Layout of unit-load and forward areas

A place for everything, and everything in its place Benjamin Franklin

Learning objectives

Differentiate the functions of main warehouse areas and material flows.
Explain how lane depth affects space utilization and accessibility.
Compare storage-location convenience in flow-through and U-flow configurations.
Describe how forward-pick areas reduce picking travel and require replenishment from reserve.

Functional areas and material flows
Layout of a unit-load area
Location of receiving and shipping
Layout for a forward area

Functional areas and material flows

Functional areas

Receiving staging area
Cross-docking staging area
Bulk storage/reserve/unit-load area
Forward-, fast-, primary-picking area
Shipping area

The five labels are functional areas in the cited warehouse model. Packing is treated as work that readies an order in the shipping area, not as a sixth independently modeled area. Staging is temporary: products then cross-dock to shipping or move into reserve or forward storage.

This paper considers warehouse configurations that include a subset of the following five functional areas: receiving, shipping, staging for cross-docking operation, reserve and forward. In the receiving area, pallet loads or individual cartons of products are received. If necessary, they are staged for a short period and then moved either to the shipping area directly (cross-docking operation) or to the storage area. In the shipping area, picked order items are readied (e.g. shrink-wrapped, packed) and staged (if necessary) for shipping to the next destination. In the staging area for cross-docking, products are sorted and accumulated for further outbound operations. The reserve area is a storage area for bulky product items that typically reside in the warehouse for a relatively longer duration. Normally, the reserve area uses high-density storage equipment to achieve the goal of high space utilization. The forward area is a relatively smaller storage area typically used for fast order picking or performing value-added operations or order collation. Thus, the following material flows are possible in a warehouse: Flow 1, receiving to cross-docking to shipping; Flow 2, receiving to reserve area to shipping; Flow 3, receiving to reserve area to forward area to shipping; and Flow 4, receiving to forward area to shipping.

Flow 1 is the cross-docking operation. Upon receipt, product items are either put into a staging area for a short period and then moved to the shipping area, or directly moved to the shipping area. The received products are typically presorted at suppliers’ facilities. The operation here is simply to pass on the product to a customer or the next facility in the supply chain.

Flow 3 is also a typical warehouse operation. Products are first stored in the reserve area typically in pallet loads, broken into smaller loads (cartons or cases) and then moved to the forward area for fast order picking, order consolidation or performing value added operations.

— Mathematical Model for Warehouse Design and Product Allocation (Heragu et al. 2005, 329–30, sec. 3).

Typical warehouse flows

The simplest type of warehouse is a unit-load warehouse, which means that only a single, common “unit” of material is handled at a time. The typical unit-load is a pallet. Because pallets are (mostly) standardized and are (mostly) handled one-at-a-time, both space and labor requirements scale: It takes about $n$ times the space to store $n$ pallets as for one; and it takes about $n$ times the labor to handle $n$ pallets as for one. An example of unit-load is a third-party transshipment warehouse that receives, stores, and forwards pallets. The third-party warehouse is a subcontractor to others for warehouse services. A third-party warehouse typically charges its customers for each pallet handled (received and later shipped); and rent for space occupied. In this chapter we study unit-load issues in the context of such a warehouse; but many warehouses have some portion of their activity devoted to moving unit-loads, as in Figure 6.1.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 51 (PDF p. 74)).

The handling unit carton or case is not standardized, but generally it refers to a rectangular box that weighs between about 5 and 50 pounds (2.3–22.7 kilograms); can be handled by one person; is conveyable (which depends on the type of conveyor); and can be stored on a pallet. When handled in volume, cartons are typically stored on pallets and so restocking is a unit-load process, but picking is not, which creates additional complexities in our models of space and labor. One consequence is that it becomes much more difficult to measure the convenience of an individual location; but it is still possible to make broad distinctions in convenience. A particularly convenient region that is replenished from within the warehouse is called a forward area or fast-pick area. The material flow on which we concentrate here is that of Figure 7.1.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 77–78 (PDF p. 100)).

Piece-picking is the most labor intensive activity in the warehouse because the product is handled at the smallest units-of-measure. Furthermore, the importance of piece-picking has greatly increased because of pressures to reduce inventory while expanding product lines. Warehouses that, 20 years ago, might have shipped cartons to customers now ship pieces and much more frequently. In a typical operation pieces are picked from cartons and neither picking nor restocking is unit-load, as shown in Figure 8.1. One of the first efficiencies a warehouse should consider is to separate the storage and the picking activities. A separate picking area, sometimes called a fast-pick or forward-pick or primary-pick area, is a sub-region of the warehouse in which one concentrates picks and orders within a small physical space. This can have many benefits, including reduced pick costs and increased responsiveness to customer demand. However, there is a science to configuring the fast-pick area.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 99–100 (PDF p. 122)).

Handling costs of different flows

Figure 2 compares the touch sequence across six receiving flows. More touches typically coincide with higher unit costs and damage rates.

Figure 2: Six receiving flows. In this example, cost per unit means the handling cost of moving one case through the complete path; damage % is the share of cases damaged.

Receiving flow optimization (Frazelle 2016, 113).

