American Institute of Mathematical Sciences

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September  2015, 10(3): 511-526. doi: 10.3934/nhm.2015.10.511

Integrating release and dispatch policies in production models

Dieter Armbruster 1, , Michael Herty 2, , Xinping Wang 3, and  Lindu Zhao 3,

1. 

Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804
2. 

Department of Mathematics, IGPM, RWTH Aachen, Aachen, Germany
3. 

Institute of Systems Engineering, School of Economics and Management, Southeast University, Nanjing, 210096, China, China

Received  December 2014 Revised  February 2015 Published  July 2015

Aggregate production planning for highly re--entrant production processes is typically generated by finding optimal release rates based on clearing function models. For production processes with very long cycle times, like in semiconductor production, dispatch policies are used to cover short term fluctuations. We extend the concept of a clearing function to allow control over both, the release rates and priority allocations in re-entrant production. This approach is used to improve the production planning problem using combined release and the allocation dispatch policy. The control parameter for priority allocation, called the push-pull point (PPP), separates the beginning of the factory which employs a push policy from the end of the factory, which uses a pull policy. The extended clearing function model describes the output of the factory as a function of the work in progress (wip) and the position of the PPP. The model's qualitative behavior is analyzed. Numerical optimization results are compared to production planning based only on releases. It is found that controlling the PPP significantly reduces the average wip in the system and hence leads to much shorter cycle times.
Keywords: partial differential equations, Production planning, dispatch control, re-entrant production..
Mathematics Subject Classification: 35B37, 35L60, 93C2.
Citation: Dieter Armbruster, Michael Herty, Xinping Wang, Lindu Zhao. Integrating release and dispatch policies in production models. Networks and Heterogeneous Media, 2015, 10 (3) : 511-526. doi: 10.3934/nhm.2015.10.511
References:
[1]

D. Armbruster, P. Degond and C. Ringhofer, A model for the dynamics of large queuing networks and supply chains, SIAM J. Applied Mathematics, 66 (2006), 896-920. doi: 10.1137/040604625.

[2]

D. Armbruster, M. Herty and C. Ringhofer, A continuum description for a des control problem, in 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE, 2012, 7372-7376. doi: 10.1109/CDC.2012.6425934.

[3]

D. Armbruster, D. Marthaler, C. Ringhofer, K. G. Kempf and T.-C. Jo, A continuum model for a re-entrant factory, Operations Research, 54 (2006), 933-950. doi: 10.1287/opre.1060.0321.

[4]

D. Armbruster and R. Uzsoy, Continuous dynamic models, clearing functions, and discrete-event simulation in aggregate production planning, in New Directions in Informatics, Optimization, Logistics, and Production (ed. J. C. Smith), vol. TutORials in Operations Research, INFORMS, 2012. doi: 10.1287/educ.1120.0102.

[5]

J. Asmundsson, R. L. Rardin, C. H. Turkseven and R. Uzsoy, Production planning with resources subject to congestion, Naval Res. Logist., 56 (2009), 142-157. doi: 10.1002/nav.20335.

[6]

J. Asmundsson, R. L. Rardin and R. Uzsoy, Tractable nonlinear production planning: Models for semiconductor wafer fabrication facilities, IEEE Transactions on Semiconductor Wafer Fabrication Facilities, 19 (2006), 95-111. doi: 10.1109/TSM.2005.863214.

[7]

J. H. Blackstone, D. T. Philips and G. L. Hogg, A state-of-the-art survey of dispatching rules for manufacturing job shop operations, International Journal of Production Research, 20 (1982), 27-45. doi: 10.1080/00207548208947745.

[8]

R. Courant, K. O. Friedrichs and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Mathematische Annalen, 100 (1928), 32-74. doi: 10.1007/BF01448839.

[9]

C. D'Apice, S. Göttlich, M. Herty and B. Piccoli, Modeling, Simulation, and Optimization of Supply Chains, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2010. doi: 10.1137/1.9780898717600.

