The shortest travel distance is 2 minfðr bÞ; ðb lÞg þ max
fðr bÞ; ðb lÞg. For example, suppose the light indicator modules
on bins 1, 2, 3, 4 and 6 are on and the picker is at bin 4 to start the
picking operation. According to Algorithm 1, right side is the first
side; so after picking the item in bin 4, the picker goes to the right
side (bin 6) first. Hence, the sequence of bin traveled is 46,321 and
the shortest travel distance is 7 units.
The following assumptions on the warehouse and the picking
operations under study are made in the paper:
(1) A container is sufficiently large to handle all the items in a
picking tour.
(2) The storage racks are long and low, i.e., the vertical travel
time is negligible.
(3) The speed of a picker is constant.
(4) The time to pick an item from a rack is constant.
(5) All items of all orders have the same sizes and weights.
(6) No orders can be spread, i.e., strict picking order policy is
implemented.
(7) A picker always chooses the shortest travel distance for each
order.
(8) Upon the completion of current order, a picker stays at the
bin of the last item on the order and starts next order from
that location.
(9) Each item is independent of the others within an order.
3. Evaluation of travel distance
The picking operations of a picker in a pick-and-pass system
can be modeled as a Markov chain. Since the starting position of