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Planning Production on an Unreliable Machine for Multiple Items Subject to Stochastic Demand

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Handbook of Newsvendor Problems

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 176))

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Abstract

We develop an extension of the classical newsvendor model that incorporates multiple items, setup times, and an unreliable machine. This model is motivated by applications at metal stamping plants where machine reliability is a key source of uncertainty. Given a fixed production schedule, a finite horizon, and a known demand distribution, we formulate an extension of the newsvendor model, derive important properties of this model, and exploit these properties to provide a solution algorithm that determines the cost minimizing production quantities. Finally, we present three simple extensions to the model: (1) a method for rescheduling within the planning horizon, (2) an extension to evaluate whether or not to purchase the option to run overtime within the planning horizon, and (3) an extension that permits the modeling of a machine that operates at a different speed depending on the part being produced.

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References

  • Al-Salamah, M., & Abudari, A. (2012). Production lot sizing & process targeting under process deterioration & machine breakdown conditions. Modeling and Simulation in Engineering, Hindawi Publishing Corporation, 7 pages doi:10.1155/2012/393495

    Google Scholar 

  • Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (1993). Nonlinear programming: Theory and algorithms(2nd ed.). New York: Wiley.

    Google Scholar 

  • Beyer, W. H. (1987). CRC handbook of mathematical sciences(6th ed.). Boca Raton: CRC Press.

    Google Scholar 

  • Birge, J., Frenk, J. B. G., Mittenthal, J., & Rinnooy Kan, A. H. G. (1990). Single-machine scheduling subject to stochastic breakdowns. Naval Research Logistics, 37, 661–677.

    Article  Google Scholar 

  • Birge, J. R., & Glazebrook, K. D. (1988). Assessing the effects of machine breakdowns in stochastic scheduling. Operations Research Letters, 7(6), 267–271.

    Article  Google Scholar 

  • Bitran, G. R., Haas, E. A., & Matsuo, H. (1986). Production planning of style goods with high setup costs and forecast revisions. Operations Research, 34(2), 226–236.

    Article  Google Scholar 

  • Ciarallo, F. W., Akella, R., & Morton, T. E. (1994). A periodic review, production planning model with uncertain capacity and uncertain demand. Management Science, 40(3), 320–332.

    Article  Google Scholar 

  • Dada, M., Petruzzi, N. C., & Schwarz, L. B. (2007). A newsvendor’s procurement problem when suppliers are unreliable. Manufacturing & Service Operations Management, 9(1), 9–32.

    Article  Google Scholar 

  • Diedrich, F., Jansen, K., Schwarz, U. M., & Trystram, D. (2009) A survey on approximation algorithms for scheduling with machine unavailability. In Algorithmics of large and complex networks: design, analysis, and simulation (pp. 50–64). Springer, Berlin.

    Google Scholar 

  • El-Ferik, S. (2008). Economic production lot-sizing for an unreliable machine under imperfect age-based maintenance policy. European Journal of Operational Research, 186(1), 150–163.

    Article  Google Scholar 

  • Epstein, L., Levin, A., Marchetti-Spaccamela, A., Megow, N., Mestre, J., Skutella, M., et al. (2010). Universal sequencing on an unreliable machine. Proceedings of the 14th international conference on integer programming and combinatorial optimization(IPCO XIV). Springer, Berlin.

    Google Scholar 

  • Evans, R. V. (1967). Inventory control of a multiproduct system with a limited production resource. Naval Research Logistics Quarterly, 14(2), 173–184.

    Article  Google Scholar 

  • Giri, B. C., Yun, W. Y., & Dohi, T. (2005). Optimal lot sizing in an unreliable two-stage serial production-inventory system. International Transactions in Operational Research, 12(1), 63–82.

    Article  Google Scholar 

  • Giri, B. C., & Dohi, T. (2004). Optimal lot sizing for an unreliable production system based on net present value approach. International Journal of Production Economics, 92(2), 157–167.

    Article  Google Scholar 

  • Gittins, J. C. (1979). Bandit processes and dynamic allocation indices. Journal of the Royal Statistical Society, Series B, 41, 148–177.

    Google Scholar 

  • Glazebrook, K. D. (1984). Scheduling stochastic jobs on a single machine subject to breakdowns. Naval Research Logistics Quarterly, 31, 251–264.

    Article  Google Scholar 

  • Groenevelt, H., Pintelon, L., & Seidmann, A. (1992a). Production batching with machine breakdowns and safety stocks. Operations Research, 40(5), 959–971.

