Mathematical aspects of the 3 × n job‐shop sequencing problem

Wlodzimierz Szwarc

Naval Research Logistics Quarterly, 1974, vol. 21, issue 1, 145-153

Abstract: The paper discusses mathematical properties of the well‐known Bellman‐Johnson 3 × n sequencing problem. Optimal rules for some special cases are developed. For the case min Bi ≥ maxAj we find an optimal sequence of the 2 × n problem for machines B and C and move one item to the front of the sequence to minimize (7); when min Bi ≥ max Cj we solve a 2 × n problem for machines A and B and move one item to the end of the optimal sequence so as to minimize (9). There is also given a sufficient optimality condition for a solution obtained by Johnson's approximate method. This explains why this method so often produces an optimal solution.

Date: 1974
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https://doi.org/10.1002/nav.3800210110

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:21:y:1974:i:1:p:145-153

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