Mah. Dempster et Rt. Thompson, EVPI-based importance sampling solution procedures for multistage stochastic linear programmes on parallel MIMD architectures, ANN OPER R, 90, 1999, pp. 161-184
Multistage stochastic linear programming has many practical applications fo
r problems whose current decisions have to be made under future uncertainty
. There are a variety of methods for solving the deterministic equivalent f
orms of these dynamic problems, including the simplex and interior-point me
thods and nested Benders decomposition, which decomposes the original probl
em into a set of smaller linear programming problems and has recently been
shown to be superior to the alternatives for large problems. The Benders su
bproblems can be visualised as being attached to the nodes of a tree which
is formed from the realisations of the random data process determining the
uncertainty in the problem. This paper describes a parallel implementation
of the nested Benders algorithm which employs a farming technique to parall
elize nodal subproblem solutions. Differing structures of the test problems
cause differing levels of speed-up on a variety of multicomputing platform
s: problems with few variables and constraints per node do not gain from th
is parallelisation. We therefore employ stage aggregation to such problems
to improve their parallel solution efficiency by increasing the size of the
nodes and therefore the time spent calculating relative to the time spent
communicating between processors. A parallel version of a sequential import
ance sampling solution algorithm based on local expected value of perfect i
nformation (EVPI) is developed which is applicable to extremely large multi
stage stochastic linear programmes which either have too many data paths to
solve directly or a continuous distribution of possible realisations. It u
tilises the parallel nested Benders algorithm and a parallel version of an
algorithm designed to calculate the local EVPI values for the nodes of the
tree and achieves near linear speed-up.