    Article  Google Scholar 

  • Groenevelt, H., Pintelon, L., & Seidmann, A. (1992b). Production lot sizing with machine breakdowns. Management Science, 38(1), 104–123.

    Article  Google Scholar 

  • Halim, K. A., Giri, B. C., & Chaudhuri, K. S. (2010). Lot sizing in an unreliable manufacturing system with fuzzy demand and repair time. International Journal of Industrial and Systems Engineering, 5(4), 485–500.

    Article  Google Scholar 

  • Huggins, E. L., & Olsen T. L. (2010). Inventory control with generalized expediting. Operations Research, 58(5), 1414–1426.

    Article  Google Scholar 

  • Jain, K., & Silver, E. A. (1995). The single period procurement problem where dedicated supplier capacity can be reserved. Naval Research Logistics Quarterly, 42, 915–934.

    Article  Google Scholar 

  • Kletter, D. B. (1994). Determining Production Lot Sizes and Safety Stocks for an Automobile Stamping Plant. S.M. Thesis, MIT.

    Google Scholar 

  • Kletter, D. B. (1996) Planning and Control of an Unreliable Machine In a Multi-item Production-Inventory System. Ph.D. Thesis, MIT.

    Google Scholar 

  • Lee, C. Y. (2004). Machine scheduling with availability constraints. In J. Y.-T. Leung (Ed.), Handbook of scheduling. Boca Raton: CRC Press.

    Google Scholar 

  • Matsuo, H. (1990). A stochastic sequencing problem for style goods with forecast revisions and hierarchical structure. Management Science, 36(3), 332–347.

    Article  Google Scholar 

  • Pinedo, M., & Rammouz, E. (1988). A note on stochastic scheduling on a single machine subject to breakdown and repair. Probability in the Engineering and Informational Sciences, 2, 41–49.

    Article  Google Scholar 

  • Pinedo, M. (2008). Scheduling: Theory, Algorithms, and Systems(3rd ed.). Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Racke, H. (2009). Survey on oblivious routing strategies. In K. Ambos-Spies, B. Lowe, & W. Merkle (Eds.), Mathematical theory and computational practice, Proceedings of 5th Conference on Computability in Europe (CiE)(pp. 419–429). Springer, Berlin.

    Google Scholar 

  • Reiman, M. I., & Wein, L. M. (1998). Dynamic scheduling of a two-class queue with setups. Operations Research, 46(4), 532–547.

    Article  Google Scholar 

  • Rose, J. S. (1992). The newsvendor with known demand and uncertain replenishment: applications to quality control and container fill. Operations Research Letters, 11(2), 111–117.

    Article  Google Scholar 

  • Schmidt, G. (2000). Scheduling with limited machine availability. European Journal of Operational Research, 121, pp. 1–15.

    Article  Google Scholar 

  • Sethi, S. P., & Zhang, Q. (1994). Hierarchical production and setup scheduling in a single machine system, Chapter 8 in hierarchical decision making in stochastic manufacturing systems. Boston: Birkhäuser.

    Google Scholar 

  • Smith, S. A., Chambers, J. C., & Shlifer, E. (1980). Optimal inventories based on job completion rate for repairs requiring multiple items. Management Science, 26(8), 849–852.

    Article  Google Scholar 

  • Yano, C. A., & Lee, H. L. (1995). Lot sizing with random yields: a review. Operations Research, 43(2), 311–334.

    Article  Google Scholar 

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Acknowledgments

This chapter is based on the author’s unpublished Ph.D. dissertation. The author would like to thank Steve Graves for his support of this research, for many helpful suggestions, and comments on earlier drafts of this manuscript. Don Rosenfield and Vien Nguyen provided valuable input on earlier drafts. Dr. Dave Vander Veen and Dr. Bill Jordan of General Motors provided the author with the opportunity to study the real-world problems that were the inspiration for this work. The author gratefully acknowledges the support and resources made available to him through the Leaders for Manufacturing Program (currently the Leaders for Global Operations Program), a partnership between MIT and global manufacturing companies. The author also appreciates the feedback and suggestions from two anonymous referees on an earlier version of this chapter.

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  1. Booz Allen Hamilton, New York, NY, USA

    David Kletter

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  1. David Kletter
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Correspondence to David Kletter .

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  1. , Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR

    Tsan-Ming Choi

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Kletter, D. (2012). Planning Production on an Unreliable Machine for Multiple Items Subject to Stochastic Demand. In: Choi, TM. (eds) Handbook of Newsvendor Problems. International Series in Operations Research & Management Science, vol 176. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3600-3_12

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