a new network simplex algorithm to reduce consecutive‎ ‎degenerate pivots and prevent ‎stalling‎

نویسندگان

z. ‎aghababazadeh‎‎

department of mathematics‎, ‎science and‎ ‎research branches‎, ‎islamic azad university‎, ‎tehran‎, ‎iran‎. m. ‎rostamy-‎malkhalifeh‎‎

department of mathematics‎, ‎science and‎ ‎research branches‎, ‎islamic azad university‎, ‎tehran‎, ‎iran‎.

چکیده

it is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n-m+k ‎ ‎k ‎ ‎end{array}‎ ‎right)$‎ ‎where $k$ is the number of degenerate arcs in the basis‎. ‎as‎ ‎well as‎, ‎the network simplex algorithm may stall if it goes through‎ ‎some long consecutive degenerate pivot‎. ‎through conditions such as‎ ‎(lrc) and (lrs) upon entering variable rules‎, ‎this upper bound can‎ ‎be reduced to $mn$ and $m^2$ respectively‎. ‎in this current paper we‎ first suggest a new algorithm for anti--stalling in which a new‎ ‎condition is provided to the entering variable and then show that‎ ‎through this algorithm there are at most $k$ consecutive degenerate ‎pivots.‎

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A new network simplex algorithm to reduce consecutive‎ ‎degenerate pivots and prevent ‎stalling‎

It is well known that in operations research‎, ‎degeneracy can cause a cycle in a network‎ ‎simplex algorithm which can be prevented by maintaining strong‎ ‎feasible bases in each pivot‎. ‎Also‎, ‎in a network consists of n arcs‎ ‎and m nodes‎, ‎not considering any new conditions on the entering‎ ‎variable‎, ‎the upper bound of consecutive degenerate pivots is equal‎ $left( ‎begin{array}{c}‎ ‎n...

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عنوان ژورنال:
international journal of industrial mathematics

جلد ۸، شماره ۳، صفحات ۲۰۹-۲۱۴

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