American Institute of Mathematical Sciences

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January  2011, 7(1): 1-18. doi: 10.3934/jimo.2011.7.1

On the admission control and demand management in a two-station tandem production system

Eungab Kim 1,

1. 

College of Business Administration, Ewha Womans University, Seoul, South Korea

Received  April 2009 Revised  September 2010 Published  January 2011

This paper considers a two-station tandem production system consisting of make-to-stock and make-to-order facilities. The make-to-stock facility produces components which are served for external demands as well as internal make-to-order operations while the make-to-order facility processes customer orders with the option to accept or reject. We address the problem of coordinating the decision of when to accept customer order and when to satisfy component demand that maximizes the total expected discounted profit. To deal with this issue, we present a Markov decision process model of two-station tandem queueing system and characterize the structure of the optimal policy. We investigate the marginal impacts of system parameters on the optimal policy and implement a numerical experiment for comparing the performance between the optimal policy and the static policy with two fixed thresholds.
Keywords: dynamic programming., demand management, tandem queueing system, Markov decision process, Admission control.
Mathematics Subject Classification: Primary: 93E20, 90B30; Secondary: 60J2.
Citation: Eungab Kim. On the admission control and demand management in a two-station tandem production system. Journal of Industrial and Management Optimization, 2011, 7 (1) : 1-18. doi: 10.3934/jimo.2011.7.1
References:
[1]

S. Benjaafar and M. Elhafsi, Production and inventory control of a single product assemble-to-order system with multiple customer classes, Management Science, 52 (2006), 1896-1912. doi: 10.1287/mnsc.1060.0588.

[2]

M. Barut and V. Sridharan, Revenue management in order-driven production systems, Decision Science, 36 (2005), 287-316. doi: 10.1111/j.1540-5414.2005.00074.x.

[3]

S. Carr and I. Duenyas, Optimal admission control and sequencing in a Make-To-Stock/Make-To-Order production system, Operations Research, 48 (2000), 709-720. doi: 10.1287/opre.48.5.709.12401.

[4]

K. Chang and Y. Lu, Tandem queues production systems with base stocks, Proceedings of the 4th International Conference on Networked Computing and Advanced Information Management, (2008).

[5]

F. de Vericourt, F. Karaesmen and Y. Dallery, Optimal stock allocation for a capacitated supply system, Management Science, 48 (2002), 1486-1501. doi: 10.1287/mnsc.48.11.1486.263.

[6]

M. Elhafsi, Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes, European Journal of Operational Research, 194 (2009), 127-142. doi: 10.1016/j.ejor.2007.12.007.

[7]

A. Y. Ha, Inventory rationing in a make-to-stock production system with several demand classes and lost sales,, Management Science, 43 (): 1093.  doi: 10.1287/mnsc.43.8.1093.

[8]

A. Y. Ha, Stock rationing policy for a make-to-stock production system with two priority classes and backordering,, Naval Research Logistics, 44 (): 457.  doi: 10.1002/(SICI)1520-6750(199708)44:5<457::AID-NAV4>3.0.CO;2-3.

[9]

A. Y. Ha, Optimal dynamic scheduling policy for a make-to-stock production system,, Operations Research, 45 (): 42.  doi: 10.1287/opre.45.1.42.

[10]

F. H. Harris and J. P. Pinder, A revenue-management approach to demand management and order booking in assemble-to-order manufacturing, Journal of Operations Management, 13 (1995), 299-309. doi: 10.1016/0272-6963(95)00029-1.

[11]

S. Lippman, Applying a new device in the optimization of exponential queueing systems, Operations Research, 23 (1975), 687-710. doi: 10.1287/opre.23.4.687.

[12]

M. Modarres and M. Sharifyazdi, Revenue management approach to stochastic capacity allocation problem, European Journal of Operational Research, 192 (2009), 442-459. doi: 10.1016/j.ejor.2007.09.044.

[13]

E. Porteus, Conditions for characterizing the structure of optimal strategies in infinite-horizon dynamic programs, Journal of Optimization Theory and Applications, 36 (1982), 419-432. doi: 10.1007/BF00934355.

[14]

M. Puterman, "Markov Decision Processes," John Wiley and Sons, 2005.

[15]

S. Stidham, Optimal control of admission to a queueing system, IEEE Transactions on Automatic Control, 8 (1985), 705-713. doi: 10.1109/TAC.1985.1104054.

[16]

R. Teunter and W. Haneveld, Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering, European Journal of Operational Research, 190 (2008), 156-178. doi: 10.1016/j.ejor.2007.06.009.

