Balanced Trailer-at-a-Time Solution Approach

The current LTL practice is for an employee to be assigned to an origin trailer. The employee then removes the first piece of freight from the trailer and transports it to the correct destination trailer. The employee returns to the same origin trailer to remove the next piece of freight. This process continues until the origin trailer is completely empty. The employee is then assigned to another origin trailer. This continues until all the origin trailers have been unloaded. Workers are currently assigned to trailers based on supervisor judgment. This solution approach uses a technique similar to assembly line balancing to assign employees to origin trailers. Since a night’s activities are not complete until the last worker is finished, an advantage of using a balancing technique is that the amount of time spent waiting on the last worker to finish is reduced.

The first step in the balanced trailer-at-a-time solution approach is to estimate the time required to completely unload an origin trailer. At this point in the solution approach, the assignment of trailers to doors is known, but the sequence that the trailers are unloaded is unknown. Thus, expression (4-1) is used to estimate the travel distance for trailer i at door m as follows:

∑∑∑

=

s j n

jn im mn sij

im b (2d )x x

Distance Travel

This expression assumes trailer-at-a-time unloading is used. In addition, this expression assumes that for the last shipment on an origin trailer, the distance to travel from the correct destination trailer to a new origin trailer can be estimated by using the distance required to return to the same origin trailer that the employee was unloading. In reality, the forklift driver will not return to the same origin trailer after the last shipment, but instead will travel to the next origin trailer in their assignment. At this point in the solution approach, however, the next origin trailer is unknown, and the distance back to the original origin trailer is used to estimate the distance to the next origin trailer. This approximation approach is also used in the literature [34][35].

The estimate of travel distance is then converted into an estimate of travel time by assuming a constant travel speed. The travel speed approximation is 7.46 feet per second and was

determined through time studies at the Greensboro hub.

The final time components used to approximate the total time required to unload an origin trailer are the times to unload freight from an origin trailer and load freight onto a destination trailer. It is assumed that each handling unit is handled separately, so the total unload and load times are the number of handling units on an origin trailer multiplied by the average unload and load times respectfully. The average unload and load times are also taken from time studies conducted at the Greensboro hub (44.505 seconds for unloading from an origin trailer and 43.380 seconds for loading onto a destination trailer). Therefore, the total time estimate for origin trailer i at door m is determined by the total travel time estimate plus the total unload time estimate plus the total load time estimate:

∑∑∑

After an estimate of time required for each origin trailer has been established, the origin trailers are assigned to the workers in an attempt to balance the total time assigned to each worker. The total time assignment of each worker is the sum of times corresponding to the origin trailers they are assigned to. In this approach, the trailers are sorted in non-increasing order of time

requirement. The origin trailer with the longest time requirement is given to the worker with the shortest total time assignment. Any ties are broken arbitrarily. Once an origin trailer is assigned to a worker, the time estimate of the origin trailer is added to the total time assignment of the worker. The origin trailer is then designated as assigned. The next origin trailer is then assigned to the employee with the minimum total time assignment. This process continues until all origin trailers have been assigned to employees.

In evaluating the trailer assignment, it is assumed that each employee unloads trailers in the order the trailers were assigned to the employee. This results in employees unloading trailers in

descending order of time required per trailer. After all the trailer assignments are made, a better time estimate for each employee is calculated using expression (2-4). This time estimate

includes a more precise distance measure of the distance between trailers when a new origin trailer is assigned to a worker. For example, the estimate used to assign trailers to workers estimates the distance between the destination of the last shipment of an origin trailer and the first shipment of a new origin trailer as the distance from the destination trailer back to the same origin trailer. The final time estimate for each employee considers which actual origin trailer he or she will be traveling to next, instead of relying on an estimate of travel distance to next origin trailer. Figure 10 illustrates the balancing technique used to assign workers to origin trailers.

Estimate unload time for each

origin trailer

Select next trailer in list

Determine which employee has

shortest time assignment, break

ties arbitrarily

Assign trailer to employee with

shortest time assignment

Add unload time of newly assigned trailer to appropriate

employee

Are there more trailers to assign?

Yes

Calculate final time required for

each employee No Sort origin trailers in non-increasing

order of time required to unload

Select first trailer in list

Determine the sequence that each employee unloads the trailers

Figure 10. Trailer-at-a-Time Assignments

The time approach presented here is slightly different from the current trailer-at-a-time approach used during a hub operation. The current approach depends heavily on supervisor judgment and does not provide a structured, repeatable approach. This approach offers a way to balance the workload among dock employees. Although this approach does not exactly replicate the way trailer to worker assignments are made, the results of this approach are considered an estimate of performance of the current approach, since the employees are still unloading shipments trailer-at-a-time.