Each storage location in a warehouse is assigned a unique address. This includes both fixed storage locations, such as a portion of a shelf and mobile locations such as the forks  of  a  lift  truck. Storage  locations  are  expensive  because  they  represent  space, with consequent costs of
rent, heating and/or air-conditioning, security, and so on.  In addition, storage locations are typically within specialized equipment, such as shelving or flow rack, which are a capital cost. These costs impel us to use storage space as efficiently as possible.

There are two main strategies used in storing product.  The simplest is dedicated storage, in which each location is reserved for an assigned product and only that prod- uct may be stored there. Because the locations of products do not change, more popular items can be stored in more convenient locations and workers can learn the layout, all of which makes order-picking more efficient.

The problem with dedicated storage is that it does not use space efficiently.  This can be seen by
tracking the amount of inventory in a given location.  If we plot the inventory level, measured for
example by volume, we would see a sawtooth shape such as in Figure 2.5 (which represents an
idealization of the inventory process.)  In one cycle the storage location is initially filled but empties as product is withdrawn to send to customers. As a result, on average this storage location is half empty.

Figure 2.5: An idealization of how the inventory level at a location changes over time

A  warehouse  may  have  thousands  or  tens-of-thousands  of  storage  locations.   If using dedicated storage, each will have an assigned product.  Each product may have a different replenishment cycle and so, upon entering such a warehouse, one expects to see many storage locations that are nearly empty, many that are half-full, and many that are nearly full. On average the storage capacity is only about 50% utilized.

To improve on this, one can use a strategy of shared storage.  The idea here is to assign a product
to more than one storage location. When one location becomes empty, it is available for reassignment, perhaps to a different product. This space then can be filled again, rather than waiting until the original product is replenished (presumably when the last of the warehouse supply has been exhausted). The more storage locations over which a product is distributed, the less product in each location, and so the sooner one of those locations is emptied and the sooner that space is recycled.  Therefore we expect better utilization of space when shared storage is used.

Unfortunately, shared storage also has some disadvantages. Most immediately, the locations of
products will change over time as locations are emptied and restocked with other products. This
means that workers cannot learn locations and so must be directed to locations by a warehouse
management (software) system.  Another disadvantage is that it becomes more time-consuming to put away newly received product because it has to be taken to more locations.  There can be other, social complications as well. For example, imagine an order picker who has been directed to the other side of the warehouse  to  pull  a  product  for  a  customer.   That  order  picker  may  be
tempted  to pick the product from a more convenient location, thus creating discrepancies between book and physical inventory at two locations. For these reasons, shared storage requires greater software support and also more disciplined warehouse processes.

Shared  storage  is  generally  more  complicated  to  manage  because  it  introduces many possible trade-offs.  In particular, one can manage the trade-off between space and time (labor) on an activity-by-activity basis. For example, one can retrieve product from the least-filled location (to empty and recycle that location as soon as possible) or from the most convenient location (to
save labor). Similarly, one can replenish product to the most nearly empty location to fill that
empty space or to the most convenient location to save labor time.

How much improvement in space utilization is possible with shared storage? Consider a product that is requested at a constant rate, as in our idealization of Figure 2.5. Suppose we hold two weeks supply of this product.   If we store it in two locations of equal size and direct all order-picking to only one location then after one week, the first location will be emptied and available for reassignment. After the second week the second location will be emptied and available for reassignment. During the first week, the first location was half full on average and the second location was completely full, so that average space utilization was 75%. During the second week the second location was half-full, for an average space utilization of 50%, and the space utilization over the two weeks was 62.5%.  More improvement is possible if a product is stored in more locations, though the improvement diminishes and, moreover, the practical problems of management increase.

More generally we can argue as follows.  Assume for convenience that demand is constant, the SKU has been stored in k locations of identical size, and all picks are from a single active pick
location until that location is exhausted.  Then the inventory cycle may be imagined as consisting
of k periods, each devoted to a particular pick location, as in Figure 2.6. The average space utilization in period i is

and the average utilization over all k periods is

Figure  2.7  shows  how  the  space  utilization  of  storing  a  SKU  in  more  locations increases but with diminishing returns.

Interestingly, there is a slight sampling bias if one were to examine space utilization directly by
taking a census within the warehouse.  This is the subject of Exercise 2.7 and it suggests that you
will tend to measure slightly smaller values than predicted by Expression 2.1.
In practice, a strategy of shared storage is typically used in the bulk storage areas, where most of the volume of product is held on pallets. Dedicated storage may be used in the most active picking areas, which are much smaller than the bulk storage.  Thus one gets efficient use of most of the space (bulk storage) with labor benefits where it matters most (active picking areas).

There are also hybrid schemes in which regions are reserved for groups of SKUs, but locations are not reserved.  For example, an aisle might be reserved for SKUs of one type or from one vendor, but within that aisle, space would be shared amongst the SKUs.

Figure 2.6: Use of k locations to hold product under a policy of shared storage. The
step function represents the space devoted to holding inventory.

Figure 2.7: Under shared storage, space utilization increases with additional storage locations, but at a diminishing rate.