Flow Path	Touches	Cost per Unit	Damage %
Direct Shipping	2	$0.83	0.50%
Cross Docking	4	$1.94	0.80%
Direct Primary Putaway	8	$3.16	1.40%
Direct Secondary Putaway	10	$3.98	1.90%
Receiving Staging	11	$5.01	2.70%
Receiving Staging & Inspection	12	$5.72	3.60%

Flow Path	Item Types	Supplier Types	Scenarios
Direct Shipping	A+ Cube Movers	A+ Reliability	Back Orders, Bulky Merchandise
Cross Docking	Consistent A Movers	A+ Reliability	Back Orders, Transfers, Customer Specials, Single SKU Unit Loads
Direct Primary Putaway	A, B & C Movers	A+ Reliability	Empty Primary
Direct Secondary Putaway	A, B & C Movers	A to B+ Reliability	Empty Secondary
Receiving Staging	A, B & C Movers	B Reliability	Quick Turn Trailers or Docks
Receiving Staging & Inspection	B & C Movers	B & C Reliability	Seasonal, High Variability

Direct shipping bypasses the warehouse completely, requiring two touches—one to load the outbound truck at the origin and one to receive the inbound truck at the destination.

Inbound loads are precisely and tightly scheduled into the warehouse, sorted immediately into outbound orders, and moved immediately to their outbound docks.

Direct primary put-away checks to see whether there are any empty primary locations and directs put-aways to those locations, thus bypassing receiving inspection, put-away, storage, and replenishment. Eight touches are required.

Direct secondary put-away bypasses receiving staging and inspection and moves product directly from unloading into reserve locations.

Traditional receiving requires staging at receiving, inspection, put-away to reserve storage, and replenishment to primary picking locations.

— World-Class Warehousing and Material Handling (Frazelle 2016, 111–12, 115).

Layout of a unit-load area

Bulk-storage/reserve/unit-load area

Only a single (“unit”) of material (e.g., pallet) handled at a time.
Many warehouses have part of their activity devoted to moving unit-loads.

How to increase space cost-efficiency (pallet-positions[^def_pallet_position]/unit area[^def_why_area])?

Alternatives:
- More layers
- Deeper lanes

The simplest type of warehouse is a unit-load warehouse, which means that only a single, common “unit” of material is handled at a time. The typical unit-load is a pallet. Because pallets are (mostly) standardized and are (mostly) handled one-at-a-time, both space and labor requirements scale: It takes about $n$ times the space to store $n$ pallets as for one; and it takes about $n$ times the labor to handle $n$ pallets as for one. An example of unit-load is a third-party transshipment warehouse that receives, stores, and forwards pallets. The third-party warehouse is a subcontractor to others for warehouse services. A third-party warehouse typically charges its customers for each pallet handled (received and later shipped); and rent for space occupied. In this chapter we study unit-load issues in the context of such a warehouse; but many warehouses have some portion of their activity devoted to moving unit-loads, as in Figure 6.1.

One revenue source of the third-party warehouse is to charge rent by the pallet-month. But because the warehouse typically tallies its own expenses by the square-foot or square-meter (for example, rent of the building, climate control, cleaning, and so on), the warehouse naturally wants many pallet positions per unit area. It can achieve this in two ways: by taking advantage of vertical space and by using deep lanes.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 51).

Optimal lane depth

A lane is a row of pallet positions, one behind the other, accessed from a single aisle.

Shallow lanes

More space lost in aisles.
Increased accessibility.
Faster position reassignment.

Deep lanes

More space for pallet positions.
Reduced compliance with FIFO.
Increased S/R times.

Lane depth counts pallet positions behind one aisle access point. Deeper lanes spread aisle space across more positions, but they also delay reassignment of empty positions and can increase handling time. They do not automatically prevent FIFO: pallet-flow and drive-through rack can preserve FIFO under appropriate operating rules.

Aisles provide accessibility, not storage, and so this space for aisles is not directly revenue-generating. Consequently we prefer to reduce aisle space to the minimum necessary to provide adequate accessibility. For this the aisles must be at least wide enough for a forklift to insert or extract a pallet. By storing product in lanes, additional pallet positions can share the same aisle space and so amortize that cost. Should lanes be four pallets deep? Six? Ten? There are many issues to consider, but the most important one is effective utilization of space. For example, double-deep layout (lanes that are two pallet positions deep) fits about 41% more pallet positions in the same floor area than does single-deep layout in the example of Figure 6.3; but is it a better layout? Are enough of the additional pallet positions usefully engaged? There is a trade-off: The single-deep layout has eight aisles and provides 196 pallet storage locations, all of which are directly accessible, which means that they are available for reassignment as soon as the current pallet is shipped out. In contrast, the double-deep layout has only six aisles and provides 280 pallet storage locations—but only 140 of them are directly accessible. Moreover, the 140 that are directly accessible are not available for reuse until the interior pallet location in the same lane becomes available. So: Deeper lanes produce more pallet storage locations but they are of diminishing value.

