Production Control with Price, Cost, and Demand Uncertainty

Abstract

An optimal production flow control problem of a make-to-stock manufacturing firm with price, cost, and demand uncertainty is studied. The objective of the flow rate control problem is maximizing the average profit that is the difference between the expected revenue and the expected production, inventory holding, and backlog costs. The uncertainties in the system are captured jointly in discrete environment states. In each environment state, the price, cost, and demand take different levels. The transitions between different environment states evolve according to a time-homogenous Markov chain. By using a continuous flow model, the optimal production policy is stated as a state-dependent hedging policy. The performance of the system where the production cost alternates between a high and a low cost level and the demand is either constant or also alternates between a high and a low level is analyzed under the double-hedging policy. According to this policy, the producer produces only when the cost is low and the surplus is between the two hedging levels. However when the backlog is below the lower hedging level, the producer produces with the maximum capacity regardless of the cost. The effects of production cost, production capacity, demand variability, and the dependence of the demand and the cost on the performance of the system are analyzed analytically and numerically. It is shown that controlling the production rate optimally allows producers respond to the fluctuations in price, cost, and demand in an effective way and maximize their profits.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  1. Ahmadi-Javid A, Malhamé R (2015) Optimal control of a multistate failure-prone manufacturing system under a conditional value-at-risk cost criterion. Journal of Optimization Theory and Applications 167(2):716–732

    Article  Google Scholar 

  2. Akella R, Kumar PR (1986) Optimal control of production rate in a failure prone manufacturing system. IEEE Transactions on Automatic Control AC–31(2):116–126

    Article  Google Scholar 

  3. Bielecki T, Kumar PR (1988) Optimality of zero-inventory policies for unreliable manufacturing systems. Operations Research 36(4):532–541

    Article  Google Scholar 

  4. Feng Y, Xiao B (2002) Optimal threshold control in discrete failure-prone manufacturing systems. IEEE Transactions on Automatic Control 47(7):1167–1174

    Article  Google Scholar 

  5. Fleming W, Sethi S, Soner H (1987) An optimal stochastic production planning with randomly fluctuating demand. SIAM Journal of Control Optimization 25:1495–1502

    Article  Google Scholar 

  6. Francie KA, Jean-Pierre K, Pierre D, Victor S, Vladimir P (2014) Stochastic optimal control of manufacturing systems under production-dependent failure rates. International Journal of Production Economics 150:174–187

    Article  Google Scholar 

  7. Gershwin SB (1994) Manufacturing Systems Engineering. Prentice-Hall,

  8. Gershwin SB, Tan B, Veatch MH (2009) Production control with backlog-dependent demand. IIE Transactions 41(6):511–523

    Article  Google Scholar 

  9. Ghosh M, Araposthathis A, Markus S (1993) Optimal control of switching diffusions with applications to flexible manufacturing systems. SIAM Journal of Control Optimization 31:1183–1204

    Article  Google Scholar 

  10. Hu J (1995) Production rate control for failure prone production with no backlog permitted. IEEE Transactions on Automatic Control 40(2):291–295

    Article  Google Scholar 

  11. Hu JQ, Vakili P, Huang L (2004) Capacity and production managment in a single product manufacturing system. Annals of Operations Research 125(1):191–204

    Article  Google Scholar 

  12. Karabağ O, Tan B (2018) Purchasing, production, and sales strategies for a production system with limited capacity and fluctuating sales and purchasing prices. IISE Transactions https://doi.org/10.1080/24725854.2018.1535217

    Article  Google Scholar 

  13. Kimemia JG, Gershwin SB (1983) An algorithm for the computer controlof production in a flexible manufacturing systems. IIE Transactions 15(4):353–362

    Article  Google Scholar 

  14. Liberopoulos G, Caramanis M (1994) Production control of manufacturing systems with production rate-dependent failure rates. IEEE Transactions on Automatic Control 39(4):889–895

    Article  Google Scholar 

  15. Malhamé R (1993) Ergodicity of hedging control policies in single-part multiple-state manufacturing systems. IEEE Transactions on Automatic Control 38(2):340–343

    Article  Google Scholar 

  16. Martinelli F (2010) Manufacturing systems with a production dependent failure rate: Structure of optimality. IEEE Transactions on Automatic Control 55(10):2401–2406

    Article  Google Scholar 

  17. Olsder GJ, Suri R (1980) Time-optimal control of flexible manufacturing systems with failure prone machines. In: Proceedings of the 19th IEEE Conference on Decision and Control. Albuquerque, New Mexico

  18. Perkins J, Srikant R (2001) Failure-prone production systems with uncertain demand. IEEE Transactions on Automatic Control 46(3):441–449

    Article  Google Scholar 

  19. Rivera-Gómez H, Gharbi A, Kenné JP, Montaño-Arango O, Hernandez-Gress ES (2016) Production control problem integrating overhaul and subcontracting strategies for a quality deteriorating manufacturing system. International Journal of Production Economics 171:134–150

    Article  Google Scholar 

  20. Sethi S, Suo W, Taksar M, Yan H (1998) Optimal production planning in a multi-product stochastic manufacturing system with long-run average cost. Discrete Event Dynamic Systems: Theory and Applications 8:37–54

    Article  Google Scholar 

  21. Sethi S, Suo W, Taksar M, Zhang Q (1997) Optimal production planning in a stochastic manufacturing system with long-run average cost. Journal of Optimization Theory and Applications 92:161–188

    Article  Google Scholar 

  22. Sharifnia A (1988) Production control of a manufacturing system with multiple machine states. IEEE Transactions on Automatic Control 33(7):620–625

    Article  Google Scholar 

  23. Shi X, Shen H, Wu T, Cheng T (2014) Production planning and pricing policy in a make-to-stock system with uncertain demand subject to machine breakdowns. European Journal of Operational Research 238(1):122–129

    Article  Google Scholar 

  24. Tan B (1997) Variance of the throughput of an \(N\)-station production line with no intermediate buffers and time dependent failures. European Journal of Operational Research 101(3):560–576

    Article  Google Scholar 

  25. Tan B (2002) Managing manufacturing risks by using capacity options. Journal of the Operational Research Society 53(2):232–242

    Article  Google Scholar 

  26. Tan B (2002) Production control of a pull system with production and demand uncertainty. IEEE Transactions on Automatic Control 47(5):779–783

    Article  Google Scholar 

  27. Tan B, Gershwin SB (2004) Production and subcontracting strategies for manufacturers with limited capacity and volatile demand. Annals of Operations Research 125(1–4):205–232

    Article  Google Scholar 

  28. Tan B, Gershwin SB (2009) Analysis of a general markovian two-stage continuous-flow production system with a finite buffer. International Journal of Production Economics 120(2):327–339

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Barış Tan.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tan, B. Production Control with Price, Cost, and Demand Uncertainty. OR Spectrum 41, 1057–1085 (2019). https://doi.org/10.1007/s00291-018-0542-2

Download citation

Keywords

  • Manufacturing
  • Fluid Flow Systems
  • Stochastic Optimal Control
  • Discrete Event Systems
  • Markov Processes