Synchronizing Schedules for Transportation

Read this article. It discusses synchronizing transportation schedules. Because the logistics segment of the cycle is a large-scale effort, the waiting and queues are magnified. How many different modes of transportation do you think are required to make a product from raw material to the customer's hand?

3. Single Machine Assembly Scheduling Problem

3.2 Backward Synchronized Scheduling Heuristic (BSSH)

Steps of BSSH are the same as FSSH except for step 4. Backward scheduling is used in step 4 in BSSH instead of forward scheduling in FSSH. 

Backward scheduling is reverse of the forward scheduling approach and schedules are defined on a reverse time frame. The start time and completion time of the same job in forward scheduling mode is related to the completion time and start time of the same job in backward scheduling mode. In other words, the completion time of each job is determined first. The release time (or start time) for each job is then obtained using the determined completion time. To arrive at a schedule after using backward scheduling approach, the processing sequence is reversed, and the schedule time frame is reversed back to forward time frame.

The backward scheduling considers inserted idle times between processing of orders. Forward scheduling is a straightforward method that schedules jobs one by one from the beginning time of the planning period. The main objective is to make sure that each job can meet its due date. The forward scheduling methodology presented in the previous section does not minimize AWT effectively. This is overcome by adopting a backward approach that inserts idle times between order groups. 

The last flight's departure time determines the completion time for the last order to be scheduled in the assembly in the planning period. To minimize order earliness before transportation, the favorable completion time for each order is their corresponding flight departure time. Hence, within each group, orders are scheduled one by one without inserted idle time in backward direction from the order group's due-date. Once the completion time for the last order to be scheduled in each group is determined, the release times for the preceding orders is calculated by subtracting its processing times from the release time of the succeeding orders. Idle times are inserted only between order groups. When the release time of the first order in the succeeding group is later than the current order group's due date, idle time is inserted between the two groups. Thus the last job of the current order group is scheduled to complete at the corresponding flight departure time. 

The pseudo code description of the backward scheduling logic is presented below:

If (job i is the last job in flight j) then
   If (flight j is the last flight) then
 Release time(job i, flight j) =Departure time(flight j)–
  Processing time(job i, flight j)
     If (Release time (the first job, fight j+1) is earlier than
        Departure time(flight j)) then
 Release time (job i, flight j)=Release time (the first job,
   flight j+1) – Processing time(job i, flight j)
 Release time (job i, flight j) =Departure time (flight j) –         
    Processing time (job i, flight j)
          End if      
     End if
 Release time (job i, flight j) =Release time (job i+1, flight j) –
   Processing time (job i, flight j)
End if  

Computational results indicate that BSSH outperforms FSSH in terms of AWT. For detailed results of the comparison, it can be referred to Li et al.