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angular linear programs by fixing the dual coupling variables. Gnanendran and Ho [1993]
investigated strategies for improving efficiency in distributed Dantzig-Wolfe decomposition by
better balancing the load between master and subproblem processors because the parallel
efficiency of the distributed approach is critically dependent on the duration of the inherently
serid master phase relative to that of the bottleneck subproblem.
Enviken [1996] presented the experimental results of using parallel Benden
decomposition to solve staircase multistage problems on a shared memory multiprocessor
cornputer which has 6 processors. He showed that paralle1 decomposition can solve a large
problem with staircase structure faster than the simplex method even when serial decomposition
is slower than the sirnplex method.
Another use of parailel processon for decomposition alprithms is for the area of
stochastic pro*ming problems since the equivaient detenninistic problem of a stochastic
model is typically very large. Dantzig and Glynn [1990] suggested the use of parallel processors
to calculate the subproblems of Benden decomposition for stochastic models. Ruszczynski
[1993] suggested parailelizing a variant of the nested decomposition algorithm by queuing
subproblems for ide processors. and Birge, Donohue. Holmes and Svintsits ki [19%] tested and
compared the parailel implementation of a nested decomposition algorithm for mupistage
stochastic linev pro+nms over a serial implementation using PVM on a network of RS/6000
model 32OH workstations connected by a local ethemet. Their computational experience on a
large test set of pmcticai problems with up to 1.5 million constraïnts and almost 5 million
variables showed that the paralle1 implementations worked very well but they require careful
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