In most warehouses a lane is dedicated entirely to a single SKU to avoid double-handling pallets. This saves time but incurs a cost in space: When the first pallet is retrieved from a lane, that position is unoccupied but unavailable to other SKUs. The deeper the lane, the greater this cost. The first pallet position in a $k$-deep lane that holds uniformly moving product will be occupied only $1/k$ of the time, the second $2/k$ of the time, and so on (Figure 6.4). This waste is called honeycombing. Deeper lanes are more susceptible to honeycombing; but shallow lanes use more space for accessibility.

To maximize space efficiency SKU $i$ should be stored in a lane of depth that minimizes floor space-time that is unoccupied but unavailable to other SKUs. The optimum lane depth can be determined by simply evaluating all possibilities, as has been done in Table 6.1. In Figure 6.5 waste has been plotted for each lane depth, and it can be seen that 2-deep lanes are most space efficient when the aisle is less than 4 pallet positions wide; otherwise 4-deep is best.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 54–56, secs. 6.1.2–6.1.3).

Deep-lane storage reduces aisle space but loses use of pallet positions due to honey-combing, the creation of empty but unusable storage positions. (The positions cannot be used until the remaining product in the same column and/or aisle are removed.) The optimal lane depth balances these two losses to get the greatest (time-averaged) occupancy of floor space. Optimal lane depth are given by Theorems 6.2 and 6.3.

In laying out pallet storage there are other issues to consider besides space utilization. For example, in some warehouses, such as those of food distributors, it is important to move product in accordance with the rule of “First In First Out” (FIFO). Some special types of rack such as pallet flow rack support FIFO; but otherwise FIFO can be guaranteed only to within the lane depth. Making lanes deeper might give better space utilization; but it reduces compliance with FIFO. In addition, deeper lanes can increase insert/extract times.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 69–70, secs. 6.3–6.4).

Lane depth and space utilization

For example, pallet-position engagement (see Figure 3) varies by lane depth:

1-deep: 8 aisles and 196 directly accessible pallet positions.
2-deep: 6 aisles and 140 directly accessible pallet positions.

A pallet position consists of the pallet footprint plus any required clearance space.

(a) 1-deep lane depth (8 aisles and 196 pallet positions)

Aisles provide accessibility, not storage, and so this space for aisles is not directly revenue-generating. Consequently we prefer to reduce aisle space to the minimum necessary to provide adequate accessibility. For this the aisles must be at least wide enough for a forklift to insert or extract a pallet.

By storing product in lanes, additional pallet positions can share the same aisle space and so amortize that cost. Should lanes be four pallets deep? Six? Ten? There are many issues to consider, but the most important one is effective utilization of space. For example, double-deep layout (lanes that are two pallet positions deep) fits about 41% more pallet positions in the same floor area than does single-deep layout in the example of Figure 6.3; but is it a better layout? Are enough of the additional pallet positions usefully engaged? There is a trade-off: The single-deep layout has eight aisles and provides 196 pallet storage locations, all of which are directly accessible, which means that they are available for reassignment as soon as the current pallet is shipped out. In contrast, the double-deep layout has only six aisles and provides 280 pallet storage locations—but only 140 of them are directly accessible. Moreover, the 140 that are directly accessible are not available for reuse until the interior pallet location in the same lane becomes available. So: Deeper lanes produce more pallet storage locations but they are of diminishing value.

By pallet position we mean the floor space required to hold a pallet. This includes not only the footprint of the pallet but also any required gap between one pallet and an adjacent one (Figure 6.4). Let the lanes be $k$ pallet positions deep. Each lane requires aisle space at its head so that pallets can be inserted and removed. Let the aisle space in front of the pallet be of area $a$, measured in pallet positions. Then the total area charged to one lane is $k + a/2$ pallet positions. This area is the sum of space devoted to storage ($k$) and space that provides accessibility ($a/2$).

In most warehouses a lane is dedicated entirely to a single SKU to avoid double-handling pallets. This saves time but incurs a cost in space: When the first pallet is retrieved from a lane, that position is unoccupied but unavailable to other SKUs. The deeper the lane, the greater this cost. The first pallet position in a $k$-deep lane that holds uniformly moving product will be occupied only $1/k$ of the time, the second $2/k$ of the time, and so on (Figure 6.4). This waste is called honeycombing. Deeper lanes are more susceptible to honeycombing; but shallow lanes use more space for accessibility.

Table 6.1 displays daily snapshots of a SKU with an order size that occupies four pallet positions and which is extracted at a rate of one pallet position per day. In single-deep rack, all the unused space is the aisle space required for accessibility. Deeper aisles require less aisle space per pallet position—but the additional pallet positions are less fully occupied.

To maximize space efficiency SKU $i$ should be stored in a lane of depth that minimizes floor space-time that is unoccupied but unavailable to other SKUs. The optimum lane depth can be determined by simply evaluating all possibilities, as has been done in Table 6.1. In Figure 6.5 waste has been plotted for each lane depth, and it can be seen that 2-deep lanes are most space efficient when the aisle is less than 4 pallet positions wide; otherwise 4-deep is best.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 54–56).

