pi the stationary probabilities that a picker stays at bin i
upon the completion of an order
dij the travel distance from bin j to bin i in a tour
dm thetravel distance given the picker starts a the pickings
of an order from bin m in a tour
C the total travel time of a picker in the picking line
Dz the travel distance of an individual picker in zone z to
complete an order, z ¼ 1; 2; . . . ; n
Xt a random variable denoting the starting position of
picking for the tth order, or equivalently, the position
of the last item in the (t 1)th order