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On EOQ cost models with arbitrary purchase and transportation costs
1. | Sabanci University, Manufacturing Systems and Industrial Engineering, Orhanli-Tuzla, 34956 Istanbul |
2. | Manufacturing Systems and Industrial Engineering, Sabancı University, Istanbul, Turkey |
3. | Erasmus University Rotterdam, Postbus 1738, 3000 DR Rotterdam, Netherlands |
References:
[1] |
P. L. Abad and V. Aggarwal, Incorporating transport cost in the lot size and pricing decisions with downward sloping demand,, International Journal of Production Economics, 95 (2005), 297.
doi: 10.1016/j.ijpe.2003.12.008. |
[2] |
F. J. Arcelus and J. E. Rowcroft, Inventory policies with freight and incremental quantity discounts,, International Journal of Systems Science, 22 (1991), 2025.
doi: 10.1080/00207729108910771. |
[3] |
J. B. Aubin, Optima and Equilibra (An introduction to nonlinear analysis), vol. 140 of Graduate Texts in Mathematics,, Springer Verlag, (1993).
doi: 10.1007/978-3-662-02959-6. |
[4] |
D. C. Aucamp, Nonlinear freight costs in the EOQ problem,, European Journal of Operational Research, 9 (1982), 61.
doi: 10.1016/0377-2217(82)90011-X. |
[5] |
W. J. Baumol and H. D. Vinod, An inventory theoretic model of freight transport demand,, Management Science, 16 (1970), 413.
doi: 10.1287/mnsc.16.7.413. |
[6] |
Z. P. Bayındır, Ş.İ. Birbil and J. Frenk, The joint replenishment problem with variable production costs,, European Journal of Operational Research, 175 (2006), 622.
doi: 10.1016/j.ejor.2005.06.005. |
[7] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms,, Third edition. Wiley-Interscience [John Wiley & Sons], (2006).
doi: 10.1002/0471787779. |
[8] |
C. R. Bector, Programming problems with convex fractional functions,, Operations Research, 16 (1968), 383.
doi: 10.1287/opre.16.2.383. |
[9] |
S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004).
doi: 10.1017/CBO9780511804441. |
[10] |
T. H. Burwell, D. S. Dave, K. E. Fitzpatrick and M. R. Roy, Economic lot size model for price-dependent demand under quantity and freight discounts,, International Journal of Production Economics, 48 (1997), 141.
doi: 10.1016/S0925-5273(96)00085-0. |
[11] |
J. R. Carter and B. G. Ferrin, Transportation costs and inventory management: Why transportation costs matter,, Production and Inventory Management Journal, 37 (1996), 58. Google Scholar |
[12] |
J. R. Carter, B. G. Ferrin and C. R. Carter, The effect of less-than-truckload rates on the purchase order lot size decision,, Transportation Journal, 34 (1995), 35. Google Scholar |
[13] |
J. R. Carter, B. G. Ferrin and C. R. Carter, On extending Russell and Krajewski's algorithm for economic purchase quantities,, Decision Sciences, 26 (1995), 819.
doi: 10.1111/j.1540-5915.1995.tb01577.x. |
[14] |
C. Das, A generalized discount structure and some dominance rules for selecting price-break EOQ,, European Journal of Operational Research, 34 (1988), 27.
doi: 10.1016/0377-2217(88)90452-3. |
[15] |
M. Drake and K. Marley, Handbook of EOQ Inventory Problems (Stochastic and Deterministic Models and Applications), chapter Century of the EOQ, 3-22,, Springer, (2014). Google Scholar |
[16] |
J. B. G. Frenk, M. Kaya and B. Pourghannad, chapter Generalizing the Ordering Cost and Holding-Backlog Cost Rate Functions in EOQ-Type Inventory Models,, Handbook of EOQ Inventory Problems (Stochastic and Deterministic Models and Applications), (2014), 79. Google Scholar |
[17] |
G. Hadley and T. Whitin, Analysis of Inventory Systems,, Prentice Hall, (1963). Google Scholar |
[18] |
F. Harris, How many parts to make at once,, Factory, 10 (1913), 135.
doi: 10.1287/opre.38.6.947. |
[19] |
R. Horst, P. M. Pardalos and N. V. Thoai, Introduction to Global Optimization,, Kluwer Academic Publishers, (1995).
|
[20] |
H. Hwang, D. H. Moon and S. W. Shinn, An EOQ model with quantity discounts for both purchasing price and freight cost,, Computers and Operations Research, 17 (1990), 73.
