Skip to main content
SpringerLink
Log in
SpringerLink
Log in

A Near-Optimal Order-Based Inventory Allocation Rule in an Assemble-To-Order System and its Applications to Resource Allocation Problems

  • Chapter
Applications of Supply Chain Management and E-Commerce Research

Part of the book series: Applied Optimization ((APOP,volume 92))

  • 2381 Accesses

Abstract

Assemble-to-order (ATO) manufacturing strategy has taken over the more traditional make-to-stock (MTS) strategy in many high-tech firms. ATO strategy has enabled these firms to deliver customized demand timely and to benefit from risk pooling due to component commonality. However, multi-component, multi-product ATO systems pose challenging inventory management problems. In this chapter, we study the component allocation problem given a specific replenishment policy and realized customer demands. We model the problem as a general multi-dimensional knapsack problem (MDKP) and propose the primal effective capacity heuristic (PECH) as an effective and simple approximate solution procedure for this NP-hard problem. Although the heuristic is primarily designed for the component allocation problem in an ATO system, we suggest that it is a general solution method for a wide range of resource allocation problems. We demonstrate the effectiveness of the heuristic through an extensive computational study which covers problems from the literature as well as randomly generated instances of the general and 0–1 MDKP. In our study, we compare the performance of the heuristic with other approximate solution procedures from the ATO system and integer programming literature.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Agrawal, N. and Cohen, M.A. (2000). Optimal material control in an assembly system with component commonality. Working paper, Department of Decision and Information Sciences, Santa Clara University, Santa Clara, CA 95053.

    Google Scholar 

  • Akçay, Y., Li, H., and Xu, S.H. (2002). An approximate algorithm for the general multidimensional knapsack problem. Working paper, Pennsylvania State University.

    Google Scholar 

  • Akçay, Y. and Xu, S.H. (2002). Joint inventory replenishment and component allocation optimization in an assemble-to-order system. Working paper, Pennsylvania State University.

    Google Scholar 

  • Axsäter, S. (2000). Inventory Control. Kluwer Academic Publishers, Boston/Dordrecht/London.

    Google Scholar 

  • Baker, K.R., Magazine, M.J., and Nuttle, H.L.W. (1986). The effect of commonality on safety stock in a simple inventory model. Management Science, 32(8):982–988.

    Google Scholar 

  • Chen, F., Ettl, M., Lin, G., and Yao, D.D. (2000). Inventory-service optimization in configure-to-order systems: From machine-type models to building blocks. Research Report RC 21781 (98077), IBM Research Division, IBM T.J. Watson Research Center, York Heights, NY 10598.

    Google Scholar 

  • Everett, H. (1963). Generalized langrange multiplier method for solving problems of optimum allocation of resources. Operations Research, 2:399–417.

    MathSciNet  Google Scholar 

  • Gallien, J. and Wein, L.M. (1998). A simple and effective procurement policy for stochastic assembly systems. Working paper, MIT Sloan School.

    Google Scholar 

  • Garey, M.R. and Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco.

    MATH  Google Scholar 

  • Gerchak, Y. and Henig, M. (1989). Component commonality in assemble-to-order systems: Models and properties. Naval Research Logistics, 36:61–68.

    MathSciNet  MATH  Google Scholar 

  • Gerchak, Y., Magazine, M.J., and Gamble, A.B. (1988). Component commonality with service level requirements. Management Science, 34(6):753–760.

    Google Scholar 

  • Glasserman, P. and Wang, Y. (1998). Leadtime inventory trade-offs in assemble-to-order systems. Operations Research, 46:858–871.

    MATH  Google Scholar 

  • Hadley, G. and Whitin, T.M. (1963). Analysis of Inventory Systems. Prentice Hall, Englewood Cliffs, NJ.

    MATH  Google Scholar 

  • Hausman, W.H., Lee, H.L., and Zhang, A.X. (1998). Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies. European Journal of Operational Research, 109:646–659.

    Article  MATH  Google Scholar 

  • Kochenberger, G.A., McCarl, B.A., and Wyman, F.P. (1974). A heuristic for general integer programming. Decision Sciences, 5:36–44.

    Google Scholar 

  • Lee, H.L. and Tang, C.S. (1997). Modelling the costs and benefits of delayed product differentiation. Management Science, 43:40–53.

    MATH  Google Scholar 

  • Lin, E.Y. (1998). A bibliographical survey on some well-known nonstandard knapsack problems. INFOR, 36(4):274–317.