[10]

C. D'Apice, R. Manzo and B. Piccoli, Optimal input flows for a PDE-ODE model of supply chains, Communications in Mathematical Sciences, 10 (2012), 1225-1240. doi: 10.4310/CMS.2012.v10.n4.a10.

[11]

C. D'Apice, R. Manzo and B. Piccoli, Numerical schemes for the optimal input flow of a supply-chain, SIAM Journal on Numerical Analysis, 51 (2013), 2634-2650. doi: 10.1137/120889721.

[12]

G. D. Eppen and R. Kipp Martin, Determining safety stock in the presence of stochastic lead time and demand, Management Science, 34 (1988), 1380-1390. doi: 10.1287/mnsc.34.11.1380.

[13]

J. W. Fowler, G. L. Hogg and S. J. Mason, Workload control in the semiconductor industry, Production Planning and Control, 13 (2002), 568-578. doi: 10.1080/0953728021000026294.

[14]

S. Göttlich, M. Herty and A. Klar, Modelling and optimization of supply chains on complex networks, Commun. Math. Sci., 4 (2006), 315-330. doi: 10.4310/CMS.2006.v4.n2.a3.

[15]

S. T. Hackman and R. C. Leachman, A general framework for modeling production, Management Science, 35 (1989), 478-495. doi: 10.1287/mnsc.35.4.478.

[16]

K. Itoh, D. Huang and T. Enkawa, Twofold look-ahead search for multi-criterion job shop scheduling, International Journal of Production Research, 31 (1993), 2215-2234. doi: 10.1080/00207549308956854.

[17]

N. B. Kacar, Fitting Clearing Functions to Empirical Data: Simulation, Optimization and Heuristic Algorithms, Ph.D Thesis, North Carolina State University, 2012.

[18]

U. S. Karmarkar, Capacity loading and release planning with work-in-progress (wip) and lead-times, Journal of Manufacturing and Operations Management, 2 (1989), 105-123.

[19]

M. La Marca, D. Armbruster, M. Herty and C. Ringhofer, Control of continuum models of production systems, IEEE Trans. Automat. Control, 55 (2010), 2511-2526. doi: 10.1109/TAC.2010.2046925.

[20]

Y. H. Lee, K. Bhaskaran and M. A. Pinedo, A heuristic to minimize the total weighted tardiness with sequence dependent setups, IEEE Transactions on Design and Manufacturing, 29 (1997), 45-52. doi: 10.1080/07408179708966311.

[21]

R.-K. Li, Y.-T. Shyu and S. Adiga, A heuristic rescheduling algorithm for computer-based production scheduling systems, International Journal of Production Research, 31 (1993), 1815-1826. doi: 10.1080/00207549308956824.

[22]

K. N. McKay, F. R. Safayeni and J. A. Buzacott, Job shop scheduling theory: What is relevant?, Interfaces, 18 (1988), 84-90. doi: 10.1287/inte.18.4.84.

[23]

H. Missbauer and R. Uzsoy, Optimization models for production planning, in Planning Production and Inventories in the Extended Enterprise: A State of the Art Handbook (eds. K. Kempf, P. Keskinocak and R. Uzsoy), Springer-Verlag, New York, 2010, 437-508.

[24]

S. S. Panwalkar and W. Iskander, A survey of scheduling rules, Operations Research, 25 (1977), 45-61. doi: 10.1287/opre.25.1.45.

[25]

D. Perdaen, D. Armbruster, K. G. Kempf and E. Lefeber, Controlling a re-entrant manufacturing line via the push-pull point, Decision Policies for Production Networks, (2012), 103-117. doi: 10.1007/978-0-85729-644-3_5.

[26]

V. Subramaniam, G. K. Lee, G. S. Hong, Y. S. Wong and T. Ramesh, Dynamic selection of dispatching rules for job shop scheduling, Management of Operations, 11 (2000), 73-81. doi: 10.1080/095372800232504.

