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An Extremal Production-Line Problem

Author

Listed:
  • Fred Supnick

    (Department of Mathematics, City College, New York, New York)

  • Jacob Solinger

    (601 West 115th Street, New York, New York)

Abstract

Let G 1 , ..., G r be groups of n 1 , ..., n r workers on a production line, all members of G i performing identical operations in the time t i on entities drawn (repeatedly) from a pool P i . When the production line starts all members of G 1 are put to work at the time T 1 , and some time thereafter all members of G 2 are put to work at the time T 2 , etc. We assume that n 1 / t 1 = (cdots) = n r / t r (equiv) R . Let d j = g.c.d. ( n j -1 , n j ). We prove the theorem. Let T j -1 = 0. Then T j = ( n j -1 + n j - d j )/ R is the earliest time at which G j can be put to work so that supply for G j is at any time greater than or equal to demand ( j = 2, ..., r ).

Suggested Citation

  • Fred Supnick & Jacob Solinger, 1960. "An Extremal Production-Line Problem," Operations Research, INFORMS, vol. 8(3), pages 381-384, June.
    • Handle: RePEc:inm:oropre:v:8:y:1960:i:3:p:381-384
    DOI: 10.1287/opre.8.3.381
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