Storage Systems
These notes are based on (Mikell P. Groover 2018)
We cover two types of automated storage systems:
- Fixed aisle automated systems
- Carousel storage systems
Definitions
Storage capacity is the number of unit loads that can be stored in a system.
Accessibility is the capability to access any desired item or load in the system.
System throughput is the rate to (1) Receive and store loads, and (2) Retrieve and deliver loads to the output station. Rates should be designed to satisfy peak demands.
The constraints of the system are the storage and retrieval (S/R) transaction times.
Storage steps
Pick up load at input station
Travel to storage location
Place load in storage location
Travel back to input station
Retrieval steps
Travel to storage location
Pick up item from storage
Travel to output station
Unload at output station.
There are two types of storage and retrieval modes:
Combination of storage and retrieval, called dual command cycle.
Only one storage or retrieval, called single command cycle.
Whenever possible, design for dual command cycles.
Performance measures
Utilization: the ratio of the time used for A/R transactions and the available time.
Availability: the ratio of time the storage system is capable for operation and the normal scheduled time.
The analysis if storage systems answers these issues:
What is the capacity of the storage system
What is its throughput performance.
Analysis of fixed aisle automated system
Capacity per aisle \(C_a\) is:
\[ C_a=2n_y n_z \tag{1}\]
Where:
\(n_z\) : number of load compartments (“pick faces”) vertically
\(n_y\) : number of load compartments horizontally
Multiplied by 2 because there are load compartments at each side of the aisle.
The AS/RS (Automated Storage and Retrieval System) is designed to move standard unit loads (e.g., a pallet).
Let the dimensions of the unit load be \(x\): depth, \(y\): width, and \(z\): height.
Therefore, the dimensions of the storage system are:
\[ W=3(x+a); \\ L=n_y(y+b); \\ H=n_z(z+c) \\ \tag{2}\]
Where \(a\), \(b\), and \(c\) are allowances to provide maneuverability. \(W\) is multiplied by the number of aisles to obtain the overall width of the storage system.
We define a transaction of the S/R system as:
Depositing a load to storage
Retrieving a load from storage
The rate of transactions that the S/R can perform is calculated considering the following assumptions from the Materials Handling Institute (“Material Handling,” n.d.)
Randomized storage of loads in the AS/RS
Pick faces are of equal size
The P&D station is located at the base and end of the aisle
Constant horizontal and vertical distances of the S/R machine
Simultaneous horizontal and vertical travel
The cycle time of the system when performing a single command cycle is:
\[ T_{cs}=2 \max(\frac{0.5L}{v_y}, \frac{0.5H}{v_z} )+2T_{pd} \tag{3}\]
Where \(T_{pd}\) is the time to pick and deposit a load, \(v_y\) is the velocity of the AS/RS along length, and \(v_z\) is the velocity of the AS/RS along the vertical direction.
If the AS/RS performs a dual command cycle:
\[ T_{cd}=2 \max(\frac{0.75L}{v_y}; \frac{0.75H}{v_z}) +4 T_{pd} \tag{4}\]
Utilization of the system \(U\) depends on the number of dual and single cycles per time: \(R_{cd}\) and \(R_{cs}\).
\[ U=R_{cs}T_{cs} +R_{cd}T_{cd} \tag{5}\]
Utilization provides total time of operation per time interval (e.g., minutes per hour). To solve Equation 5 we need to assign the proportion of dual and single cycles \(R_{cd}\), \(R_{cs}\).
The total hourly cycle rate, in cycles per time, is then:
\[ R_c=R_{cs}+R_{cd} \tag{6}\]
The total number of transactions per time interval \(R_t\) will be greater than Equation 6 unless \(R_{cd}=0\). Considering two transactions per dual cycle:
\[ T_t=R_{cs}+2R_{cd} \tag{7}\]
Analysis of carousel systems
To calculate the capacity of a carousel system, let \(C\) be the circumference of the oval conveyor track. Then:
\[ C=2(L-W)+ \pi W \tag{8}\]
Let,
\(n_b\): number of bins hanging vertically
\(n_c\): number of carriers around the periphery of the rail
Then, the total number of bins is \(n_cn_b\).
If \(s_c\) is the center to center spacing of carriers in the oval track, the following relation holds:
\[ C=s_cn_c \tag{9}\]
As for throughput analysis, we consider the following assumptions:
Only single-command cycles are performed
A bin is accessed only to load and unload items
Carousel operates at constant speed \(v_c\). There is no acceleration or deceleration considered
There is random storage: any station is equally likely to be selected for any S/R transaction
Carousel can move in any direction. Thus, the mean distance between P&D location and a bin randomly located in the carousel is: \(C/4\).
The cycle time of the S/R is:
\[ T_c= \frac{C}{4v_c}+T_{pd} \]
\(T_{pd}\): Average P&D time.
The rate of transactions \(R_c=R_t\) is equal to \(\frac{1}{T_c}\).