Optimal Ordering Policy of Deteriorating Items with Mixed Cargo Transportation Over a Finite Planning Horizon

Affiliation(s)

Department of Industrial Engineering & Management, National Chaio Tung University, Hsinchu, Chinese Taipei.

Department of Industrial Engineering & Management, National Chaio Tung University, Hsinchu, Chinese Taipei.

ABSTRACT

In this paper, we propose a deteriorating items inventory model with constant demand and deterioration rates, and mixed cargo transportation modes. The transportation modes are full container load (FCL) and less than container load (LCL). Deteriorating items, such as specialty gases which are applied in semiconductor fabrication, deteriorate owing to environmental variation. Exact algorithms are proposed to determine the optimal inventory policies over a finite and an infinite planning horizon. Numerical examples are given to illustrate the proposed solution procedures. In addition, when the deterioration rate is large, the results of the proposed model perform better compared to the inventory model proposed by Rieksts and Ventura (2008).

In this paper, we propose a deteriorating items inventory model with constant demand and deterioration rates, and mixed cargo transportation modes. The transportation modes are full container load (FCL) and less than container load (LCL). Deteriorating items, such as specialty gases which are applied in semiconductor fabrication, deteriorate owing to environmental variation. Exact algorithms are proposed to determine the optimal inventory policies over a finite and an infinite planning horizon. Numerical examples are given to illustrate the proposed solution procedures. In addition, when the deterioration rate is large, the results of the proposed model perform better compared to the inventory model proposed by Rieksts and Ventura (2008).

Cite this paper

H. Hsu and Z. Chen, "Optimal Ordering Policy of Deteriorating Items with Mixed Cargo Transportation Over a Finite Planning Horizon,"*American Journal of Operations Research*, Vol. 2 No. 1, 2012, pp. 106-121. doi: 10.4236/ajor.2012.21013.

H. Hsu and Z. Chen, "Optimal Ordering Policy of Deteriorating Items with Mixed Cargo Transportation Over a Finite Planning Horizon,"

References

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[2] S. K. Goyal and B. C. Giri, “Recent Trends in Modeling of Deteriorating Inventory,” European Journal of Operational Research, Vol. 134, No. 1, 2001, pp. 1-16. doi:10.1016/S0377-2217(00)00248-4

[3] R. Li, H. Lan and J. R. Mawhinney, “A Review on Deteriorating Inventory Study,” Journal of Service Science and Management, Vol. 3, No. 1, 2010, pp. 117-129. doi:10.4236/jssm.2010.31015

[4] B. Rieksts and J. Ventura, “Two-Stage Inventory Models with a Bi-Modal Transportation Cost,” Computers and Operations Research, Vol. 37, No. 1, 2010, pp. 20-31. doi:10.1016/j.cor.2009.02.026

[5] D. Aucamp, “Nonlinear Freight Costs in the EOQ Problem,” European Journal of Operational Research, Vol. 9, No. 1, 1982, pp. 61-63. doi:10.1016/0377-2217(82)90011-X

[6] S. Lippman, “Economic Order Quantities and Multiple Set-Up Costs,” Management Science, Vol. 18, No. 1, 1971, pp. 39-47. doi:10.1287/mnsc.18.1.39

[7] C. Y. Lee, “The Economic Order Quantity for Freight Discount Costs,” IIE Transactions, Vol. 18, No. 3, 1986, pp. 318-320. doi:10.1080/07408178608974710

[8] H. Hwang, D. Moon and S. Shinn, “An EOQ Model with Quantity Discounts for both Purchasing Price and Freight Cost,” Computers and Operations Research, Vol. 17, No. 1, 1990, pp. 73-78. doi:10.1016/0305-0548(90)90029-7

[9] R. Tersine, S. Barman and R. Toelle, “Composite lot Sizing with Quantity and Freight Discounts,” Computers and Industrial Engineering, Vol. 28, No. 1, 1995, pp. 107-122. doi:10.1016/0360-8352(94)00031-H

[10] W. Adelwahab and M. Sargious, “Freight Rate Structure and Optimal Shipment Size in Freight Transportation,” Logistics and Transportation Review, Vol. 26, No. 3, 1990, pp. 271-292.

