Material Handling Systems
These notes are based on the excellent work by (Mikell P. Groover 2018), our textbook.
There are two basic systems covered:
Vehicle based
Conveyors
We also define a unit load as the mass of material moved or handled at one time. The unit load can be as large as practically possible.
Vehicle based material transport systems
These types of systems include manned trucks and Automated Guided Vehicle Systems or AGVS.
Assumptions for analysis:
Movement is performed at constant velocity
The material movement cycle consist of:
Loading materials at pick-up station
Traveling to a drop-off station
Unloading of materials
Empty travel back to pick up station.
\(T_c\) is the delivery time of the system, and it consists of the following components:
\(T_L\): Time to load
\(L_d\): Average distance traveled
\(v_c\): Carrier velocity
\(T_U\): Time to unload
\(L_e\): Average distance traveling empty
Where,
\[ T_{c}=T_L + \frac{L_d}{v_c}+T_U + \frac{L_e}{v_c} \tag{1}\]
The questions to answer for vehicle transport systems are:
What is the rate of deliveries per vehicle?
What is the number of vehicles needed to satisfy a delivery requirement?
To answer these questions we have to consider losses associated to the transport system:
Availability, the proportion of time a vehicle is down or being repaired. This is a measure of reliability.
Congestion, usually expressed with a traffic factor \(F_t\). When \(F_t=1\) there is no congestion in the system.
Driver efficiency for worker operated vehicles \(E_w\). This is the ratio of the actual worker’s rate with respect to an expected rate.
Considering the three factors above, the available time for a transport system can be expressed as:
\[ AT=AF_tE_w \tag{2}\]
For this analysis, other losses are not considered.1
Thus, the rate of deliveries can be expressed as a function of available time and delivery cycle time.
\[ R_{dv}=\frac{AT}{T_c} \tag{3}\]
If the requirements of the vehicle transportation system are determined by a specified flow rate of deliveries \(R_f\), the workload of the system can be expressed as:
\[ WL=R_fT_c \tag{4}\]
Thus, the number of vehicles needed to satisfy the rate of delivery desired by the client operation are:
\[ n_c=\frac{WL}{AT} \tag{5}\]
or:
\[ n_c=\frac{R_f}{R_{dv}} \tag{6}\]
Conveyors
Three types of conveyors are considered:
Single direction
Continuous loop
Recirculating
Single direction conveyors
If we define \(L_d\) as the conveyor’s deliverable distance from load to unload at speed \(v_c\). Then, the delivery time is:
\[ T_d=\frac{L_d}{v_c} \tag{7}\]
The flow rate \(R_f\) of materials on the conveyor is a function of the loading rate \(R_L\) at the loading station. This loading rate also determines the center to center spacing of unit loads on the conveyor \(S_c\). This yields:
\[ R_f=R_L=\frac{v_c}{S_c} \leq \frac{1}{T_L} \tag{8}\]
Where \(T_L\) is the time to load a unit in the conveyor.
It is important to note that the loading rate is not necessarily the reciprocal of the load time. The load rate is a function of the demand or flow rate: \(R_L=f(R_f)\).
The time to load depends on the ergonomics of the loading station (when manned). Thus, the worker must perform faster than the flow rate without being unsafe and unhealthy.
If we define the time to unload as \(T_U\), we should design the conveyor system such that \(T_U \leq \frac{1}{R_f}\), otherwise we will have accumulation of unit loads in the conveyor.
If we use containers as unit loads, we can define as \(n_p\) the number of parts per container. Therefore, the flow rate can be expressed as:
\[ R_f=\frac{n_p v_c}{S_c} \leq \frac{1}{T_L} \tag{9}\]
In this case \(S_c\) is the center to center spacing between containers and \(T_L\) is the load time per container.
Continuous loop conveyors
Let \(L_d\) be the distance traveled to deliver a load from the loading station to the unloading station. Then, \(L_c\) is the empty distance traveled from the unload to the load station. Thus, the total length of the conveyor is \(L=L_d +L_c\).
The calculation of the conveyor’s cycle time is then:
\[ T_c=\frac{L}{v_c} \tag{10}\]
We name \(T_d\) the time a load spends in the delivery or forward loop:
\[ T_d=\frac{L_d}{v_c} \tag{11}\]
If we define \(S_c\) as the distance between loads or carriers, and \(n_c=\frac{L}{S_c}\) as the total number of carriers, then the total number of parts in the system is:
\[ N=\frac{n_p n_c L_d}{L} \tag{12}\]
where \(n_p\) is the number of parts per container.
The maximum flow rate between load and unload stations is:
\[ R_f= \frac{n_p v_c}{S_c} \tag{13}\]
Recirculating conveyors
Two problems in the operation of recirculating conveyors are:
No empty carriers immediately available at the loading station when they are needed.
No loaded carriers immediately available at the unloading station when they are needed.
Kwo (Kwo 1958) recommends obeying the following three principles when designing a recirculating conveyor.
Speed rule. The speed of the conveyor must satisfy: \(\frac{n_p v_c}{S_c} \geq \max(R_L, R_U)\)
where \(R_L\) is the required loading rate, and \(R_U\) is the required unloading rate.
The upper limit is determined by the material handlers doing the loading and unloading. Thus, \(T_L\) and \(T_U\), such that: \(\frac{v_c}{S_C} \leq \min( \frac{1}{T_L},\frac{1}{T_U})\)
One additional constraint is that the operating speed must not exceed the limits of the physical conveyor.
Capacity constraint. The capacity of the conveyor must be at least equal to the flow rate \(R_f\) required by the process. This is: \(\frac{n_p v_c}{S_C} \geq R_f\)
Uniformity principle. Loads should be uniformly distributed along the conveyor. This means that no sections of the conveyor should be full while other sections are empty. The idea is to avoid long waiting times at the loading and unloading stations.
References
Footnotes
Inefficient routing layout, assignment of vehicles, etc.↩︎