Lane depth and storage policies

Dedicated policy:
- Poor space utilization (“honeycombing”).
- Efficient handling.
Randomized (shared) policy:
- Efficient space utilization.
- May incur pallet double handling (blockage issues).
  - Inventory/SKU is low -> Allow blockage.
  - Inventory/SKU is high -> No blockage.

The optimal lane depth minimizes floor space-time that is unoccupied but unavailable to other SKUs.

Figure 4: A dedicated storage policy may lead to honeycombing in deep lanes (source).

In laying out pallet storage there are other issues to consider besides space utilization. For example, in some warehouses, such as those of food distributors, it is important to move product in accordance with the rule of “First In First Out” (FIFO). Some special types of rack such as pallet flow rack support FIFO; but otherwise FIFO can be guaranteed only to within the lane depth. Making lanes deeper might give better space utilization; but it reduces compliance with FIFO. In addition, deeper lanes can increase insert/extract times.

Aisles provide accessibility, not storage, and so this space for aisles is not directly revenue-generating. Consequently we prefer to reduce aisle space to the minimum necessary to provide adequate accessibility. For this the aisles must be at least wide enough for a forklift to insert or extract a pallet. By storing product in lanes, additional pallet positions can share the same aisle space and so amortize that cost. Should lanes be four pallets deep? Six? Ten? There are many issues to consider, but the most important one is effective utilization of space. For example, double-deep layout (lanes that are two pallet positions deep) fits about 41% more pallet positions in the same floor area than does single-deep layout in the example of Figure 6.3; but is it a better layout? Are enough of the additional pallet positions usefully engaged? There is a trade-off: The single-deep layout has eight aisles and provides 196 pallet storage locations, all of which are directly accessible, which means that they are available for reassignment as soon as the current pallet is shipped out. In contrast, the double-deep layout has only six aisles and provides 280 pallet storage locations—but only 140 of them are directly accessible. Moreover, the 140 that are directly accessible are not available for reuse until the interior pallet location in the same lane becomes available. So: Deeper lanes produce more pallet storage locations but they are of diminishing value.

In most warehouses a lane is dedicated entirely to a single SKU to avoid double-handling pallets. This saves time but incurs a cost in space: When the first pallet is retrieved from a lane, that position is unoccupied but unavailable to other SKUs. The deeper the lane, the greater this cost. The first pallet position in a $k$-deep lane that holds uniformly moving product will be occupied only $1/k$ of the time, the second $2/k$ of the time, and so on (Figure 6.4). This waste is called honeycombing. Deeper lanes are more susceptible to honeycombing; but shallow lanes use more space for accessibility.

To maximize space efficiency SKU $i$ should be stored in a lane of depth that minimizes floor space-time that is unoccupied but unavailable to other SKUs. The optimum lane depth can be determined by simply evaluating all possibilities, as has been done in Table 6.1. In Figure 6.5 waste has been plotted for each lane depth, and it can be seen that 2-deep lanes are most space efficient when the aisle is less than 4 pallet positions wide; otherwise 4-deep is best.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 54–56, 69–70).

Exercise 1 Space utilization in a warehouse lane

Consider the pallet positions A, B, C, shown in Figure 5. If the warehouse has a single SKU occupying these positions and the demand is 1 pallet per day. Each pallet position occupies area $p$ and the aisle space in front of the pallet is of area $a/2$.

What is the utilization rate $u_{A}$, $u_{B}$, and $u_{C}$ for each position?
What is the total unoccupied area across the three days for the lane in terms of $p$ and $a$?

Figure 5: Pallet positions A, B, and C with area $p$ and aisle front area $a/2$. SKU demand is 1 pallet per day.

Exercise 1 Space utilization in a warehouse lane

Answer

We analyze the occupancy of each pallet position over three days, given that one pallet is removed each day from the front position (i.e., position C). The utilization rate for each position is:

$u_{A} = 1$
$u_{B} = 2/3$
$u_{C} = 1/3$

The total unoccupied area-days for the lane is calculated as follows:

Day 1: $\frac{a}{2}$
Day 2: $p + \frac{a}{2}$
Day 3: $2p + \frac{a}{2}$

Total: $3p + \frac{3a}{2}$

Lane depth and storage equipment

The choice of lane depth also influences the selection of storage equipment. Different equipment types are suited to varying lane depths and operational requirements:
- Selective Pallet Racking: Ideal for shallow lanes (1-2 deep), offering direct access to each pallet. It is flexible and allows for easy reconfiguration but may not maximize space utilization.
- Double-Deep Racking: Suitable for medium lane depths (2-4 deep), providing a balance between accessibility and space efficiency. It requires specialized forklifts for accessing the second pallet.
- Drive-In/Drive-Through Racking: Best for deep lanes (4+ deep), maximizing storage density. However, it limits accessibility and may complicate FIFO compliance.

The choice of storage equipment should align with the warehouse’s operational goals, SKU characteristics, and handling requirements.

Lane depth and aisle width

Aisle space is not directly revenue-generating, so minimizing aisle width is desirable.
The aisle must be wide enough to accommodate the material handling equipment (MHE) used in the warehouse.
Narrowing the aisle to 1 gives 336 pallet positions: 140 (71.43%) more than the 1-deep layout in Figure 3 (a), and 56 (20.00%) more than the 2-deep layout in Figure 3 (b). Both comparison layouts use aisle width 3.