[27]

R. Uzsoy, C. Y. Lee and L. A. Martin-Vega, A review of production planning and scheduling models in the semiconductor industry part II: Shop-floor control, IIE Transactions, 26 (1994), 44-55. doi: 10.1080/07408179408966627.

[28]

R. Vancheeswaran and M. A. Townsend, Two-stage heuristic procedure for scheduling job shops, Journal of Manufacturing Systems, 12 (1993), 315-325. doi: 10.1016/0278-6125(93)90322-K.

[29]

L. M. Wein, Scheduling semiconductor wafer fabrication, IEEE Transactions on Semiconductor Manufacturing, 1 (1988), 115-130. doi: 10.1109/66.4384.

[30]

M. J. Zeestraten, The look ahead dispatching procedure, International Journal of Production Research, 28 (1990), 369-384. doi: 10.1080/00207549008942717.

show all references

References:
[1]

D. Armbruster, P. Degond and C. Ringhofer, A model for the dynamics of large queuing networks and supply chains, SIAM J. Applied Mathematics, 66 (2006), 896-920. doi: 10.1137/040604625.

[2]

D. Armbruster, M. Herty and C. Ringhofer, A continuum description for a des control problem, in 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE, 2012, 7372-7376. doi: 10.1109/CDC.2012.6425934.

[3]

D. Armbruster, D. Marthaler, C. Ringhofer, K. G. Kempf and T.-C. Jo, A continuum model for a re-entrant factory, Operations Research, 54 (2006), 933-950. doi: 10.1287/opre.1060.0321.

[4]

D. Armbruster and R. Uzsoy, Continuous dynamic models, clearing functions, and discrete-event simulation in aggregate production planning, in New Directions in Informatics, Optimization, Logistics, and Production (ed. J. C. Smith), vol. TutORials in Operations Research, INFORMS, 2012. doi: 10.1287/educ.1120.0102.

[5]

J. Asmundsson, R. L. Rardin, C. H. Turkseven and R. Uzsoy, Production planning with resources subject to congestion, Naval Res. Logist., 56 (2009), 142-157. doi: 10.1002/nav.20335.

[6]

J. Asmundsson, R. L. Rardin and R. Uzsoy, Tractable nonlinear production planning: Models for semiconductor wafer fabrication facilities, IEEE Transactions on Semiconductor Wafer Fabrication Facilities, 19 (2006), 95-111. doi: 10.1109/TSM.2005.863214.

[7]

J. H. Blackstone, D. T. Philips and G. L. Hogg, A state-of-the-art survey of dispatching rules for manufacturing job shop operations, International Journal of Production Research, 20 (1982), 27-45. doi: 10.1080/00207548208947745.

[8]

R. Courant, K. O. Friedrichs and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Mathematische Annalen, 100 (1928), 32-74. doi: 10.1007/BF01448839.

[9]

C. D'Apice, S. Göttlich, M. Herty and B. Piccoli, Modeling, Simulation, and Optimization of Supply Chains, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2010. doi: 10.1137/1.9780898717600.

[10]

C. D'Apice, R. Manzo and B. Piccoli, Optimal input flows for a PDE-ODE model of supply chains, Communications in Mathematical Sciences, 10 (2012), 1225-1240. doi: 10.4310/CMS.2012.v10.n4.a10.

[11]

C. D'Apice, R. Manzo and B. Piccoli, Numerical schemes for the optimal input flow of a supply-chain, SIAM Journal on Numerical Analysis, 51 (2013), 2634-2650. doi: 10.1137/120889721.

[12]

G. D. Eppen and R. Kipp Martin, Determining safety stock in the presence of stochastic lead time and demand, Management Science, 34 (1988), 1380-1390. doi: 10.1287/mnsc.34.11.1380.

[13]

J. W. Fowler, G. L. Hogg and S. J. Mason, Workload control in the semiconductor industry, Production Planning and Control, 13 (2002), 568-578. doi: 10.1080/0953728021000026294.

