Skip to main content
SpringerLink
Log in
Book cover

Production Planning with Capacitated Resources and Congestion pp 143–189Cite as

Univariate Clearing Functions

  • Chapter
  • First Online:

  • 789 Accesses

Abstract

In this chapter, we introduce the concept of the clearing function (CF), a metamodel of a production resource that relates the expected output of a resource to some measure of the work available to it in the planning period. We focus on clearing functions with a single state variable and examine a variety of functional forms that have been proposed in the production and traffic literature. We then formulate release planning models using these functions and show that while single-product models yield tractable convex optimization problems, the presence of multiple products competing for capacity at a shared resource creates significant difficulties. The allocated clearing function formulation is presented to address these issues and shown to yield more informative dual prices for resource capacity than conventional LP models.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Asmundsson J, Rardin RL, Uzsoy R (2006) Tractable nonlinear production planning models for semiconductor wafer fabrication facilities. IEEE Trans Semicond Manuf 19(1):95–111

    Article  Google Scholar 

  • Asmundsson J, Rardin RL, Turkseven CH, Uzsoy R (2009) Production planning with resources subject to congestion. Naval Res Logistics 56(2):142–157

    Article  Google Scholar 

  • Boyd S, Vandenberghe L (2009) Convex optimization. Cambridge University Press, Cambridge

    Google Scholar 

  • Buzacott JA, Shanthikumar JG (1993) Stochastic models of manufacturing systems. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Carey M (1987) Optimal time-varying flows on congested networks. Oper Res 35(1):58–69

    Article  Google Scholar 

  • Carey M (1992) Nonconvexity of the dynamic traffic assignment problem. Transport Res B 26B(2):127–133

    Article  Google Scholar 

  • Carey M, Bowers M (2012) A review of properties of flow–density functions. Transport Rev 32(1):49–73

    Article  Google Scholar 

  • Carey M, Subrahmanian E (2000a) An approach to modelling time-varying flows on congested networks. Transport Res B 34:157–183

    Article  Google Scholar 

  • Carey M, Subrahmanian E (2000b) An approach to modelling time-varying flows on congested networks. Transport Res Pt B Methodological 34(6):547

    Article  Google Scholar 

  • Curry GL, Feldman RM (2000) Manufacturing systems modelling and analysis. Springer, Berlin

    Google Scholar 

  • Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res Natl Bureau Standard B Math Sci 73B(2):91–118

    Article  Google Scholar 

  • Franklin RE (1961) The structure of a traffic shock wave. Civil Eng Publ Works Rev 56:1186–1188

    Google Scholar 

  • Gopalswamy K, Uzsoy R (2018) Conic programming reformulations of production planning problems research report. Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University. Raleigh, NC

    Google Scholar 

  • Gopalswamy K, Uzsoy R (2019) A data-driven iterative refinement approach for estimating clearing functions from simulation models of production systems. Int J Prod Res 57(19), 6013–6030.

    Article  Google Scholar 

  • Gopalswamy K, Fathi Y, Uzsoy R (2019) Valid inequalities for concave piecewise linear regression. Oper Res Lett 47:52–58

    Article  Google Scholar 

  • Graves SC (1986) A tactical planning model for a job shop. Oper Res 34(4):522–533

    Article  Google Scholar 

  • Graves SC (1988) Safety stocks in manufacturing systems. J Manuf Oper Manag 1:67–101

    Google Scholar 

  • Graves SC, Kletter DB, Hetzel WB (1998) Dynamic model for requirements planning with application to supply chain optimization. Oper Res 46(3):35–49

    Article  Google Scholar 

  • Hackman ST, Leachman RC (1989) A general framework for modeling production. Manag Sci 35(4):478–495

    Article  Google Scholar 

  • Hannah LA, Dunson LA (2013) Multivariate convex regression with adaptive partitioning. J Mach Learn Res 14(1):3261–3294

    Google Scholar 

  • Hopp WJ, Spearman ML (2008) Factory physics: foundations of manufacturing management. Irwin/McGraw-Hill, Boston