Figure 6: Warehouse layout with narrow aisles. More space is available for storage.

The capacity percentages on this slide are generated by the displayed course layout, so they are model outputs rather than values reported by the source. The general mechanism is that aisle width must satisfy equipment access requirements; changing the rack or truck can reduce access space, but it also changes equipment, floor, guidance, and operating requirements.

Aisles provide accessibility, not storage, and so this space for aisles is not directly revenue-generating. Consequently we prefer to reduce aisle space to the minimum necessary to provide adequate accessibility. For this the aisles must be at least wide enough for a forklift to insert or extract a pallet. By storing product in lanes, additional pallet positions can share the same aisle space and so amortize that cost. Should lanes be four pallets deep? Six? Ten? There are many issues to consider, but the most important one is effective utilization of space. For example, double-deep layout (lanes that are two pallet positions deep) fits about 41% more pallet positions in the same floor area than does single-deep layout in the example of Figure 6.3; but is it a better layout? Are enough of the additional pallet positions usefully engaged? There is a trade-off: The single-deep layout has eight aisles and provides 196 pallet storage locations, all of which are directly accessible, which means that they are available for reassignment as soon as the current pallet is shipped out. In contrast, the double-deep layout has only six aisles and provides 280 pallet storage locations—but only 140 of them are directly accessible. Moreover, the 140 that are directly accessible are not available for reuse until the interior pallet location in the same lane becomes available. So: Deeper lanes produce more pallet storage locations but they are of diminishing value.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 54–55, sec. 6.1.2).

Selective rack or single-deep rack stores pallets one deep, as in Figure 5.1. Due to rack supports each pallet is independently accessible, and so any SKU can be retrieved from any pallet location at any level of the rack. This gives complete freedom to retrieve any individual pallet but requires relatively more aisle space to access the pallets.

Double-deep rack essentially consists of two single-deep racks placed one behind the other, and so pallets are stored two deep. Due to rack supports each 2-deep lane is independently accessible, and so any SKU can be stored in any lane at any level of the rack. To avoid double-handling, it is usual that each lane be filled with a single SKU, which means that some pallet locations will be unoccupied whenever some SKU is present in an odd number of pallets. Another disadvantage of deep lanes is that slightly more work is required to store and retrieve product. However, deep lanes have the advantage of requiring fewer aisles to access the pallets, which means that the warehouse can hold more product. A special truck is required to reach past the first pallet position.

Reach and double-reach lift truck is equipped with a reach mechanism that allows its forks to extend to store and retrieve a pallet. The double-reach truck is required to access the rear positions in double deep rack storage. Each truck requires an aisle width of 7–9 feet (2.1–2.7 meters), their lift height is limited to 30 feet (9.1 meters), and they travel at about 50 feet/minute (15.2 meters/minute).

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 39–41, sec. 5.1.1).

Lane depth and MHE

Aisle size and space savings involve a compromise between MHE requirements and costs and the savings achieved by narrower aisles.
Example: Very Narrow Aisle (VNA) forklifts can operate in aisles as narrow as 1.5 m (see, e.g., Figure 7).

Figure 7: Example of VNA forklift (ArRacking Storage Solutions).

Double-deep rack essentially consists of two single-deep racks placed one behind the other, and so pallets are stored two deep. Another disadvantage of deep lanes is that slightly more work is required to store and retrieve product. However, deep lanes have the advantage of requiring fewer aisles to access the pallets, which means that the warehouse can hold more product. A special truck is required to reach past the first pallet position. Drive-in or drive-through rack allows a lift truck to drive within the rack frame to access the interior loads.

Except for automated storage-and-retrieval systems (AS/RS), some type of lift truck is required to access the loads in pallet rack; and specialized racks may require specialized trucks. A double-reach lift truck is required to access the rear positions in double-deep rack storage.

— Warehouse & Distribution Science (printed pp. 39–41; PDF pp. 61–63) (Bartholdi and Hackman 2019, 39–41).

Optimal lane depth for block stacking

Block stacking involves storing pallets of a single Stock Keeping Unit (SKU) in floor lanes, stacked to a fixed height, and accessed from one side.
This method is commonly used for high-density storage, where pallets are organized in multiple bays of lanes separated by aisles to optimize space utilization and accessibility.
Two primary sources of space inefficiency arise in this system:
- Honeycombing waste within lanes.
- Accessibility waste for aisles that provide access.

Figure 8: Block stacking is a common practice in beverage and food warehouses, optimizing space utilization while maintaining accessibility.

Block stacking is a floor-storage system rather than a rack system. A lane is normally dedicated to one SKU to avoid relocations, so empty positions behind or beneath accessible stock can become temporarily unusable. The cited model supports broad manufacturing and distribution-center use; the photograph is an example and does not establish how prevalent the method is in beverage or food warehouses.

