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 & 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. doi: 10.1137/040604625. Google Scholar

[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), (2012), 7372. doi: 10.1109/CDC.2012.6425934. Google Scholar

[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. doi: 10.1287/opre.1060.0321. Google Scholar

[4]

D. Armbruster and R. Uzsoy, Continuous dynamic models, clearing functions, and discrete-event simulation in aggregate production planning,, in New Directions in Informatics, (2012). doi: 10.1287/educ.1120.0102. Google Scholar

[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. doi: 10.1002/nav.20335. Google Scholar

[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. doi: 10.1109/TSM.2005.863214. Google Scholar

[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. doi: 10.1080/00207548208947745. Google Scholar

[8]

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

[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), (2010). doi: 10.1137/1.9780898717600. Google Scholar

[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. doi: 10.4310/CMS.2012.v10.n4.a10. Google Scholar

[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. doi: 10.1137/120889721. Google Scholar

[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. doi: 10.1287/mnsc.34.11.1380. Google Scholar

[13]

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

[14]

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

[15]

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

[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. doi: 10.1080/00207549308956854. Google Scholar

[17]

N. B. Kacar, Fitting Clearing Functions to Empirical Data: Simulation, Optimization and Heuristic Algorithms,, Ph.D Thesis, (2012). Google Scholar

[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. Google Scholar

[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. doi: 10.1109/TAC.2010.2046925. Google Scholar

[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. doi: 10.1080/07408179708966311. Google Scholar

[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. doi: 10.1080/00207549308956824. Google Scholar

[22]

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

[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, (2010), 437. Google Scholar

[24]

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

[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. doi: 10.1007/978-0-85729-644-3_5. Google Scholar

[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. doi: 10.1080/095372800232504. Google Scholar

[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. doi: 10.1080/07408179408966627. Google Scholar

[28]

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

[29]

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

[30]

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

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. doi: 10.1137/040604625. Google Scholar

[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), (2012), 7372. doi: 10.1109/CDC.2012.6425934. Google Scholar

[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. doi: 10.1287/opre.1060.0321. Google Scholar

[4]

D. Armbruster and R. Uzsoy, Continuous dynamic models, clearing functions, and discrete-event simulation in aggregate production planning,, in New Directions in Informatics, (2012). doi: 10.1287/educ.1120.0102. Google Scholar

[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. doi: 10.1002/nav.20335. Google Scholar

[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. doi: 10.1109/TSM.2005.863214. Google Scholar

[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. doi: 10.1080/00207548208947745. Google Scholar

[8]

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

[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), (2010). doi: 10.1137/1.9780898717600. Google Scholar

[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. doi: 10.4310/CMS.2012.v10.n4.a10. Google Scholar

[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. doi: 10.1137/120889721. Google Scholar

[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. doi: 10.1287/mnsc.34.11.1380. Google Scholar

[13]

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

[14]

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

[15]

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

[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. doi: 10.1080/00207549308956854. Google Scholar

[17]

N. B. Kacar, Fitting Clearing Functions to Empirical Data: Simulation, Optimization and Heuristic Algorithms,, Ph.D Thesis, (2012). Google Scholar

[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. Google Scholar

[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. doi: 10.1109/TAC.2010.2046925. Google Scholar

[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. doi: 10.1080/07408179708966311. Google Scholar

[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. doi: 10.1080/00207549308956824. Google Scholar

[22]

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

[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, (2010), 437. Google Scholar

[24]

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

[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. doi: 10.1007/978-0-85729-644-3_5. Google Scholar

[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. doi: 10.1080/095372800232504. Google Scholar

[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. doi: 10.1080/07408179408966627. Google Scholar

[28]

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

[29]

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

[30]

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

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