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A heuristic algorithm for the optimization of M/M/$s$ queue with multiple working vacations
Optimal inventory control with fixed ordering cost for selling by internet auctions
1. | School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, China |
2. | School of Management, Fudan University, Shanghai 200433 |
References:
[1] |
K. J. Arrow, T. E. Harris and J. Marschak, Optimal inventory policy, Econometrica, 19 (1951), 250-272.
doi: 10.2307/1906813. |
[2] |
D. Bertsekas, "Dynamic Programming and Optimal Control," Vol. 2, 1st edition, Athena Scientific, Belmont, MA, 1995. |
[3] |
D. Blackwell, Discrete dynamic programming, Annals of Mathematics Statistics, 33 (1962), 719-726.
doi: 10.1214/aoms/1177704593. |
[4] |
S. Bollapragada and T. E. Morton, A simple heuristic for computing nonstationary $(s, S)$ policies, Operations Research, 47 (1999), 576-584.
doi: 10.1287/opre.47.4.576. |
[5] |
L. Caccetta and E. Mardaneh, Joint pricing and production planning for fixed priced multiple products with backorders, Journal of Industrial and Management Optimization, 6 (2010), 123-147. |
[6] |
F. Chen, Auctioning supply contracts, Management Science, 53 (2007), 1562-1576.
doi: 10.1287/mnsc.1070.0716. |
[7] |
X. Chen and D. Simchi-Levi, Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case, Operations Research, 52 (2004), 887-896.
doi: 10.1287/opre.1040.0127. |
[8] |
X. Chen and D. Simchi-Levi, Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The infinite horizon case, Mathematics of Operations Research, 29 (2004), 698-723.
doi: 10.1287/moor.1040.0093. |
[9] |
Y. Chen, S. Ray and Y. Song, Optimal pricing and inventory control policy in periodic-review sysytems with fixed ordering cost and lost sales, Naval Research Logistics, 53 (2006), 117-136.
doi: 10.1002/nav.20127. |
[10] |
H. A. David, "Order Statistics," 2nd edition, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York, 1981. |
[11] |
L. Du, Q. Hu and W. Yue, Analysis and evaluation for optimal allocation in sequential internet auction systems with reserve price, Dynamics of Continuous, Discrete and Impulsive System, Series B: Application and Algorithms, 12 (2005), 617-631. |
[12] |
A. Federgruen and A. Heching, Combined pricing and inventory control under uncertainty, Operations Research, 47 (1999), 454-475.
doi: 10.1287/opre.47.3.454. |
[13] |
E. L. Feiberg and M. E. Lewis, Optimality inequalities for average cost Markov decision processes and the optimality of $(s, S)$ policies, Working paper, Technical Report TR1442, Cornell University, 2006. Available from: http://legacy.orie.cornell.edu/techreports/TR1442.pdf. |
[14] |
Q. Feng, S. P. Sethi, H. Yan and H. Zhang, Optimality and nonoptimality of the base-stock policy in inventory problems with multiple delivery modes, Journal of Industrial and Management Optimization, 2 (2006), 19-42.
doi: 10.3934/jimo.2006.2.19. |
[15] |
Q. Hu and W. Yue, "Markov Decision Processes with Their Applications," Advances in Mechanics and Mathematics, 14, Springer, New York, 2008. |
[16] |
W. T. Huh and G. Janakiraman, $(s, S)$ optimality in joint inventory-pricing control: An alternate approach, Operations Research, 56 (2008), 783-790.
doi: 10.1287/opre.1070.0462. |
[17] |
W. T. Huh and G. Janakiraman, Inventory management with auctions and other sales channels: Optimality of $(s, S)$ policies, Management Science, 54 (2008), 139-150.
doi: 10.1287/mnsc.1070.0767. |
[18] |
D. Iglehart, Optimality of $(s, S)$ policies in the infinite-horizon dynamic inventory problem, Management Science, 9 (1963), 259-267.