[14]

S. Göttlich, M. Herty and A. Klar, Modelling and optimization of supply chains on complex networks, Commun. Math. Sci., 4 (2006), 315-330. doi: 10.4310/CMS.2006.v4.n2.a3.

[15]

S. T. Hackman and R. C. Leachman, A general framework for modeling production, Management Science, 35 (1989), 478-495. doi: 10.1287/mnsc.35.4.478.

[16]

K. Itoh, D. Huang and T. Enkawa, Twofold look-ahead search for multi-criterion job shop scheduling, International Journal of Production Research, 31 (1993), 2215-2234. doi: 10.1080/00207549308956854.

[17]

N. B. Kacar, Fitting Clearing Functions to Empirical Data: Simulation, Optimization and Heuristic Algorithms, Ph.D Thesis, North Carolina State University, 2012.

[18]

U. S. Karmarkar, Capacity loading and release planning with work-in-progress (wip) and lead-times, Journal of Manufacturing and Operations Management, 2 (1989), 105-123.

[19]

M. La Marca, D. Armbruster, M. Herty and C. Ringhofer, Control of continuum models of production systems, IEEE Trans. Automat. Control, 55 (2010), 2511-2526. doi: 10.1109/TAC.2010.2046925.

[20]

Y. H. Lee, K. Bhaskaran and M. A. Pinedo, A heuristic to minimize the total weighted tardiness with sequence dependent setups, IEEE Transactions on Design and Manufacturing, 29 (1997), 45-52. doi: 10.1080/07408179708966311.

[21]

R.-K. Li, Y.-T. Shyu and S. Adiga, A heuristic rescheduling algorithm for computer-based production scheduling systems, International Journal of Production Research, 31 (1993), 1815-1826. doi: 10.1080/00207549308956824.

[22]

K. N. McKay, F. R. Safayeni and J. A. Buzacott, Job shop scheduling theory: What is relevant?, Interfaces, 18 (1988), 84-90. doi: 10.1287/inte.18.4.84.

[23]

H. Missbauer and R. Uzsoy, Optimization models for production planning, in Planning Production and Inventories in the Extended Enterprise: A State of the Art Handbook (eds. K. Kempf, P. Keskinocak and R. Uzsoy), Springer-Verlag, New York, 2010, 437-508.

[24]

S. S. Panwalkar and W. Iskander, A survey of scheduling rules, Operations Research, 25 (1977), 45-61. doi: 10.1287/opre.25.1.45.

[25]

D. Perdaen, D. Armbruster, K. G. Kempf and E. Lefeber, Controlling a re-entrant manufacturing line via the push-pull point, Decision Policies for Production Networks, (2012), 103-117. doi: 10.1007/978-0-85729-644-3_5.

[26]

V. Subramaniam, G. K. Lee, G. S. Hong, Y. S. Wong and T. Ramesh, Dynamic selection of dispatching rules for job shop scheduling, Management of Operations, 11 (2000), 73-81. doi: 10.1080/095372800232504.

[27]

R. Uzsoy, C. Y. Lee and L. A. Martin-Vega, A review of production planning and scheduling models in the semiconductor industry part II: Shop-floor control, IIE Transactions, 26 (1994), 44-55. doi: 10.1080/07408179408966627.

[28]

R. Vancheeswaran and M. A. Townsend, Two-stage heuristic procedure for scheduling job shops, Journal of Manufacturing Systems, 12 (1993), 315-325. doi: 10.1016/0278-6125(93)90322-K.

[29]

L. M. Wein, Scheduling semiconductor wafer fabrication, IEEE Transactions on Semiconductor Manufacturing, 1 (1988), 115-130. doi: 10.1109/66.4384.

[30]

M. J. Zeestraten, The look ahead dispatching procedure, International Journal of Production Research, 28 (1990), 369-384. doi: 10.1080/00207549008942717.

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