ANALYSIS AND CONTROL OF PICKER BLOCKING

In this section, we develop analytical models of picker blocking and methods to mitigate picker blocking for bucket brigade OPS. Recognizing that both standard multiple-aisle rectangular order picking systems and bucket brigade order picking systems can be characterized using the circular-aisle OPS abstraction, we apply the blocking control model developed in Chapter V to a bucket brigade OPS under the assumption of no passing. Finally, we utilize the control model to demonstrate the reduction that can be achieved.

3.1 Picker blocking in a circular order picking aisle with two pickers

Gue et al. (2006) investigate the effects of picker blocking under a no-passing policy, considering only single-pick situations. The circular order picking aisle abstraction is used in developing both analytical models and a simulation study. Table 11, column 1, shows the closed-form expression for percentage of time blocked for two pick to walk time ratios developed in Gue et al. (2006). Column 2 presents our results in Chapter V. The analysis is undertaken for a two-picker OPS. Both approaches consider two extreme cases: 1) walk speed is equal to unit pick time per pick face (pick time:walk time = 1:1), and 2) walk speed is infinite (pick time:walk time = 1:0). The results in Table 11 are developed for a rectangular multiple aisle warehouse with cross aisles at the front and back of the picking area. Pickers take a one-way traversal route and passing is

not allowed. At a pick face, a batch includes an item with a probability p. Further, q denotes 1-p, the probability of no item at a pick face. The models of Gue et al. (2006) and Chapter V are distinguished by the number of picks per pick location, single vs. multiple. The multiple-pick model can repeat a pick at the same pick face with probability p.

Table 11. The percentage of time blocked when two pickers work (p=pick density, n=the number of pick faces)

Pick:walk

time (Gue et al., 2006) Single-pick (see Chapter V)Multiple-picks 1:0

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Gue et al. (2006) explain that the batch picking strategy can experience less picker blocking when the pick density is either very low or very high. Chapter V and Parikh and Meller (2010) show that the variation in pick density can be as important as the level of pick density in determining the amount of blocking in a circular-aisle OPS. One important observation in Chapter V is that batch picking can reduce picker blocking.

3.2 Picker blocking in bucket brigade order picking

Bucket brigade order picking has a special release mechanism of a new batch and the mechanism impacts the picker blocking model. Thus, first, the release mechanism of a new batch is explained. Second, picker blocking will be discussed. Note that in this study we show the equivalence of the picker blocking models of the bucket brigade order picking and the circular-aisle abstraction under specific situations, instead of a

direct development of the picker blocking model of bucket brigade order picking. Figure 33 describes a series of hand-offs after completion of a batch. k pickers are sequenced from the loading station to the unloading station in a decreasing sequence of k,k-1,…, 2,1. When a batch (denote this batch ith _{batch) is finished by the picker most}

downstream (picker 1), a new batch must enter the system. Picker 1 becomes idle and moves backward to take over the batch of picker 2 who is moving forward with the i+1st

batch. Obviously, the hand-off occurs when they meet. Picker 2 changes direction (backward towards the loading station) to take a new batch from a picker further upstream (i.e., picker 3), when he/she meets an upstream picker he/she takes over i+2nd

batch, and then turns and continues picking in a forward direction. Finally, the picker most upstream (picker k) arrives at the loading station to take over i+kth _{batch, and}

his/her arrival time at the loading station becomes the starting time of a new batch (i.e., i+kth batch). The difference between the completion time of the ith batch and the starting time of the i+kth _{batch, which is a batch paired to the i}th _{released batch, equals the sum of}

Figure 33. A description of chain reaction after completion of batch i to release a new batch i+k.

Assume that there is no hand-off delay and backward walk speed (empty travel walking speed) is instantaneous similar to Bartholdi and Eisenstein (1996a). In addition, k pickers have identical pick performance and walk speed as we assumed in Section 1. Interestingly, with infinite backward walk speed and no hand-off delays, the circular-

aisle abstraction of the traversal routing rectangular picking system can be used to characterize a bucket brigade OPS in terms of picker blocking. Further, the same picker blocking model can be used for both analyses.

The equivalence can be easily shown by replacing ―pickers‖ with ―batches‖. By definition, picker blocking occurs while pickers repeat picking, walking, and blocking, and the picking locations and durations are determined by batches. Thus, without loss of generality, the picker blocking mechanism can be derived from the batches. In bucket brigade order picking, picker blocking occurs when an upstream batch has no item to be picked, but a downstream batch has some picks at the next pick face and holds the next

pick face. Then, the upstream batch may stay at the current pick face, which causes a delay and becomes a picker blocking situation. A more rigorous proof follows.