doi: 10.1287/mnsc.9.2.259. |
[19] |
D. Iglehart, Dynamic programming and the analysis of inventory problems, in "Multistage Inventory Models and Technique" (eds. H. Scarf, D. Gilford and M. Shelly), Chap. 1, Stanford, 1963. |
[20] |
E. Maskin and J. Riley, Optimal multi-unit auctions, in "The Economic Theory of Auctions" (ed. P. Klemperer), Vol. 2, E. Elgar Publishing, U. K., (2000), 312-336. |
[21] |
R. Myerson, Optimal auction design, Mathematics of Operations Research, 6 (1981), 58-73.
doi: 10.1287/moor.6.1.58. |
[22] |
S. Nahmias, "Production and Operation Analysis," 4th edition, McGraw-Hill/Irwin, Boston, 2001. |
[23] |
E. L. Porteus, "Foundations of Stochastic Inventory Theory," Stanford University Press, Stanford, California, Stanford University Press, Stanford, California, 2002. |
[24] |
E. Pinker, A. Seidmann and Y. Vakrat, Using transaction data for the design of sequential, multi-unit, online auctions, Working paper CIS-00-03, William E. Simon Graduate School of Business Administration, University of Rochaster, Rochaster, NY, 2001. |
[25] |
E. Pinker, A. Seidmann and Y. Vakrat, Managing online auctions: Current business and research issues, Management Science, 49 (2003), 1457-1484.
doi: 10.1287/mnsc.49.11.1457.20584. |
[26] |
H. Scarf, The optimality of $(s, S)$ policies in the dynamic inventory problem, in "Mathematical Methods in the Social Sciences," 1959, Stanford University Press, Stanford, California, (1960), 196-202. |
[27] |
A. Segev, C. Beam and J. Shanthikumar, Optimal design of internet-based auctions, Information Technology and Mangement, 2 (2001), 121-163.
doi: 10.1023/A:1011411801246. |
[28] |
S. P. Sethi and F. Cheng, Optimality of $(s, S)$ policies in inventory models with Markovian demand, Operations Research, 45 (1997), 931-939.
doi: 10.1287/opre.45.6.931. |
[29] |
Y. Song, S. Ray and T. Boyaci, Optimal dynamic joint inventory-pricing control for multiplicative demand with fixed order costs and lost sales, Operations Research, 57 (2009), 245-250.
doi: 10.1287/opre.1080.0530. |
[30] |
A. F. Veinott, On the optimality of $(s, S)$ inventory policies: New conditions and a new proof, SIAM Journal on Applied Mathematics, 14 (1966), 1067-1083.
doi: 10.1137/0114086. |
[31] |
G. Vulcano, G. J. van Ryzin and C. Maglaras, Optimal dynamic auctions for revenue management, Management Science, 48 (2002), 1388-1407.
doi: 10.1287/mnsc.48.11.1388.269. |
[32] |
R. J. Weber, Multiple-object auctions, in "Auctions, Bidding, and Contracting: Uses and Theory" (eds. Richard Engelbrechtp-Wiggans, Martin Shubik and Robert M. Stark), Chapter 3, New York University Press, New York, 165-191; also in "The Economics Theory of Auctions" (ed. Paul Klemperer), Vol. II, Edward Elgar Publishing Limited, Cheltenham, UK / Edward Elgar Publishing, Inc., Northampton, USA, (1983), 240-266. |
[33] |
C. A. Yano and S. M. Gilbert, Coordinated pricing and producion/procurement decisions, A review, in "Managing Business Interfaces: Marketing, Engineering, and Manufacturing Perspectives" (eds. A. K. Chakravarty and J. Eliashberg), Kluwer Academic Publshers, Boston, Massachusetts, 2004. |
[34] |
Y. S. Zheng, A simple proof for optimality of $(s, S)$ policies in the infinite-horizon inventory systems, Journal of Applied Probability, 28 (1991), 802-810.
doi: 10.2307/3214683. |
[35] |
Y. S. Zheng and A. Federgruen, Finding optimal $(s, S)$ policies is about as simple as evaluating a single policy, Operations Research, 39 (1991), 654-665.