Block stacking is an inexpensive and conventional storage system whose performance depends on the efficient use of space. It is a unit load storage system in which pallets of stock keeping units (SKUs) are stacked on top of one another in lanes on the warehouse floor. Pallets are stacked to the maximum stacking height which depends on the conditions and heights of the pallets, load weights, safety limits, clearance height of the warehouse and so on. No racking or storage facility is required for this system and it can be employed in any warehouse with wide floor space. This makes it an inexpensive storage system to implement but challenging to manage in terms of space planning.

When the inventories of the SKUs are big enough to justify assigning a lane to a single SKU, no blockage policy is enforced. In this case, to avoid blockage and relocation, a lane is dedicated to a SKU once it occupies the first position of the lane. This case mainly occurs in the warehouses located in manufacturing systems or the distribution centres where plenty of pallets of different SKUs are block-stacked. However, this restriction wastes storage spaces in a lane when it is filled or depleted as there will be some unoccupied pallet positions in the lane that are just available to the pallets of the assigned SKU. This effect is termed honeycombing and waste associated with it is incurred to the system until a lane becomes entirely occupied or empty. In addition to honeycombing, aisles also contribute to the overall wasted space. Aisles are required to have access to the lanes but their devoted spaces are not directly used for storage.

— Optimising Space Utilisation in Block Stacking Warehouses (Derhami et al. 2017, 6436–37, sec. 1).

Storing a batch of pallets in deep lanes increases the honeycombing waste, but the space required for aisles decreases, while the reverse is true for the shallow lanes. Hence, a trade-off between the lane depth and width must be considered to optimise space utilisation.

Minimising the waste of storage space maximises space utilisation. So, one can obtain the optimal lane depth that maximises the space utilisation by deriving a mathematical expression to calculate waste of storage space and then finding the optimal lane depth that minimises this waste expression. The waste of storage space is obtained by calculating three types of waste: (1) waste of storage space caused by honeycombing, $W_H$; (2) waste of storage space dedicated to the aisles, $W_A$; and (3) waste of unoccupied storage space on top of the occupied lanes, $W_U$.

— Optimising Space Utilisation in Block Stacking Warehouses (Derhami et al. 2017, 6437–39, secs. 1 and 3).

Optimal lane depth: Problem description

Consider a block stacking warehouse where:
- SKUs are stored in lanes of fixed depth.
- Lanes are last-in first-out (LIFO) (i.e., the most recently added pallet is the first to be removed).
- Lanes are accessible from one side (i.e., the front).
- Batch arrivals are deterministic (i.e., known arrival times and quantities).
- Batch arrivals are either:
  - instantaneous (i.e., all pallets arrive at once), or
  - at finite rate (i.e., pallets arrive over time).
Goal: Determine the optimal common lane depth that minimizes average space waste across all SKUs, where average space waste is defined as the sum of honeycombing and aisle accessibility waste.

Optimal lane depth: Typical problem formulation

Let $N$ be the number of SKUs. For each SKU $i \in \{1,\dots,N\}$:
- $Q_i$: batch size in pallets.
- $P_i$: production or storage rate in pallets per hour.
- $\lambda_i$: depletion or demand rate in pallets per hour.
- $Z_i$: stack height in pallets.
- $A$: aisle width in pallet units.
- $Z_i*x_c$: total lane depth in pallet units, where $x_c$ is the common lane depth to be determined.
Objective. Find the optimal common lane depth $x_c^*$ that minimizes average space waste across all SKUs.

Optimal lane depth: Common approaches

Analytical models
- Classical models (e.g., Matson 1982; Kind 1975) assume:
  1. Dedicated storage policy (i.e., each SKU occupies its own lane).
  2. Deterministic, instantaneous batch arrivals.
- More recent models (e.g., Derhami et al. 2017) account for finite production or replenishment rates ($P_i < \lambda_i$ or $P_i > \lambda_i$ besides $P_i = \infty$).
(Mixed-)integer linear programming models
- Accorsi et al. (2017) present a decision-support model to assign product lots to the optimal lane depth, storage mode, and zone in block storage warehouses, minimizing costs generated by space and time inefficiencies.
- Derhami et al. (2019) propose a model to determine the optimal bay depths and the number of aisles in a block stacking warehouse, minimizing space waste.

This paper illustrates an original decision-support model to (1) manage existing block storage warehouses, and (2) to aid the design of new block storage systems from green field. The management of a warehouse (1) deals with the assignment of the incoming product lots to the optimal lane depth, storage mode, and zone in a constrained and capacitated storage environment. The design of a warehouse from green field (2) is aided by identifying the optimal configuration of lane depths and storage modes that minimizes the infrastructural costs. The proposed model is formulated via integer linear programming (ILP) and minimizes mutually the costs generated by space and time inefficiencies. The illustrated results obtained by its application to a real case study from the beverage industry, candidate the model as a tool to aid operative and strategic layout issues in deep-lane storage systems.

— Design and Manage Deep Lane Storage Systems: Optimizing Space Efficiency by a New Decision Support Model (Accorsi et al. 2017, 57).