doi: 10.1016/0305-0548(90)90029-7. |
[21] |
K. Iwaniec, An inventory model with full load ordering,, Management Science, 25 (1979), 374.
doi: 10.1287/mnsc.25.4.374. |
[22] |
J. V. Jucker and M. J. Rosenblatt, Single-period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure,, Naval Research Logistics Quarterly, 32 (1985), 537.
doi: 10.1002/nav.3800320402. |
[23] |
T. W. Knowles and P. Pantumsinchai, All-units discounts for standard container sizes,, Decision Sciences, 19 (1988), 848.
doi: 10.1111/j.1540-5915.1988.tb00307.x. |
[24] |
D. Konur and A. Toptal, Analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices,, International Journal of Production Economics, 140 (2012), 521.
doi: 10.1016/j.ijpe.2012.07.003. |
[25] |
P. D. Larson, The economic transportation quantity,, Transportation Journal, 28 (1988), 43. Google Scholar |
[26] |
C. Lee, The economic order quantity for freight discount costs,, IIE Transactions, 18 (1986), 318.
doi: 10.1080/07408178608974710. |
[27] |
S. A. Lippman, Optimal inventory policy with multiple set-up costs,, Management Science, 16 (1969), 118.
doi: 10.1287/mnsc.16.1.118. |
[28] |
S. A. Lippman, Economic order quantities and multiple set-up costs,, Management Science, 18 (1971), 39.
doi: 10.1287/mnsc.18.1.39. |
[29] |
A. Mendoza and J. A. Ventura, Incorporating quantity discounts to the EOQ model with transportation costs,, International Journal of Production Economics, 113 (2008), 754.
doi: 10.1016/j.ijpe.2007.10.010. |
[30] |
J. A. Muckstadt and A. Sapra, Principles of Inventory Management: When You Are Down to Four Order More,, Springer, (2010).
doi: 10.1007/978-0-387-68948-7. |
[31] |
S. Nahmias, Production and Operations Analysis (Third Edition),, Irwin/McGraw-Hill, (1997). Google Scholar |
[32] |
E. Porteus, Handbooks in Operations Research and Management Science, Volume 2, Stochastic Models, chapter Stochastic Inventory Theory, 605-652,, North-Holland, (1990).
|
[33] |
B. Q. Rieksts and J. A. Ventura, Two-stage inventory models with a bi-modal transportation cost,, Computers & Operations Research, 37 (2010), 20.
doi: 10.1016/j.cor.2009.02.026. |
[34] |
B. Q. Rieskts and J. A. Ventura, Optimal inventory policies with two modes of freight transportation,, European Journal of Operational Research, 186 (2008), 576.
doi: 10.1016/j.ejor.2007.01.042. |
[35] |
A. Roberts and E. Varberg, Convex Functions,, Academic Press, (1973).
|
[36] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1997).
|
[37] |
R. M. Russell and L. J. Krajewski, Optimal purchase and transportation cost lot sizing for a single item,, Decision Sciences, 22 (1991), 940.
doi: 10.1111/j.1540-5915.1991.tb00373.x. |
[38] |
E. A. Silver, D. F. Pyke and R. Peterson, Inventory Management and Production Planning and Scheduling,, John Wiley and Sons, (1998). Google Scholar |
[39] |
S. R. Swenseth and M. R. Godfrey, Incorporating transportation costs into inventory replenishment decisions,, International Journal of Production Economics, 77 (2002), 113.
doi: 10.1016/S0925-5273(01)00230-4. |
[40] |
R. J. Tersine and S. Barman, Economic inventory/transport lot sizing with quantity and freight rate discounts,, Decision Sciences, 22 (1991), 1171.
doi: 10.1111/j.1540-5915.1991.tb01914.x. |
[41] |
A. Toptal, Replenishment decisions under an all-units discount schedule and stepwise freight costs,, European Journal of Operational Research, 198 (2009), 504.
doi: 10.1016/j.ejor.2008.09.037. |
[42] |
A. Toptal and S. Bingöl, Transportation pricing of a truckload carrier,, European Journal of Operational Research, 214 (2011), 559.
