Skip to main content
SpringerLink
Log in

Applications to Production and Inventory

  • Chapter
  • First Online:
Optimal Control Theory

  • 2351 Accesses

Abstract

Applications of optimization methods to production and inventory problems date back at least to the classical EOQ (Economic Order Quantity) model or the lot size formula of Harris (1913) . The EOQ is essentially a static model in the sense that the demand is constant and only a stationary solution is sought. A dynamic version of the lot size model was analyzed by Wagner and Whitin (1958) . The solution methodology used there was dynamic programming.

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

Access this chapter

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 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  • Bensoussan A , Crouhy M , Proth J-M (1983) Mathematical theory of production planning. North-Holland, Amsterdam

    Google Scholar 

  • Bes C, Sethi SP (1988) Concepts of forecast and decision horizons: applications to dynamic stochastic optimization problems. Math Oper Res 13(2):295–310

    Article  Google Scholar 

  • Brown RG (1959) Statistical forecasting for inventory control. McGraw-Hill Book, New York

    Google Scholar 

  • Brown RG (1963) Smoothing, forecasting and prediction. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Chand S , Hsu VN , Sethi SP (2002) Forecast, solution and rolling horizons in operations management problems: a classified bibliography. Manufact Service Oper Manag 4(1):25–43

    Article  Google Scholar 

  • Clarke FH (1989) Methods of dynamic and nonsmooth optimization. Society for Industrial and Applied Mathematics, Philadelphia

    Google Scholar 

  • Feichtinger G, Hartl RF (1985b) On the use of Hamiltonian and maximized Hamiltonian in non-differentiable control theory. J Optim Theory Appl 46:493–504

    Google Scholar 

  • Harris FW (1913) How many parts to make at once. Factory Mag Manag 10:135–136, 152

    Google Scholar 

  • Hartl RF (1986a) A forward algorithm for a generalized wheat trading model. Z Oper Res 30:A 135–A 144

    Google Scholar 

  • Hartl RF (1988a) A wheat trading model with demand and spoilage. In: Feichtinger G (ed) Optimal control theory and economic analysis, vol 3. North-Holland, Amsterdam, pp 235–244

    Google Scholar 

  • Hartl RF (1989a) On forward algorithms for a generalized wheat trading model. In: Chikan A (ed) Progress in inventory research (proceedings of 4th international symposium on inventories). Hungarian Academy of Science, Budapest

    Article  Google Scholar 

  • Haurie A, Sethi SP (1984) Decision and forecast horizons, agreeable plans, and the maximum principle for infinite horizon control problems. Oper Res Lett 3(5):261–265

    Article  Google Scholar 

  • Holt CC , Modigliani F , Muth JF, Simon HA (1960) Planning production, inventories and workforce. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Ijiri Y, Thompson GL (1970) Applications of mathematical control theory to accounting and budgeting (the continuous wheat trading model). Account Rev 45:246–258

    Google Scholar 

  • Ijiri Y, Thompson GL (1972) Mathematical control theory solution of an interactive accounting flows model. Naval Res Logist Quart 19:411–422

    Article  Google Scholar 

  • Kleindorfer PR, Lieber Z (1979) Algorithms and planning horizon results for production planning problems with separable costs. Oper Res 27:874–887

    Article  Google Scholar 

  • Lieber Z (1973) An extension of Modigliani and Hohn’s planning horizon results. Manag Sci 20:319–330

    Google Scholar 

  • Lundin RA, Morton TE (1975) Planning horizons for the dynamic lot size model: protective procedures and computational results. Oper Res 23:711–734

    Google Scholar 

  • Modigliani F, Hohn F (1955) Production planning over time. Econometrica 23:46–66

    Article  Google Scholar 

  • Morton TE (1978) Universal planning horizons for generalized convex production scheduling. Oper Res 26:1046–1057

    Article  Google Scholar 

  • Norström CJ (1978) The continuous wheat trading model reconsidered. An application of mathematical control theory with a state constraint, W.P. 58–77-78, GSIA, Carnegie Mellon University, Pittsburgh

    Google Scholar 

  • Pekelman D (1974) Simultaneous price-production decision. Oper Res 22:788–794

    Article  Google Scholar 

  • Pekelman D (1975) Production smoothing with fluctuating price. Manag Sci 21:576–590

    Article  Google Scholar 

  • Pekelman D (1979) On optimal utilization of production processes. Oper Res 27:260–278

    Article  Google Scholar 

  • Rempala R (1986) Horizon for the dynamic family of wheat trading problems. In: Proceedings fourth international symposium on inventories, Budapest

    Google Scholar 

  • Rempala R, Sethi SP (1988) Forecast horizons in single product inventory models. In: Feichtinger G (ed) Optimal control theory and economic analysis, vol 3. North-Holland, Amsterdam, pp 225–233

    Google Scholar 

  • Rempala R, Sethi SP (1992) Decision and forecast horizons for one-dimensional optimal control problems: existence results and applications. Optimal Control Appl Methods 13:179–192

    Article  Google Scholar 

  • Sethi SP (1978a) A survey of management science applications of the deterministic maximum principle. TIMS Stud Manag Sci 9:33–67

    Google Scholar 

  • Sethi SP (1984) Application of the maximum principle to production and inventory problems. In: Proceedings third international symposium on inventories, Budapest, pp 753–756

    Google Scholar 

  • Sethi SP (1990) Decision and forecast horizons in dynamic optimization. In: Singh MG (ed) Systems and control encyclopedia supplementary, vol 1. Pergamon Press, Oxford, pp 192–198

    Google Scholar 

  • Sethi SP, Thompson GL (1982) Planning and forecast horizons in a simple wheat trading model. In: Feichtinger G, Kall P (eds) Operations research in progress. D. Reidel Publishing Company, Dordrecht, pp 203–214

    Chapter  Google Scholar 

  • Thompson GL, Sethi SP (1980) Turnpike horizons for production planning. Manag Sci 26:229–241

    Article  Google Scholar 

  • Vanthienen L (1975) A simultaneous price-reduction decision making with production adjustment costs. In: Proceedings XX international meeting of TIMS held in Tel Aviv, Israel on 24–29 June 1973, vol 1. Jerusalem Academic Press, Jerusalem, pp 249–254

    Google Scholar 

  • Wagner HM, Whitin TM (1958) Dynamic version of the economic lot size model. Manag Sci 5:89–96

    Article  Google Scholar 

  • Zwillinger D (2003) Standard mathematical tables and formulae. Chapman & Hall/CRC, Boca Raton

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Jindal School of Management, SM30, University of Texas at Dallas, Richardson, TX, USA

    Suresh P. Sethi

Authors
  1. Suresh P. Sethi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sethi, S.P. (2019). Applications to Production and Inventory. In: Optimal Control Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-98237-3_6

Download citation

Publish with us

Policies and ethics

Search

Navigation