Annals of Operations Research

, Volume 150, Issue 1, pp 31–46 | Cite as

Minimum cost multi-product flow lines

  • Arianna Alfieri
  • Gaia Nicosia


In this paper, the problem of finding the minimum cost flow line able to produce different products is considered. This problem can be formulated as a shortest path problem on an acyclic di-graph when the machines graph associated with each product family is a chain or a comb. These graphs are relevant in production planning when dealing with pipelined assembly systems. We solve the problem using A * algorithm which can be efficiently exploited when there is a good estimate on the value of an optimal solution. Therefore, we adapt a known bound for the Shortest Common Supersequence problem to our case and show the effectiveness of the approach by presenting an extensive computational experience.


Flow lines optimization Shortest path algorithms 


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  1. Agnetis, A., C. Arbib, M. Lucertini, and F. Nicolò. (1995). “Task Assignment and Sub-Assembly Scheduling in Flexible Assembly Lines.” IEEE Transactions on Robotics and Automation, 11, 1–20.CrossRefGoogle Scholar
  2. Askin, R.G. and C.R. Standridge. (1993). Modeling and Analysis of Manufacturing Systems. Wiley: New York.Google Scholar
  3. Askin, R.G. and M. Zhou. (1998). “Formation of Independent Flow-Line Cells Based on Operation Requirements and Machine Capabilities.” IIE Transaction, 30, 319–329.CrossRefGoogle Scholar
  4. Becker, C. and A. Scholl. (2003). “A Survey on Problems and Methods in Generalized Assembly Line Balancing.” European Journal of Operational Research, 168, 694–715.CrossRefGoogle Scholar
  5. Bukchin, J. and M. Tzur. (2000). “Design of Flexible Assembly Line to Minimize Equipment Cost.” IIE Transactions, 32, 585–598.CrossRefGoogle Scholar
  6. Fine, C. and R. Freund. (1990). “Optimal Investment in Product-Flexible Manufacturing Capacity.” Management Science, 36, 449–466.Google Scholar
  7. Foulser, D.E., M. Li, and Q. Yang. (1992). “Theory and Algorithms for Plan Merging.” Artificial Intelligence, 57, 143–181.CrossRefGoogle Scholar
  8. Fraser, C.B. (1995). Subsequences and Supersequences of String. PhD. Thesis, University of Glasgow, UK.Google Scholar
  9. Fraser, C.B. and R.W. Irving. (1995). “Approximation Algorithms for the Shortest Common Supersequence.” Nordic Journal of Computing, 2, 303–325.Google Scholar
  10. Hart, P.E., N.J. Nilsson, and B. Raphael. (1968). “A Formal Basis for the Heuristic Determination of Minimum Cost Paths.” IEEE Transactions on Systems and Cybernetics, 4, 100–108.CrossRefGoogle Scholar
  11. Jiang, T. and M. Li. (1995). “On the Approximation of Shortest Common Supersequences and Longest Common Subsequences.” SIAM Journal on Computing, 24, 1122–1139.CrossRefGoogle Scholar
  12. Kimms, A. (2000). “Minimal Investment Budgets for Flow Line Configuration.” IIE Transactions, 32, 287–298.CrossRefGoogle Scholar
  13. Lucertini, M. and G. Nicosia. (1997). “On a Generalized Version of the Shortest Common Supersequence Problem.” Technical Report n. 275, Dipartimento di Informatica, Sistemi e Produzione—Centro “Vito Volterra”, Università di Roma “Tor Vergata”.Google Scholar
  14. Maier, D. (1978). “The Complexity of Some Problems on Subsequences and Supersequences.” Journal of ACM, 25, 322–336.CrossRefGoogle Scholar
  15. Middendorf, M. (1994). “More on the Complexity of Common Superstring and Supersequence Problems.” Theoretical Computer Science, 125, 205–228.CrossRefGoogle Scholar
  16. Nicosia, G. and G. Oriolo. (2003). “An Approximate A * Algorithm and its Application to the SCS Problem.” Theoretical Computer Science, 290, 2021–2029.CrossRefGoogle Scholar
  17. Nilsson, N.J. (1971). Problem Solving Methods in Artificial Intelligence. McGraw-Hill: New York.Google Scholar
  18. Pinto, P.A., D.G. Dannenbring, and B.M. Khumawala. (1983). “Assembly Line Balancing with Processing Alternatives: An Application.” Management Science, 29, 817–830.CrossRefGoogle Scholar
  19. Räihä, K. and E. Ukkonen. (1981), “The Shortest Common Supersequence Problem Over Binary Alphabet is NP-Complete.” Theoretical Computer Science, 16, 187–198.CrossRefGoogle Scholar
  20. Rodeh, M., V.R. Pratt, and S. Even. (1981). “Linear Algorithm for Data Compression via String Matching.” Journal of ACM, 28(1), 16–24.CrossRefGoogle Scholar
  21. Timkovskii, V.G. (1990). “Complexity of Common Subsequence and Supersequence Problems and Related Problems.” Cybernetics, 25, 565–580.CrossRefGoogle Scholar
  22. Wilhelm, W.E. and R. Gadidov. (2004). “A Branch-and-Cut Approach for a Generic Multiple-Product Assembly-System Design Problem.” INFORMS Journal on Computing, 16, 39–55.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Politecnico di Torino, Dipt. Sistemi di Produzione ed EconomiaTorinoItaly
  2. 2.Dipartimento di Informatica e AutomazioneUniversità “Roma Tre”RomeItaly

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