[11] S, Swenseth and M. Godfrey, “Incorporating Transportation Costs into Inventory Replenishment Decisions,” International Journal of Production Economics, Vol. 77, No. 2, 2002, pp. 113-130. doi:10.1016/S0925-5273(01)00230-4

[12] L. Burns, R. Hall and D. Blumenfeld, “Distribution Strategies That Minimize Transportation and Inventory Costs,” Operations Research, Vol. 33, No. 3, 1985, pp. 469-490. doi:10.1287/opre.33.3.469

[13] P. Larson, “The Economic Transportation Quantity,” Transportation Journal, Vol. 28, No. 2, 1988, pp. 43-48.

[14] K.-J. Chung and C.-N. Lin, “Optimal Inventory Replenishment Models for Deteriorating Items Taking Account of Time Discounting,” Computers and Operations Research, Vol. 28, No. 1, 2001, pp. 67-83. doi:10.1016/S0305-0548(99)00087-8

[15] L. Benkherouf, A. Boumenir and L. Aggoun, “A Diffusion Inventory Model for Deteriorating Items,” Applied Mathematics and Computation, Vol. 138, No. 1, 2003, pp. 21-39. doi:10.1016/S0096-3003(02)00097-8

[16] K. J. Heng, J. Labban and R. L. Lim, “An Order-Level Lot Size Inventory Model for Deteriorating Items with Finite Replenishment Rate,” Computer and Industrial Engineering, Vol. 20, No. 2, 1991, pp. 187-197. doi:10.1016/0360-8352(91)90024-Z

[17] F. Raafat, P. M. Wolfe and H. K. Eldin, “An Inventory Model for Deteriorating Items,” Computers and Industrial Engineering, Vol. 20, No. 2, 1991, pp. 89-94. doi:10.1016/0360-8352(91)90043-6

[18] C. H. Goh, B. S. Greenberg and H. Matsuo, “Two-Stage Perishable Inventory Models,” Management Science, Vol. 39, No. 5, 1993, pp. 633-649. doi:10.1287/mnsc.39.5.633

[19] H. Yan and T. C. E. Cheng, “Optimal Production Stopping and Restarting Times for an EOQ Model with Deterioration Items,” Journal of the Operational Research Society, Vol. 49, No. 12, 1998, pp. 1288-1295.

[20] B. C. Giri, T. Chakrabarty and K. S. Chaudhuri, “A Note on a Lot Sizing Heuristic for Deteriorating Items with Time Varying Demands and Shortages,” Computers and Operations Research, Vol. 27, No. 6, 2000, pp. 495-505. doi:10.1016/S0305-0548(99)00013-1

[21] J.-T. Teng, H.-J. Chang, C.-Y. Dye and C.-H. Hung, “An Optimal Replenishment Policy for Deteriorating Items with Time-Varying Demand and Partial Backlogging,” Operations Research Letters, Vol. 30, No. 6, 2002, pp. 387-393. doi:10.1016/S0167-6377(02)00150-5

[22] K.-J. Chung, P. Chu and S.-P. Lan, “A Note on EOQ Models for Deteriorating Items under Stock Dependent Selling Rate,” European Journal of Operational Research, Vol. 124, No. 3, 2000, pp. 550-559. doi:10.1016/S0377-2217(99)00203-9

[23] B. C. Giri and K. S. Chaudhuri, “Deterministic Models of Perishable Inventory with Stock-Dependent Demand Rate and Nonlinear Holding Cost,” European Journal of Operational Research, Vol. 105, No. 3, 1998, pp. 467-474. doi:10.1016/S0377-2217(97)00086-6

[24] D. K. Bhattachaya, “Production, Manufacturing and Logistics on Multi-Item Inventory,” European Journal of Operational Research, Vol. 162, No. 3, 2005, pp. 786- 791.