We have developed a model to design a space-efficient layout for block stacking warehouses. We showed the CLD model is not appropriate to find bay depths for a layout and developed a new waste function to estimate the total waste of storage volume in the layout. We optimized this function with a mixed-integer programming model to find the optimal bay depths and the number of aisles in the layout. We developed various cuts to reduce the problem symmetry and effectively bounded the decision variables to tighten the lower bound of the LP relaxation (MBDC and MBDCE models). Although both models produce good quality solutions, we found the MBDCE model more likely performs better and faster on small- to medium-sized problems (less than 700 SKUs), and the MBDC model performs better on large-sized problems.

— Optimising Space Utilisation in Block Stacking Warehouses (Derhami et al. 2017, 970).

The depths of the bays and the number of aisles determine the storage space utilization. Using an analytical model, we show that the traditional lane depth model underestimates accessibility waste and therefore does not provide an optimal lane depth. We propose a new model of wasted storage space and embed it in a mixed-integer program to find the optimal bay depths. The model improves space utilization by allowing multiple bay depths and allocating SKUs to appropriate bays. Our computational study shows the proposed model is capable of solving large-scale problems with a relatively small optimality gap. We use simulation to evaluate performance of the proposed model on small- to industrial-sized warehouses. We also include a case study from the beverage industry.

— Space-Efficient Layouts for Block Stacking Warehouses (Derhami et al. 2019, 957).

Location of receiving and shipping

Most convenient locations: flow-through layout

What are the most convenient storage locations of unit-load U-shaped and I-shaped warehouses?

Figure 9: Flow-through layout. Lighter cells mark storage locations closer to the input/output (I/O) positions.

In a flow-through layout, receiving and shipping lie on opposite sides, so product generally crosses the building. The source explains the resulting convenience pattern and why the best geometry depends on SKU velocity. The Manhattan-distance shading and the exact I/O coordinates in the figure are course-model choices.

The layout of the warehouse determines the cost associated with each storage location. In the layout of Figure 6.10 the average positions of receiving and shipping are in the middle of opposite sides of the warehouse. This is sometimes referred to as a flow-through configuration because all product flows from one side of the facility to the other. As a result all the storage locations along one side of an aisle are equally convenient.

If both receiving and shipping are on the same side of the warehouse this induces a different economic terrain within, as shown in Figure 6.11. Because product flows in and out the same side of the warehouse, this is sometimes referred to as a U-flow configuration.

Now the best storage locations, which are at the middle of the common receiving and shipping dock, are very convenient indeed because a location that is close to receiving would also be close to shipping. However, there are relatively few such prime locations and there are more inconvenient locations than before; and the least convenient locations, at the far top corners are even less convenient than the least convenient of Figure 6.10.

Which layout is better? In this case, as with so many of the design decisions, it depends on the populations of SKUs passing through the warehouse. If there are few very fast-moving SKUs, as is typical in cosmetics, apparel, or other fashion businesses, it may be more efficient to put receiving and shipping on the same side of the facility, because the savings from the few very convenient locations may offset any loss due to the greater number of less convenient locations.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 65–67, sec. 6.2.3).

Most convenient locations: U-shaped layout

Figure 10: U-shaped layout. Lighter cells mark storage locations closer to the input/output (I/O) positions and shorter travel distance.

Now the best storage locations, which are at the middle of the common receiving and shipping dock, are very convenient indeed because a location that is close to receiving would also be close to shipping. However, there are relatively few such prime locations and there are more inconvenient locations than before; and the least convenient locations, at the far top corners are even less convenient than the least convenient of Figure 6.10.

Which layout is better? In this case, as with so many of the design decisions, it depends on the populations of SKUs passing through the warehouse. If there are few very fast-moving SKUs, as is typical in cosmetics, apparel, or other fashion businesses, it may be more efficient to put receiving and shipping on the same side of the facility, because the savings from the few very convenient locations may offset any loss due to the greater number of less convenient locations.

U-flow configuration: Receiving and shipping are located on the same side of the warehouse. This makes the most convenient locations still more convenient and less convenient locations even worse. It is appropriate when product movement has strong ABC skew (that is, when very few SKUs account for most of the activity). It provides dock flexibility for both shipping and receiving: If one experiences a surge of activity, it can make use of additional doors from the other function. It permits more efficient use of forklifts: When a forklift reports for an assignment, it may be given a put-away and a retrieval, matched to reduce dead-heading. It minimizes truck apron and roadway and allows expansion along the other three sides of the warehouse.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 65–67).

Layout for a forward area

Fast-, forward-, or primary-pick area

Sub-region of the warehouse (warehouse-within-warehouse):

Most popular SKUs in small amounts.
Picks concentrated in small space.
Reduced pick costs and increased responsiveness.
Less unproductive travel time (prime real estate).

Figure 11: Large/slow-moving SKUs are better picked from the reserve area (Bartholdi and Hackman 2019).

Piece-picking is the most labor intensive activity in the warehouse because the product is handled at the smallest units-of-measure. Furthermore, the importance of piece-picking has greatly increased because of pressures to reduce inventory while expanding product lines. Warehouses that, 20 years ago, might have shipped cartons to customers now ship pieces and much more frequently. In a typical operation pieces are picked from cartons and neither picking nor restocking is unit-load, as shown in Figure 8.1. One of the first efficiencies a warehouse should consider is to separate the storage and the picking activities. A separate picking area, sometimes called a fast-pick or forward-pick or primary-pick area, is a sub-region of the warehouse in which one concentrates picks and orders within a small physical space. This can have many benefits, including reduced pick costs and increased responsiveness to customer demand. However, there is a science to configuring the fast-pick area.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 99).