doi: 10.1016/j.ejor.2011.05.005. |
[43] |
A. F. Veinott Jr, The status of mathematical inventory theory,, Management Science, 12 (1966), 745.
doi: 10.1287/mnsc.12.11.745. |
[44] |
P. H. Zipkin, Foundations of Inventory Management,, McGraw-Hill, (2000). Google Scholar |
show all references
References:
[1] |
P. L. Abad and V. Aggarwal, Incorporating transport cost in the lot size and pricing decisions with downward sloping demand,, International Journal of Production Economics, 95 (2005), 297.
doi: 10.1016/j.ijpe.2003.12.008. |
[2] |
F. J. Arcelus and J. E. Rowcroft, Inventory policies with freight and incremental quantity discounts,, International Journal of Systems Science, 22 (1991), 2025.
doi: 10.1080/00207729108910771. |
[3] |
J. B. Aubin, Optima and Equilibra (An introduction to nonlinear analysis), vol. 140 of Graduate Texts in Mathematics,, Springer Verlag, (1993).
doi: 10.1007/978-3-662-02959-6. |
[4] |
D. C. Aucamp, Nonlinear freight costs in the EOQ problem,, European Journal of Operational Research, 9 (1982), 61.
doi: 10.1016/0377-2217(82)90011-X. |
[5] |
W. J. Baumol and H. D. Vinod, An inventory theoretic model of freight transport demand,, Management Science, 16 (1970), 413.
doi: 10.1287/mnsc.16.7.413. |
[6] |
Z. P. Bayındır, Ş.İ. Birbil and J. Frenk, The joint replenishment problem with variable production costs,, European Journal of Operational Research, 175 (2006), 622.
doi: 10.1016/j.ejor.2005.06.005. |
[7] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms,, Third edition. Wiley-Interscience [John Wiley & Sons], (2006).
doi: 10.1002/0471787779. |
[8] |
C. R. Bector, Programming problems with convex fractional functions,, Operations Research, 16 (1968), 383.
doi: 10.1287/opre.16.2.383. |
[9] |
S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004).
doi: 10.1017/CBO9780511804441. |
[10] |
T. H. Burwell, D. S. Dave, K. E. Fitzpatrick and M. R. Roy, Economic lot size model for price-dependent demand under quantity and freight discounts,, International Journal of Production Economics, 48 (1997), 141.
doi: 10.1016/S0925-5273(96)00085-0. |
[11] |
J. R. Carter and B. G. Ferrin, Transportation costs and inventory management: Why transportation costs matter,, Production and Inventory Management Journal, 37 (1996), 58. Google Scholar |
[12] |
J. R. Carter, B. G. Ferrin and C. R. Carter, The effect of less-than-truckload rates on the purchase order lot size decision,, Transportation Journal, 34 (1995), 35. Google Scholar |
[13] |
J. R. Carter, B. G. Ferrin and C. R. Carter, On extending Russell and Krajewski's algorithm for economic purchase quantities,, Decision Sciences, 26 (1995), 819.
doi: 10.1111/j.1540-5915.1995.tb01577.x. |
[14] |
C. Das, A generalized discount structure and some dominance rules for selecting price-break EOQ,, European Journal of Operational Research, 34 (1988), 27.
doi: 10.1016/0377-2217(88)90452-3. |
[15] |
M. Drake and K. Marley, Handbook of EOQ Inventory Problems (Stochastic and Deterministic Models and Applications), chapter Century of the EOQ, 3-22,, Springer, (2014). Google Scholar |
[16] |
J. B. G. Frenk, M. Kaya and B. Pourghannad, chapter Generalizing the Ordering Cost and Holding-Backlog Cost Rate Functions in EOQ-Type Inventory Models,, Handbook of EOQ Inventory Problems (Stochastic and Deterministic Models and Applications), (2014), 79. Google Scholar |
[17] |
G. Hadley and T. Whitin, Analysis of Inventory Systems,, Prentice Hall, (1963). Google Scholar |
[18] |
F. Harris, How many parts to make at once,, Factory, 10 (1913), 135.
doi: 10.1287/opre.38.6.947. |
[19] |
R. Horst, P. M. Pardalos and N. V. Thoai, Introduction to Global Optimization,, Kluwer Academic Publishers, (1995).
|
[20] |
H. Hwang, D. H. Moon and S. W. Shinn, An EOQ model with quantity discounts for both purchasing price and freight cost,, Computers and Operations Research, 17 (1990), 73.