    Google Scholar 

  • Imamoto A, Tang B (2008) Optimal piecewise linear approximation of convex functions. World Congress on Engineering and Computer Science, San Francisco, CA

    Google Scholar 

  • Johnson LA, Montgomery DC (1974) Operations research in production planning, scheduling and inventory control. Wiley, New York

    Google Scholar 

  • Kacar NB, Moench L, Uzsoy R (2016) Modelling cycle times in production planning models for wafer fabrication. IEEE Trans Semicond Manuf 29(2):153–167

    Article  Google Scholar 

  • Karmarkar US (1989) Capacity loading and release planning with work-in-progress (WIP) and lead-times. J Manuf Oper Manag 2(1):105–123

    Google Scholar 

  • Kefeli A, Uzsoy R (2016) Identifying potential bottlenecks in production systems using dual prices from a mathematical programming model. Int J Prod Res 54(7):2000–2018

    Article  Google Scholar 

  • Leachman RC (2001) Semiconductor production planning. In: Pardalos PM, Resende MGC (eds) Handbook of applied optimization. Oxford University Press, New York, pp 746–762

    Google Scholar 

  • Merchant DK, Nemhauser GL (1978) A model and an algorithm for the dynamic traffic assignment problems. Transport Sci 12(3):183–199

    Article  Google Scholar 

  • Missbauer H (1998) Bestandsregelung als Basis für eine Neugestaltung von PPS-Systemen. Physica, Heidelberg

    Book  Google Scholar 

  • Missbauer H (2002) Aggregate order release planning for time-varying demand. Int J Prod Res 40:688–718

    Article  Google Scholar 

  • Newell G (1961) A theory of traffic flow in tunnels. In: Herman R (ed) Theory of traffic flow. Elsevier, Amsterdam, pp 193–206

    Google Scholar 

  • Nyhuis P, Wiendahl HP (2009) Fundamentals of production logistics: theory, tools and applications. Springer, Berlin

    Book  Google Scholar 

  • Parrish SH (1987) Extensions to a model for tactical planning in a job shop environment. Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA

    Google Scholar 

  • Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: the past, the present and the future. Netw Spat Econ 1(3-4):233–265

    Article  Google Scholar 

  • Pochet Y, Wolsey LA (2006) Production planning by mixed integer programming. Springer Science and Business Media, New York

    Google Scholar 

  • Srinivasan A, Carey M, Morton TE (1988) Resource pricing and aggregate scheduling in manufacturing systems. Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA

    Google Scholar 

  • Teo C, Bhatnagar R, Graves SC (2011) Setting planned lead times for a make-to-order production system with master schedule smoothing. IIE Trans 43:399–414

    Article  Google Scholar 

  • Teo C, Bhatnagar R, Graves SC (2012) An application of master schedule smoothing and planned lead time control. Prod Oper Manag 21(2):211–223

    Article  Google Scholar 

  • Toriello A, Vielma JP (2012) Fitting piecewise linear continuous functions. Eur J Oper Res 219:86–95

    Article  Google Scholar 

  • Turkseven CH (2005) Computational evaluation of production planning formulations using clearing functions. School of Industrial Engineering, Purdue University, West Lafayette, IN

    Google Scholar 

  • Van Aerde M, Rakha H (1995) Multivariate calibration of single regime speed–flow–density relationships. 6th Vehicle Navigation and Information Systems (VNIS) Conference, Seattle, WA

    Google Scholar 

  • Van Ooijen HPG, Bertrand JWM (2003) The effects of a simple arrival rate control policy on throughput and work-in-process in production systems with workload dependent processing rates. Int J Prod Econ 85(1):61–68

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Systems, Production and Logistics Management, University of Innsbruck, Innsbruck, Austria

    Hubert Missbauer

  2. Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, USA

    Reha Uzsoy

Authors
  1. Hubert Missbauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reha Uzsoy
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Science+Business Media, LLC, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Missbauer, H., Uzsoy, R. (2020). Univariate Clearing Functions. In: Production Planning with Capacitated Resources and Congestion. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0354-3_7

Download citation

Publish with us

Policies and ethics

Search

Navigation