Multiple fast-pick areas

Figure 12: Pick areas may have different economics (e.g., flow-rack or carousel) (Bartholdi and Hackman 2019).

Suppose there are $m$ fast-pick areas, each with its own economics: savings per pick (compared to from reserve) and restock costs, as suggested by Figure 8.6. Now the question becomes which SKUs go to which fast-pick areas and which to reserve. Each of the $n$ SKUs can be picked from at most one area. Brute-force search can find the best stocking strategy within $O(m^n)$ steps by enumerating all possible assignments of SKUs to storage modes and then evaluating the result. However, this is completely impractical for realistic values ($m = 2, 3$ and $n$ on the order of tens of thousands).

Some optimal stocking strategy has the following structure: If all SKUs are ranked by bang-for-buck then the top $k_1$ SKUs would be assigned to the storage mode with largest savings per pick, the next $k_2$ would be assigned to the next best storage mode, and so on. Note that “best storage” depends only on savings per pick and is independent of restock costs.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 120–21).

Setting up a forward-pick area

Main questions when setting up a fast-picking area:

Which SKUs to store?
How much of each SKU to store?

Trade-off: The fast-pick area may require replenishment from reserve.

Figure 13: Restock costs consume any pick savings if too little is stored (Bartholdi and Hackman 2019).

The fast-pick area of a warehouse functions as a “warehouse within the warehouse”: Many of the most popular stock keeping units (SKUs) are stored there in relatively small amounts, so that most picking can be accomplished within a relatively small area. This means that pickers do less unproductive travel and may be more easily supervised. The trade-off is that the fast-pick area may require replenishment from bulk storage, or reserve. The basic issues in the design of a fast-pick area are: Which SKUs to store in the fast-pick area? And how much of each SKU to store?

The net benefit realized by storing a SKU as a function of the quantity stored. The net benefit is zero if SKU $i$ is not stored in the forward area; but if too little is stored, restock costs consume any pick savings. Note that from the shape of the objective function there is a minimum sensible amount of each SKU to store in the fast-pick area.

— Warehouse & Distribution Science (Bartholdi and Hackman 2019, 99, 113).

References

Accorsi, Riccardo, Giulia Baruffaldi, and Riccardo Manzini. 2017. “Design and Manage Deep Lane Storage System Layout. An Iterative Decision-Support Model.” The International Journal of Advanced Manufacturing Technology 92 (1): 57–67. https://doi.org/10.1007/s00170-016-9962-9.

Bartholdi, J. J., and S. T. Hackman. 2019. Warehouse & Distribution Science. 0.98.1 ed. Georgia Institute of Technology. https://www.warehouse-science.com/book/editions/wh-sci-0.98.1.pdf.

Derhami, Shahab, Jeffrey S. Smith, and Kevin R. Gue. 2017. “Optimising Space Utilisation in Block Stacking Warehouses.” International Journal of Production Research 55 (21): 6436–52. https://doi.org/10.1080/00207543.2016.1154216.

Derhami, Shahab, Jeffrey S. Smith, and Kevin R. Gue. 2019. “Space-Efficient Layouts for Block Stacking Warehouses.” IISE Transactions 51 (9): 957–71. https://doi.org/10.1080/24725854.2018.1539280.

Frazelle, Edward. 2016. World-Class Warehousing and Material Handling. Second Edition. McGraw-Hill Education.

Heragu, S. S., L. Du, R. J. Mantel, and P. C. Schuur. 2005. “Mathematical Model for Warehouse Design and Product Allocation.” International Journal of Production Research 43 (2): 327–38. https://doi.org/10.1080/00207540412331285841.

Kind, D. A. 1975. “Elements of Space Utilization.” Transportation and Distribution Management 15: 29–34.

Matson, Jan O. 1982. “The Analysis of Selected Unit Load Storage Systems.” PhD thesis, Georgia Institute of Technology.

Layout of unit-load and forward areas

Learning objectives

Contents

Functional areas and material flows

Functional areas

Typical warehouse flows

Handling costs of different flows

Layout of a unit-load area

Bulk-storage/reserve/unit-load area

Optimal lane depth

Lane depth and space utilization

Lane depth and storage policies

Exercise 1 Space utilization in a warehouse lane

Exercise 1 Space utilization in a warehouse lane

Lane depth and storage equipment

Lane depth and aisle width

Lane depth and MHE

Optimal lane depth for block stacking

Optimal lane depth: Problem description

Optimal lane depth: Typical problem formulation

Optimal lane depth: Common approaches

Location of receiving and shipping

Most convenient locations: flow-through layout

Most convenient locations: U-shaped layout

Layout for a forward area

Fast-, forward-, or primary-pick area

Multiple fast-pick areas

Setting up a forward-pick area

References