doi: 10.1016/0305-0548(90)90029-7. |
[21] |
K. Iwaniec, An inventory model with full load ordering,, Management Science, 25 (1979), 374.
doi: 10.1287/mnsc.25.4.374. |
[22] |
J. V. Jucker and M. J. Rosenblatt, Single-period inventory models with demand uncertainty and quantity discounts: Behavioral implications and a new solution procedure,, Naval Research Logistics Quarterly, 32 (1985), 537.
doi: 10.1002/nav.3800320402. |
[23] |
T. W. Knowles and P. Pantumsinchai, All-units discounts for standard container sizes,, Decision Sciences, 19 (1988), 848.
doi: 10.1111/j.1540-5915.1988.tb00307.x. |
[24] |
D. Konur and A. Toptal, Analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices,, International Journal of Production Economics, 140 (2012), 521.
doi: 10.1016/j.ijpe.2012.07.003. |
[25] |
P. D. Larson, The economic transportation quantity,, Transportation Journal, 28 (1988), 43. Google Scholar |
[26] |
C. Lee, The economic order quantity for freight discount costs,, IIE Transactions, 18 (1986), 318.
doi: 10.1080/07408178608974710. |
[27] |
S. A. Lippman, Optimal inventory policy with multiple set-up costs,, Management Science, 16 (1969), 118.
doi: 10.1287/mnsc.16.1.118. |
[28] |
S. A. Lippman, Economic order quantities and multiple set-up costs,, Management Science, 18 (1971), 39.
doi: 10.1287/mnsc.18.1.39. |
[29] |
A. Mendoza and J. A. Ventura, Incorporating quantity discounts to the EOQ model with transportation costs,, International Journal of Production Economics, 113 (2008), 754.
doi: 10.1016/j.ijpe.2007.10.010. |
[30] |
J. A. Muckstadt and A. Sapra, Principles of Inventory Management: When You Are Down to Four Order More,, Springer, (2010).
doi: 10.1007/978-0-387-68948-7. |
[31] |
S. Nahmias, Production and Operations Analysis (Third Edition),, Irwin/McGraw-Hill, (1997). Google Scholar |
[32] |
E. Porteus, Handbooks in Operations Research and Management Science, Volume 2, Stochastic Models, chapter Stochastic Inventory Theory, 605-652,, North-Holland, (1990).
|
[33] |
B. Q. Rieksts and J. A. Ventura, Two-stage inventory models with a bi-modal transportation cost,, Computers & Operations Research, 37 (2010), 20.
doi: 10.1016/j.cor.2009.02.026. |
[34] |
B. Q. Rieskts and J. A. Ventura, Optimal inventory policies with two modes of freight transportation,, European Journal of Operational Research, 186 (2008), 576.
doi: 10.1016/j.ejor.2007.01.042. |
[35] |
A. Roberts and E. Varberg, Convex Functions,, Academic Press, (1973).
|
[36] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1997).
|
[37] |
R. M. Russell and L. J. Krajewski, Optimal purchase and transportation cost lot sizing for a single item,, Decision Sciences, 22 (1991), 940.
doi: 10.1111/j.1540-5915.1991.tb00373.x. |
[38] |
E. A. Silver, D. F. Pyke and R. Peterson, Inventory Management and Production Planning and Scheduling,, John Wiley and Sons, (1998). Google Scholar |
[39] |
S. R. Swenseth and M. R. Godfrey, Incorporating transportation costs into inventory replenishment decisions,, International Journal of Production Economics, 77 (2002), 113.
doi: 10.1016/S0925-5273(01)00230-4. |
[40] |
R. J. Tersine and S. Barman, Economic inventory/transport lot sizing with quantity and freight rate discounts,, Decision Sciences, 22 (1991), 1171.
doi: 10.1111/j.1540-5915.1991.tb01914.x. |
[41] |
A. Toptal, Replenishment decisions under an all-units discount schedule and stepwise freight costs,, European Journal of Operational Research, 198 (2009), 504.
doi: 10.1016/j.ejor.2008.09.037. |
[42] |
A. Toptal and S. Bingöl, Transportation pricing of a truckload carrier,, European Journal of Operational Research, 214 (2011), 559.
doi: 10.1016/j.ejor.2011.05.005. |
[43] |
A. F. Veinott Jr, The status of mathematical inventory theory,, Management Science, 12 (1966), 745.
doi: 10.1287/mnsc.12.11.745. |
[44] |
P. H. Zipkin, Foundations of Inventory Management,, McGraw-Hill, (2000). Google Scholar |
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