Service Science, 4 (2012), 331.  doi: 10.1287/serv.1120.0027.  Google Scholar

[21]

B. Sarkar, An EOQ model with delay in payments and time varying deterioration rate,, Mathematical and Computer Modelling, 55 (2012), 367.  doi: 10.1016/j.mcm.2011.08.009.  Google Scholar

[22]

T. Sarkar, S. K. Ghosh and K. S. Chaudhuri, An optimal inventory replenishment policy for a deteriorating item with time quadratic demand and time dependent partial backlogging with shortages in all cycles,, Applied Mathematics and Computation, 218 (2012), 9147.  doi: 10.1016/j.amc.2012.02.072.  Google Scholar

[23]

H. Soni, N. H. Shah and C. K. Jaggi, Inventory models and trade credit,, J. Con. Cyb., 39 (2010), 867.   Google Scholar

[24]

A. A. Taleizadeh and M. Nematollahi, An inventory control problem for deteriorating items with back-ordering and financial considerations,, Appl. Math.Model., 38 (2014), 93.  doi: 10.1016/j.apm.2013.05.065.  Google Scholar

[25]

A. A. Taleizadeh, D. W. Pentico, M. S. Jabal-ameli and M. Aryanezhad, An EOQ model with partial delayed payment and partial backordering,, Omega, 41 (2013), 354.  doi: 10.1016/j.omega.2012.03.008.  Google Scholar

[26]

P. S. Ting, The EPQ model with deteriorating items under two levels of trade credit in a supply chain system,, Journal of Industrial and Management Optimization, 11 (2015), 479.  doi: 10.3934/jimo.2015.11.479.  Google Scholar

[27]

M. Valliathal and R. Uthayakumar, An EOQ model for perishable items under stock and time dependent selling rate with shortages,, ARPN Journal of Engineering and Applied Sciences, 4 (2009), 8.   Google Scholar

[28]

G. A. Widyadana, L. E. Cárdenas-Barrón and H. M. Wee, Economic order quantity model for deteriorating items with planned backorder level,, Mathematical and Computer Modelling, 54 (2011), 1569.  doi: 10.1016/j.mcm.2011.04.028.  Google Scholar

show all references

References:
[1]

S. P. Aggarwal and C. K. Jaggi, Ordering policies of deteriorating items under permissible delay in payments,, Journal of the Operational Research Society, 46 (1995), 658.   Google Scholar

[2]

M. Bakker, J. Riezebos and R. H. Teunter, Review of inventory systems with deterioration since 2001,, European journal of Operational Research, 221 (2012), 275.  doi: 10.1016/j.ejor.2012.03.004.  Google Scholar

[3]

C. T. Chang, L. Y. Ouyang and Y. T. Teng, An EOQ model for deteriorating items under supplier credits linked to ordering quantity,, Applied Mathematical Modelling, 27 (2003), 983.  doi: 10.1016/S0307-904X(03)00131-8.  Google Scholar

[4]

C. T. Chang, An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity,, Int. J. Prod.Econ., 88 (2004), 307.  doi: 10.1016/S0925-5273(03)00192-0.  Google Scholar

[5]

C. T. Chang, S. J. Wu and L. C. Chen, Optimal payment time with deteriorating items under inflation and permissible delay in payment,, International Journal of system Science, 40 (2009), 985.  doi: 10.1080/00207720902974561.  Google Scholar

[6]

J. M. Chen, An inventory model for deteriorating items with time-proportional demand and shortages under inflation and time discounting,, Int. J. Prod.Econ., 55 (1998), 21.  doi: 10.1016/S0925-5273(98)00011-5.  Google Scholar

[7]

C. Y. Chiu, M. F. Yang, C. Jung and Y. Lin, Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity,, Journal of Industrial and Management Optimization, 9 (2013), 945.  doi: 10.3934/jimo.2013.9.945.  Google Scholar

[8]

K. J. Chung, An EOQ model with defective items and partially permissible delay in payments linked to order quantity derived analytically in the supply chain management,, Appl. Math. Model., 37 (2013), 2317.  doi: 10.1016/j.apm.2012.05.014.  Google Scholar

[9]

K. J. Chung and P. S. Ting, The inventory model under supplier's partial trade credit policy in a supply chain system,, Journal of Industrial and Management Optimization, 11 (2015), 1175.  doi: 10.3934/jimo.2015.11.1175.  Google Scholar

[10]

M. Ghoreishi, A. Mirzazadeh, G. W. Weber, A. Turkey and I. Nakhai-Kamalabadi, Joint pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation- and selling price-dependent demand and customer returns,, Journal of Industrial and Management Optimization, 11 (2015), 933.  doi: 10.3934/jimo.2015.11.933.  Google Scholar