[25] K.-S. Wu, L.-Y. Ouyang and C.-T. Yang, “An Optimal Replenishment Policy for Non-Instantaneous Deteriorating Items with Stock-Dependent Demand and Partial Backlogging,” International Journal of Production Economics, Vol. 101, No. 2, 2006, pp. 369-384. doi:10.1016/j.ijpe.2005.01.010

[26] H. M. Wee, “A Replenishment Policy for Items with a Price-Dependent Demand and a Varying Rate of Deterioration,” Production Planning and Control, 8, No. 5, 1997, pp. 494-499. doi:10.1080/095372897235073

[27] H.-M. Wee and S.-T. Law, “Economic Production Lot Size for Deteriorating Items Taking Account of the Time- Value of Money,” Computers and Operations Research, Vol. 26, No. 6, 1999, pp. 545-558. doi:10.1016/S0305-0548(98)00078-1

[28] P. M. Ghare and G. P. Schrader, “A Model for an Exponentially Decaying Inventory,” Journal of Industrial Engineering, Vol. 14, No. 5, 1963, pp. 238-243.

[29] Y. K. Shah and M. C. Jaiswal, “An Order-Level Inventory Model for a System with Constant Rate of Deterioration,” Opsearch, Vol. 14, 1977, pp. 174-184.

[30] G. Padmanabhana and P. Vratb, “EOQ Models for Perishable Items under Stock Dependent Selling Rate,” European Journal of Operational Research, Vol. 86, No. 2, 1995, pp. 281-292. doi:10.1016/0377-2217(94)00103-J

[31] A. K. Bhunia and M. Maiti, “An Inventory Model of Deteriorating Items with Lot-Size Dependent Replenishment Cost and a Linear Trend in Demand,” Applied Mathematical Modeling, Vol. 23, No. 4, 1999, pp. 301-308. doi:10.1016/S0307-904X(98)10089-6

[32] A. K. Bhunia and M. Maiti, “Deterministic Inventory Model for Deteriorating Items with Finite Rate of Replenishment Dependent on Inventory Level,” Computers and Operations Research, Vol. 25, No. 11, 1998, pp. 997- 1006. doi:10.1016/S0305-0548(97)00091-9

[33] P. L. Abad, “Optimal Price and Order Size for a Reseller under Partial Backordering,” Computers and Operations Research, Vol. 28, No. 1, 2001, pp. 53-65. doi:10.1016/S0305-0548(99)00086-6

[34] S. Mukhopadhyay, R. N. Mukherjee and K. S. Chaudhuri, “Joint Pricing and Ordering Policy for a Deteriorating Inventory,” Computers and Industrial Engineering, Vol. 47, No. 4, 2004, pp. 339-349. doi:10.1016/j.cie.2004.06.007

[35] N. K. Mahapatra, “Decision Process for Multi-Objective, Multi-Item Production-Inventory System via Interactive Fuzzy Satisficing Technique,” Computers and Mathematics with Applications, Vol. 49, No. 5, 2005, pp. 805- 821. doi:10.1016/j.camwa.2004.07.020

[36] L. Schwarz, “Economic Order Quantities for Products with Finite Demand Horizons,” AIIE Transactions, Vol. 4, No. 3, 1972, pp. 234-237. doi:10.1080/05695557208974855

[1] B. Rieksts and J. Ventura, “Optimal Inventory Policies with Two Modes of Freight Transportation,” European Journal of Operational Research, Vol. 186, No. 2, 2008, pp. 576-585. doi:10.1016/j.ejor.2007.01.042

[2] S. K. Goyal and B. C. Giri, “Recent Trends in Modeling of Deteriorating Inventory,” European Journal of Operational Research, Vol. 134, No. 1, 2001, pp. 1-16. doi:10.1016/S0377-2217(00)00248-4

[3] R. Li, H. Lan and J. R. Mawhinney, “A Review on Deteriorating Inventory Study,” Journal of Service Science and Management, Vol. 3, No. 1, 2010, pp. 117-129. doi:10.4236/jssm.2010.31015

[4] B. Rieksts and J. Ventura, “Two-Stage Inventory Models with a Bi-Modal Transportation Cost,” Computers and Operations Research, Vol. 37, No. 1, 2010, pp. 20-31. doi:10.1016/j.cor.2009.02.026

[5] D. Aucamp, “Nonlinear Freight Costs in the EOQ Problem,” European Journal of Operational Research, Vol. 9, No. 1, 1982, pp. 61-63. doi:10.1016/0377-2217(82)90011-X