doi: 10.1287/opre.39.4.654. |
[36] |
P. H. Zipkin, "Foundations of Inventory Management," McGraw Hill, Boston, 2000. |
show all references
References:
[1] |
K. J. Arrow, T. E. Harris and J. Marschak, Optimal inventory policy, Econometrica, 19 (1951), 250-272.
doi: 10.2307/1906813. |
[2] |
D. Bertsekas, "Dynamic Programming and Optimal Control," Vol. 2, 1st edition, Athena Scientific, Belmont, MA, 1995. |
[3] |
D. Blackwell, Discrete dynamic programming, Annals of Mathematics Statistics, 33 (1962), 719-726.
doi: 10.1214/aoms/1177704593. |
[4] |
S. Bollapragada and T. E. Morton, A simple heuristic for computing nonstationary $(s, S)$ policies, Operations Research, 47 (1999), 576-584.
doi: 10.1287/opre.47.4.576. |
[5] |
L. Caccetta and E. Mardaneh, Joint pricing and production planning for fixed priced multiple products with backorders, Journal of Industrial and Management Optimization, 6 (2010), 123-147. |
[6] |
F. Chen, Auctioning supply contracts, Management Science, 53 (2007), 1562-1576.
doi: 10.1287/mnsc.1070.0716. |
[7] |
X. Chen and D. Simchi-Levi, Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case, Operations Research, 52 (2004), 887-896.
doi: 10.1287/opre.1040.0127. |
[8] |
X. Chen and D. Simchi-Levi, Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The infinite horizon case, Mathematics of Operations Research, 29 (2004), 698-723.
doi: 10.1287/moor.1040.0093. |
[9] |
Y. Chen, S. Ray and Y. Song, Optimal pricing and inventory control policy in periodic-review sysytems with fixed ordering cost and lost sales, Naval Research Logistics, 53 (2006), 117-136.
doi: 10.1002/nav.20127. |
[10] |
H. A. David, "Order Statistics," 2nd edition, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York, 1981. |
[11] |
L. Du, Q. Hu and W. Yue, Analysis and evaluation for optimal allocation in sequential internet auction systems with reserve price, Dynamics of Continuous, Discrete and Impulsive System, Series B: Application and Algorithms, 12 (2005), 617-631. |
[12] |
A. Federgruen and A. Heching, Combined pricing and inventory control under uncertainty, Operations Research, 47 (1999), 454-475.
doi: 10.1287/opre.47.3.454. |
[13] |
E. L. Feiberg and M. E. Lewis, Optimality inequalities for average cost Markov decision processes and the optimality of $(s, S)$ policies, Working paper, Technical Report TR1442, Cornell University, 2006. Available from: http://legacy.orie.cornell.edu/techreports/TR1442.pdf. |
[14] |
Q. Feng, S. P. Sethi, H. Yan and H. Zhang, Optimality and nonoptimality of the base-stock policy in inventory problems with multiple delivery modes, Journal of Industrial and Management Optimization, 2 (2006), 19-42.
doi: 10.3934/jimo.2006.2.19. |
[15] |
Q. Hu and W. Yue, "Markov Decision Processes with Their Applications," Advances in Mechanics and Mathematics, 14, Springer, New York, 2008. |
[16] |
W. T. Huh and G. Janakiraman, $(s, S)$ optimality in joint inventory-pricing control: An alternate approach, Operations Research, 56 (2008), 783-790.
doi: 10.1287/opre.1070.0462. |
[17] |
W. T. Huh and G. Janakiraman, Inventory management with auctions and other sales channels: Optimality of $(s, S)$ policies, Management Science, 54 (2008), 139-150.
doi: 10.1287/mnsc.1070.0767. |
[18] |
D. Iglehart, Optimality of $(s, S)$ policies in the infinite-horizon dynamic inventory problem, Management Science, 9 (1963), 259-267.
