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Minimization of Makespan in Generalized Assignment Problem

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Abstract

A quantitative combinatorial search problem consisting of m sources supplying in bulk to n(> m) destinations is considered in this paper. Each destination receives its full quota of a homogeneous product from a single source but a source can supply to many destinations subject to its capacity restrictions. If tij, which without loss of generality can be assumed to be a positive integer, is the time of transportation for shipping the goods from the source i to the destination j, then the total time used by the ith source is sum of the transportation time to the destinations that are served by this source. The time of transportation, called makespan, for a feasible solution of this generalized assignment problem (also called bulk transportation problem) is the maximum total time used by a source. The objective is to find a feasible solution that minimizes the makespan. A lexicographic search algorithm is developed which avoids scanning through all the possible feasible solutions though the search is exhaustive enough to obtain an optimal feasible solution at an early stage of the search. A starting upper bound on the value of objective function computed heauristically is used as a supplementary aid in reducing the search. Some results are established which, though of computational nature, help to reduce both the memory requirements and computational time.

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References

  1. H.L. BHATIA, “A note on a zero-one time minimizing problem”, NZOR 7 (1979) 159–165.

    Google Scholar 

  2. T.C.E. Cheng and C.C.S. Sin, “A state-of-art review of parallel machine scheduling research”, EJOR 47 (1990) 271–292.

    Article  Google Scholar 

  3. M.L. FISHER, R. JAIKUMAR AND L.N. VAN WASSENHOVE, A multipher adjustment method for the generalized assignment problem”, Management Science 32 (1986) 1095–1103.

    Article  Google Scholar 

  4. R. GARRY PARKER, “Deterministic Scheduling Theory”, Chapma and Hall (1995).

    Google Scholar 

  5. GHOSE AND SHILA, “The maximum capacity routes: A lexi-search approach”, Operations Research 8(3) (1971) 969–982.

    Google Scholar 

  6. E.S. GOTTLIEB AND M.R. RAO, “The generalized assignment problem: Valid inequalities and facets”, Mathematical Programming 46 (1990) 31–52.

    Article  Google Scholar 

  7. E.S. GOTTLIEB AND M.R. RAO, “(1, k)-Configuration facets for the generalized assignment problem”, Mathematical Programming 46 (1990) 53–60.

    Article  Google Scholar 

  8. T.D. KALSTORIN, “An effective subgradient algorithm for the generalized assignment problem”, Computers and Operations Research 6 (1979) 155–164.

    Article  Google Scholar 

  9. E.L. LAWLER, J.K. LENSTRA, A.H.G. RINNOY KAN AND D.B. SHMOYS, “Sequencing and Scheduling: Algorithms and Complexity”, Report B5-R8909, Centre for Mathematics and Computers Science, Amsterdam (1989).

    Google Scholar 

  10. MAIO, ADRIANO DE AND C. ROVEDA, “An all zero-one algorithm for a certain class of transportation problem”, Operations Research 19 (1971) 1406–1418.

    Article  Google Scholar 

  11. S. MARTELLO AND P. TOTH, “An algorithm for the generalized assignment problem”, In J.P. Brans (ed.), Operational Research, North-Holland Amsterdam 81 (1981) 589–603.

    Google Scholar 

  12. J.B MAZZOLA, A.W. NEEBE AND C.V.R. DUNN “Production planning of a flexible manufacturing system in a material requirements planning environment”, International Journal of Flexible Manufacturing Systems 1/2 (1989) 115–142.

    Article  Google Scholar 

  13. M.S. MURTHY, “A bulk transportation problem”, Opsearch 13 (3–4) (1976) 143–155.

    Google Scholar 

  14. A. W. NEEB AND M.R. RAO, “An algorithm for the fixed - charge assigning users to sources problem”, Journal of Operational Research Society 34 (1983) 1107–1113.

    Article  Google Scholar 

  15. S.N.N. PANDIT AND Y.V. SUBRAHMANYAM, “Enumeration of all optimal job sequence”, Opsearch 12 (1–2) (1975) 35–39.

    Google Scholar 

  16. G.T. ROSS AND R.M. SOLAND, “A branch and bound algorithm for the generalized assignment problem”, Mathematical Programming 8 (1975) 91–103.

    Article  Google Scholar 

  17. V. SRINIVASAN AND G.L. THOMPSON, “An algorithm for assigning uses to sources in a special class of transportation problems”, Operations Research 21 (1973) 284–295.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Delhi Hauz Khas, New Delhi, 110016, India

    Shalini Arora & M. C. Puri

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  1. Shalini Arora
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  2. M. C. Puri
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Arora, S., Puri, M.C. Minimization of Makespan in Generalized Assignment Problem. OPSEARCH 36, 360–373 (1999). https://doi.org/10.1007/BF03398589

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