[6] S. Lippman, “Economic Order Quantities and Multiple Set-Up Costs,” Management Science, Vol. 18, No. 1, 1971, pp. 39-47. doi:10.1287/mnsc.18.1.39

[7] C. Y. Lee, “The Economic Order Quantity for Freight Discount Costs,” IIE Transactions, Vol. 18, No. 3, 1986, pp. 318-320. doi:10.1080/07408178608974710

[8] H. Hwang, D. Moon and S. Shinn, “An EOQ Model with Quantity Discounts for both Purchasing Price and Freight Cost,” Computers and Operations Research, Vol. 17, No. 1, 1990, pp. 73-78. doi:10.1016/0305-0548(90)90029-7

[9] R. Tersine, S. Barman and R. Toelle, “Composite lot Sizing with Quantity and Freight Discounts,” Computers and Industrial Engineering, Vol. 28, No. 1, 1995, pp. 107-122. doi:10.1016/0360-8352(94)00031-H

[10] W. Adelwahab and M. Sargious, “Freight Rate Structure and Optimal Shipment Size in Freight Transportation,” Logistics and Transportation Review, Vol. 26, No. 3, 1990, pp. 271-292.

[11] S, Swenseth and M. Godfrey, “Incorporating Transportation Costs into Inventory Replenishment Decisions,” International Journal of Production Economics, Vol. 77, No. 2, 2002, pp. 113-130. doi:10.1016/S0925-5273(01)00230-4

[12] L. Burns, R. Hall and D. Blumenfeld, “Distribution Strategies That Minimize Transportation and Inventory Costs,” Operations Research, Vol. 33, No. 3, 1985, pp. 469-490. doi:10.1287/opre.33.3.469

[13] P. Larson, “The Economic Transportation Quantity,” Transportation Journal, Vol. 28, No. 2, 1988, pp. 43-48.

[14] K.-J. Chung and C.-N. Lin, “Optimal Inventory Replenishment Models for Deteriorating Items Taking Account of Time Discounting,” Computers and Operations Research, Vol. 28, No. 1, 2001, pp. 67-83. doi:10.1016/S0305-0548(99)00087-8

[15] L. Benkherouf, A. Boumenir and L. Aggoun, “A Diffusion Inventory Model for Deteriorating Items,” Applied Mathematics and Computation, Vol. 138, No. 1, 2003, pp. 21-39. doi:10.1016/S0096-3003(02)00097-8

[16] K. J. Heng, J. Labban and R. L. Lim, “An Order-Level Lot Size Inventory Model for Deteriorating Items with Finite Replenishment Rate,” Computer and Industrial Engineering, Vol. 20, No. 2, 1991, pp. 187-197. doi:10.1016/0360-8352(91)90024-Z

[17] F. Raafat, P. M. Wolfe and H. K. Eldin, “An Inventory Model for Deteriorating Items,” Computers and Industrial Engineering, Vol. 20, No. 2, 1991, pp. 89-94. doi:10.1016/0360-8352(91)90043-6

[18] C. H. Goh, B. S. Greenberg and H. Matsuo, “Two-Stage Perishable Inventory Models,” Management Science, Vol. 39, No. 5, 1993, pp. 633-649. doi:10.1287/mnsc.39.5.633

[19] H. Yan and T. C. E. Cheng, “Optimal Production Stopping and Restarting Times for an EOQ Model with Deterioration Items,” Journal of the Operational Research Society, Vol. 49, No. 12, 1998, pp. 1288-1295.

[20] B. C. Giri, T. Chakrabarty and K. S. Chaudhuri, “A Note on a Lot Sizing Heuristic for Deteriorating Items with Time Varying Demands and Shortages,” Computers and Operations Research, Vol. 27, No. 6, 2000, pp. 495-505. doi:10.1016/S0305-0548(99)00013-1

[21] J.-T. Teng, H.-J. Chang, C.-Y. Dye and C.-H. Hung, “An Optimal Replenishment Policy for Deteriorating Items with Time-Varying Demand and Partial Backlogging,” Operations Research Letters, Vol. 30, No. 6, 2002, pp. 387-393. doi:10.1016/S0167-6377(02)00150-5