    Google Scholar 

  • Loulou, R. and Michaelides, E. (1979). New greedy-like heuristics for the multidimensional 0–1 knapsack problem. Operations Research, 27:1101–1114.

    MathSciNet  MATH  Google Scholar 

  • Magazine, M.J. and Oguz, O. (1984). A heuristic algorithm for the multidimensional zero-one knapsack problem. European Journal of Operational Research, 16:319–326.

    Article  MathSciNet  MATH  Google Scholar 

  • Pirkul, H. (1987). A heuristic solution procedure for the multiconstraint zero-one knapsack problem. Naval Research Logistics, 34:161–172.

    MATH  Google Scholar 

  • Pirkul, H. and Narasimhan, S. (1986). Efficient algorithms for the multiconstraint general knapsack problem. HE Transactions, pages 195–203.

    Google Scholar 

  • Schraner, E. (1995). Capacity/inventory trade-offs in assemble-to-order systems. Working paper, Department of Operations Research, Stanford University, Stanford, CA 94306.

    Google Scholar 

  • Senju, S. and Toyoda, Y. (1968). An approach to linear programming with 0–1 variables. Management Science, 15(4):B196–B207.

    Google Scholar 

  • Song, J. (1998). On the order fill rate in a multi-item, base-stock inventory system. Operations Research, 46(6):831–845.

    MATH  Google Scholar 

  • Song, J., Xu, S.H., and Liu, B. (1999). Order fulfillment performance measures in an assemble-to-order system with stochastic leadtimes. Operations Research, 47:131–149.

    MATH  Google Scholar 

  • Song, J. and Yao, D.D. (2000). Performance analysis and optimization of assemble-to-order systems with random leadtimes. preprint.

    Google Scholar 

  • Swaminathan, J.M. and Tayur, S.R. (1999). Stochastic Programming Models for Managing Product Variety. in Quantitative Models for Supply Chain Management, Tayur, Ganashan and Magazine (eds), Kluwer Academic Publishers, 585–624, Boston/Dordrecht/London.

    Google Scholar 

  • Toyoda, Y. (1975). A simplified algorithm for obtaining approximate solutions to zero-one programming problems. Management Science, 21(12):1417–1427.

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, Y. (1999). Near-optimal base-stock policies in assemble-to-order systems under service level requirements. Working paper, MIT Sloan School.

    Google Scholar 

  • Xu, S.H. (1999). Structural analysis of a queueing system with multiclasses of correlated arrivals and blocking. Operations Research, 47:264–276.

    MATH  MathSciNet  Google Scholar 

  • Xu, S.H. (2001). Dependence Analysis of Assemble-to-Order Systems. in Supply Chain Structures: Condition, Information and Optimization, Song and Yao (eds), Kluwer Academic Publishers, 359–414, Boston/Dordrecht/London.

    Google Scholar 

  • Zanakis, S.H. (1977). Heuristic 0–1 linear programming: Comparisons of three methods. Management Science, 24:91–103.

    MATH  MathSciNet  Google Scholar 

  • Zhang, A.X. (1997). Demand fulfillment rates in an assemble-to-order system with multiple products and dependent demands. Production and Operations Management, 6(3):309–323.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Administrative Sciences and Economics, Koç University, Rumeli Feneri Yolu Sariyer, Istanbul, 34450, Turkey

    Yalçın Akçay

  2. Department of Supply Chain and Information Systems The Smeal College of Business Administration, Penn State University, University Park, Pennsylvania, 16802

    Susan H. Xu

Authors
  1. Yalçın Akçay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Susan H. Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Florida, Gainesville, USA

    Joseph Geunes , Elif Akçali , Panos M. Pardalos , H. Edwin Romeijn  & Zuo-Jun Max Shen , , ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Akçay, Y., Xu, S.H. (2005). A Near-Optimal Order-Based Inventory Allocation Rule in an Assemble-To-Order System and its Applications to Resource Allocation Problems. In: Geunes, J., Akçali, E., Pardalos, P.M., Romeijn, H.E., Shen, ZJ.M. (eds) Applications of Supply Chain Management and E-Commerce Research. Applied Optimization, vol 92. Springer, Boston, MA. https://doi.org/10.1007/0-387-23392-X_2

Download citation

Publish with us

Policies and ethics

Search

Navigation