pickings for each order in a zone is a random variable, it is
necessary to calculate the stationary probability that a picker
stays at bin i in a zone upon the completion of an order. First,
we find the probability that a picker reaches bin j from bin i
in the zone for an order fulfillment so that the transition matrix
of a picker can be established. Using the transition matrix, we
can find the steady probability of a picker staying at the bin i
and the expected distance traveled per order can be computed
accordingly.