[11]

S. K. Goyal, EOQ under conditions of permissible delay in payments,, Journal of the Operational Research Society, 36 (1985), 335.   Google Scholar

[12]

Y. F. Huang, Optimal retailer's ordering polices in the EOQ model under trade credit financing,, Journal of Operational Research, 176 (2003), 911.   Google Scholar

[13]

A. Jamal, B. Sarker and S. Wang, Optimal payment time for a retailer under permitted delay of payment by the wholesaler,, Int. J. Prod.Econ., 66 (2000), 59.  doi: 10.1016/S0925-5273(99)00108-5.  Google Scholar

[14]

N. Khanlarzade, B. YousefiYegane, I. NakhaiKamalabadi and H. Farughid, Inventory control with deteriorating items: A state-of-the-art literature review,, International Journal of Industrial Engineering Computations, 5 (2014), 179.  doi: 10.5267/j.ijiec.2013.11.003.  Google Scholar

[15]

R. Li, H. Lan and J. R. Mawhinney, A review on deteriorating inventory study,, Journal of Service Science and Management, 3 (2010), 117.  doi: 10.4236/jssm.2010.31015.  Google Scholar

[16]

H. Liao and Y. Chen, Optimal payment time for retailers' inventory system,, International Journal of System Science, 34 (2003), 245.  doi: 10.1080/0020772031000158546.  Google Scholar

[17]

L. Y. Ouyang, C. T. Yang, Y. T. Chan and L. E. Cárdenas-Barrón, A comprehensive extension of the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity,, Applied Mathematics and Computation, 224 (2013), 268.  doi: 10.1016/j.amc.2013.08.062.  Google Scholar

[18]

B. Pal, S. S. Sana and K. S. Chaudhuri, Three stage trade credit policy in a three-layer supply chain: A production inventory model,, International Journal of Systems Science, 45 (2014), 1844.  doi: 10.1080/00207721.2012.757383.  Google Scholar

[19]

J. Ray and K. S. Chaudhuri, An EOQ model with stock-dependent demand, shortage, inflation and time discounting,, Int. J. Prod. Econ., 53 (1997), 171.  doi: 10.1016/S0925-5273(97)00112-6.  Google Scholar

[20]

S. Sana, An economic order quantity model for nonconforming quality products,, Service Science, 4 (2012), 331.  doi: 10.1287/serv.1120.0027.  Google Scholar

[21]

B. Sarkar, An EOQ model with delay in payments and time varying deterioration rate,, Mathematical and Computer Modelling, 55 (2012), 367.  doi: 10.1016/j.mcm.2011.08.009.  Google Scholar

[22]

T. Sarkar, S. K. Ghosh and K. S. Chaudhuri, An optimal inventory replenishment policy for a deteriorating item with time quadratic demand and time dependent partial backlogging with shortages in all cycles,, Applied Mathematics and Computation, 218 (2012), 9147.  doi: 10.1016/j.amc.2012.02.072.  Google Scholar

[23]

H. Soni, N. H. Shah and C. K. Jaggi, Inventory models and trade credit,, J. Con. Cyb., 39 (2010), 867.   Google Scholar

[24]

A. A. Taleizadeh and M. Nematollahi, An inventory control problem for deteriorating items with back-ordering and financial considerations,, Appl. Math.Model., 38 (2014), 93.  doi: 10.1016/j.apm.2013.05.065.  Google Scholar

[25]

A. A. Taleizadeh, D. W. Pentico, M. S. Jabal-ameli and M. Aryanezhad, An EOQ model with partial delayed payment and partial backordering,, Omega, 41 (2013), 354.  doi: 10.1016/j.omega.2012.03.008.  Google Scholar

[26]

P. S. Ting, The EPQ model with deteriorating items under two levels of trade credit in a supply chain system,, Journal of Industrial and Management Optimization, 11 (2015), 479.  doi: 10.3934/jimo.2015.11.479.  Google Scholar

[27]

M. Valliathal and R. Uthayakumar, An EOQ model for perishable items under stock and time dependent selling rate with shortages,, ARPN Journal of Engineering and Applied Sciences, 4 (2009), 8.   Google Scholar

[28]

G. A. Widyadana, L. E. Cárdenas-Barrón and H. M. Wee, Economic order quantity model for deteriorating items with planned backorder level,, Mathematical and Computer Modelling, 54 (2011), 1569.  doi: 10.1016/j.mcm.2011.04.028.  Google Scholar

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