[17]

M. P. Van Oyen, Monotonicity of optimal performance measures for polling systems, Probability in the Engineering and Informational Sciences, 11 (1997), 219-228. doi: 10.1017/S0269964800004770.

[18]

M. H. Veatch and L. M. Wein, Optimal control of a two-station tandem production/inventory system, Operations Research, 42 (1994), 337-350. doi: 10.1287/opre.42.2.337.

[19]

J. Yang, X. Qi, Y. Xia and G. Yu, Inventory control with Markovian capacity and the option of order rejection, European Journal of Operational Research, 174 (2006), 622-645. doi: 10.1016/j.ejor.2004.12.016.

show all references

References:
[1]

S. Benjaafar and M. Elhafsi, Production and inventory control of a single product assemble-to-order system with multiple customer classes, Management Science, 52 (2006), 1896-1912. doi: 10.1287/mnsc.1060.0588.

[2]

M. Barut and V. Sridharan, Revenue management in order-driven production systems, Decision Science, 36 (2005), 287-316. doi: 10.1111/j.1540-5414.2005.00074.x.

[3]

S. Carr and I. Duenyas, Optimal admission control and sequencing in a Make-To-Stock/Make-To-Order production system, Operations Research, 48 (2000), 709-720. doi: 10.1287/opre.48.5.709.12401.

[4]

K. Chang and Y. Lu, Tandem queues production systems with base stocks, Proceedings of the 4th International Conference on Networked Computing and Advanced Information Management, (2008).

[5]

F. de Vericourt, F. Karaesmen and Y. Dallery, Optimal stock allocation for a capacitated supply system, Management Science, 48 (2002), 1486-1501. doi: 10.1287/mnsc.48.11.1486.263.

[6]

M. Elhafsi, Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes, European Journal of Operational Research, 194 (2009), 127-142. doi: 10.1016/j.ejor.2007.12.007.

[7]

A. Y. Ha, Inventory rationing in a make-to-stock production system with several demand classes and lost sales,, Management Science, 43 (): 1093.  doi: 10.1287/mnsc.43.8.1093.

[8]

A. Y. Ha, Stock rationing policy for a make-to-stock production system with two priority classes and backordering,, Naval Research Logistics, 44 (): 457.  doi: 10.1002/(SICI)1520-6750(199708)44:5<457::AID-NAV4>3.0.CO;2-3.

[9]

A. Y. Ha, Optimal dynamic scheduling policy for a make-to-stock production system,, Operations Research, 45 (): 42.  doi: 10.1287/opre.45.1.42.

[10]

F. H. Harris and J. P. Pinder, A revenue-management approach to demand management and order booking in assemble-to-order manufacturing, Journal of Operations Management, 13 (1995), 299-309. doi: 10.1016/0272-6963(95)00029-1.

[11]

S. Lippman, Applying a new device in the optimization of exponential queueing systems, Operations Research, 23 (1975), 687-710. doi: 10.1287/opre.23.4.687.

[12]

M. Modarres and M. Sharifyazdi, Revenue management approach to stochastic capacity allocation problem, European Journal of Operational Research, 192 (2009), 442-459. doi: 10.1016/j.ejor.2007.09.044.

[13]

E. Porteus, Conditions for characterizing the structure of optimal strategies in infinite-horizon dynamic programs, Journal of Optimization Theory and Applications, 36 (1982), 419-432. doi: 10.1007/BF00934355.

[14]

M. Puterman, "Markov Decision Processes," John Wiley and Sons, 2005.

[15]

S. Stidham, Optimal control of admission to a queueing system, IEEE Transactions on Automatic Control, 8 (1985), 705-713. doi: 10.1109/TAC.1985.1104054.

[16]

R. Teunter and W. Haneveld, Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering, European Journal of Operational Research, 190 (2008), 156-178. doi: 10.1016/j.ejor.2007.06.009.

[17]

M. P. Van Oyen, Monotonicity of optimal performance measures for polling systems, Probability in the Engineering and Informational Sciences, 11 (1997), 219-228. doi: 10.1017/S0269964800004770.

[18]

M. H. Veatch and L. M. Wein, Optimal control of a two-station tandem production/inventory system, Operations Research, 42 (1994), 337-350. doi: 10.1287/opre.42.2.337.

[19]

J. Yang, X. Qi, Y. Xia and G. Yu, Inventory control with Markovian capacity and the option of order rejection, European Journal of Operational Research, 174 (2006), 622-645. doi: 10.1016/j.ejor.2004.12.016.

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