doi: 10.1287/mnsc.9.2.259. |
[19] |
D. Iglehart, Dynamic programming and the analysis of inventory problems, in "Multistage Inventory Models and Technique" (eds. H. Scarf, D. Gilford and M. Shelly), Chap. 1, Stanford, 1963. |
[20] |
E. Maskin and J. Riley, Optimal multi-unit auctions, in "The Economic Theory of Auctions" (ed. P. Klemperer), Vol. 2, E. Elgar Publishing, U. K., (2000), 312-336. |
[21] |
R. Myerson, Optimal auction design, Mathematics of Operations Research, 6 (1981), 58-73.
doi: 10.1287/moor.6.1.58. |
[22] |
S. Nahmias, "Production and Operation Analysis," 4th edition, McGraw-Hill/Irwin, Boston, 2001. |
[23] |
E. L. Porteus, "Foundations of Stochastic Inventory Theory," Stanford University Press, Stanford, California, Stanford University Press, Stanford, California, 2002. |
[24] |
E. Pinker, A. Seidmann and Y. Vakrat, Using transaction data for the design of sequential, multi-unit, online auctions, Working paper CIS-00-03, William E. Simon Graduate School of Business Administration, University of Rochaster, Rochaster, NY, 2001. |
[25] |
E. Pinker, A. Seidmann and Y. Vakrat, Managing online auctions: Current business and research issues, Management Science, 49 (2003), 1457-1484.
doi: 10.1287/mnsc.49.11.1457.20584. |
[26] |
H. Scarf, The optimality of $(s, S)$ policies in the dynamic inventory problem, in "Mathematical Methods in the Social Sciences," 1959, Stanford University Press, Stanford, California, (1960), 196-202. |
[27] |
A. Segev, C. Beam and J. Shanthikumar, Optimal design of internet-based auctions, Information Technology and Mangement, 2 (2001), 121-163.
doi: 10.1023/A:1011411801246. |
[28] |
S. P. Sethi and F. Cheng, Optimality of $(s, S)$ policies in inventory models with Markovian demand, Operations Research, 45 (1997), 931-939.
doi: 10.1287/opre.45.6.931. |
[29] |
Y. Song, S. Ray and T. Boyaci, Optimal dynamic joint inventory-pricing control for multiplicative demand with fixed order costs and lost sales, Operations Research, 57 (2009), 245-250.
doi: 10.1287/opre.1080.0530. |
[30] |
A. F. Veinott, On the optimality of $(s, S)$ inventory policies: New conditions and a new proof, SIAM Journal on Applied Mathematics, 14 (1966), 1067-1083.
doi: 10.1137/0114086. |
[31] |
G. Vulcano, G. J. van Ryzin and C. Maglaras, Optimal dynamic auctions for revenue management, Management Science, 48 (2002), 1388-1407.
doi: 10.1287/mnsc.48.11.1388.269. |
[32] |
R. J. Weber, Multiple-object auctions, in "Auctions, Bidding, and Contracting: Uses and Theory" (eds. Richard Engelbrechtp-Wiggans, Martin Shubik and Robert M. Stark), Chapter 3, New York University Press, New York, 165-191; also in "The Economics Theory of Auctions" (ed. Paul Klemperer), Vol. II, Edward Elgar Publishing Limited, Cheltenham, UK / Edward Elgar Publishing, Inc., Northampton, USA, (1983), 240-266. |
[33] |
C. A. Yano and S. M. Gilbert, Coordinated pricing and producion/procurement decisions, A review, in "Managing Business Interfaces: Marketing, Engineering, and Manufacturing Perspectives" (eds. A. K. Chakravarty and J. Eliashberg), Kluwer Academic Publshers, Boston, Massachusetts, 2004. |
[34] |
Y. S. Zheng, A simple proof for optimality of $(s, S)$ policies in the infinite-horizon inventory systems, Journal of Applied Probability, 28 (1991), 802-810.
doi: 10.2307/3214683. |
[35] |
Y. S. Zheng and A. Federgruen, Finding optimal $(s, S)$ policies is about as simple as evaluating a single policy, Operations Research, 39 (1991), 654-665.
doi: 10.1287/opre.39.4.654. |
[36] |
P. H. Zipkin, "Foundations of Inventory Management," McGraw Hill, Boston, 2000. |
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