Chris Dance, Onno Zoeter, Haengju Lee
International Conference on Operations Research, Hong Kong, 14-16 March, 2012.
We consider the stochastic joint replenishment
problem in which several items must be ordered in the face
of stochastic demand. Previous authors proposed multiple
heuristic policies for this economically-important problem. We
show that several such policies are not good approximations
to an optimal policy, since as some items grow more expensive
than others, the cost rate of the heuristic policy can grow
arbitrarily larger than that of an optimal policy. These policies
include the well-known RT policy, the P(s; S) policy, the
Q(s; S) policy and the recently-proposed (Q; S; T) policy. To
compensate for this problem, we propose a QI(s; S) policy,
which is a generalization of the Q(s; S) policy, and in which
items are ordered if an expensive item is demanded or if
demand for other items reaches Q. Our numerical results
demonstrate that QI(s; S) policies do indeed overcome the
weakness of the other heuristics, and can cost less than the
Q(s; S) heuristic even when the ratio of the cost of expensive items to other items is only a factor of three.
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