[22] K.-J. Chung, P. Chu and S.-P. Lan, “A Note on EOQ Models for Deteriorating Items under Stock Dependent Selling Rate,” European Journal of Operational Research, Vol. 124, No. 3, 2000, pp. 550-559. doi:10.1016/S0377-2217(99)00203-9

[23] B. C. Giri and K. S. Chaudhuri, “Deterministic Models of Perishable Inventory with Stock-Dependent Demand Rate and Nonlinear Holding Cost,” European Journal of Operational Research, Vol. 105, No. 3, 1998, pp. 467-474. doi:10.1016/S0377-2217(97)00086-6

[24] D. K. Bhattachaya, “Production, Manufacturing and Logistics on Multi-Item Inventory,” European Journal of Operational Research, Vol. 162, No. 3, 2005, pp. 786- 791.

[25] K.-S. Wu, L.-Y. Ouyang and C.-T. Yang, “An Optimal Replenishment Policy for Non-Instantaneous Deteriorating Items with Stock-Dependent Demand and Partial Backlogging,” International Journal of Production Economics, Vol. 101, No. 2, 2006, pp. 369-384. doi:10.1016/j.ijpe.2005.01.010

[26] H. M. Wee, “A Replenishment Policy for Items with a Price-Dependent Demand and a Varying Rate of Deterioration,” Production Planning and Control, 8, No. 5, 1997, pp. 494-499. doi:10.1080/095372897235073

[27] H.-M. Wee and S.-T. Law, “Economic Production Lot Size for Deteriorating Items Taking Account of the Time- Value of Money,” Computers and Operations Research, Vol. 26, No. 6, 1999, pp. 545-558. doi:10.1016/S0305-0548(98)00078-1

[28] P. M. Ghare and G. P. Schrader, “A Model for an Exponentially Decaying Inventory,” Journal of Industrial Engineering, Vol. 14, No. 5, 1963, pp. 238-243.

[29] Y. K. Shah and M. C. Jaiswal, “An Order-Level Inventory Model for a System with Constant Rate of Deterioration,” Opsearch, Vol. 14, 1977, pp. 174-184.

[30] G. Padmanabhana and P. Vratb, “EOQ Models for Perishable Items under Stock Dependent Selling Rate,” European Journal of Operational Research, Vol. 86, No. 2, 1995, pp. 281-292. doi:10.1016/0377-2217(94)00103-J

[31] A. K. Bhunia and M. Maiti, “An Inventory Model of Deteriorating Items with Lot-Size Dependent Replenishment Cost and a Linear Trend in Demand,” Applied Mathematical Modeling, Vol. 23, No. 4, 1999, pp. 301-308. doi:10.1016/S0307-904X(98)10089-6

[32] A. K. Bhunia and M. Maiti, “Deterministic Inventory Model for Deteriorating Items with Finite Rate of Replenishment Dependent on Inventory Level,” Computers and Operations Research, Vol. 25, No. 11, 1998, pp. 997- 1006. doi:10.1016/S0305-0548(97)00091-9

[33] P. L. Abad, “Optimal Price and Order Size for a Reseller under Partial Backordering,” Computers and Operations Research, Vol. 28, No. 1, 2001, pp. 53-65. doi:10.1016/S0305-0548(99)00086-6

[34] S. Mukhopadhyay, R. N. Mukherjee and K. S. Chaudhuri, “Joint Pricing and Ordering Policy for a Deteriorating Inventory,” Computers and Industrial Engineering, Vol. 47, No. 4, 2004, pp. 339-349. doi:10.1016/j.cie.2004.06.007

[35] N. K. Mahapatra, “Decision Process for Multi-Objective, Multi-Item Production-Inventory System via Interactive Fuzzy Satisficing Technique,” Computers and Mathematics with Applications, Vol. 49, No. 5, 2005, pp. 805- 821. doi:10.1016/j.camwa.2004.07.020

[36] L. Schwarz, “Economic Order Quantities for Products with Finite Demand Horizons,” AIIE Transactions, Vol. 4, No. 3, 1972, pp. 234-237. doi:10.1080/05695557208974855