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?

4. Single Machine Assembly Scheduling Problem with random delay

4.3 Schedule Repair Heuristics

In many production situations, it is not desirable to reschedule all the non-delayed jobs along with the delayed jobs. Instead, the required changes should be performed in such a way that the entire system is affected as little as possible. This process is termed schedule repair in this chapter. To repair an unfinished schedule which has delayed orders, its valid parts (or the remaining unaffected schedule) should be re-used as far as possible, and only the parts touched by the disturbance are adjusted. At the beginning of assembly, the schedule obtained using BSSH is executed. Suppose the delay is caused by machine breakdown starting from time t and the assembly resumes after time length DU. Jobs that are to be released between t and t+DU in original schedule are only influenced by the disturbance. In line with the concept of schedule repair, the schedule after time t+DU is valid part and should be kept unchanged. The schedule of the influenced jobs between time t and t+DU should be adjusted.

The schedule generated using BSSH methodology will have idle times between job groups, during which the assembly does not work at its full capacity. The idle time can be utilized to process the delayed jobs. Therefore, a heuristic to repair the disturbed schedule is proposed is this section. The main motive is to insert the disturbed job into the idle time spans so that the assembly utilization is improved at the advantage of minimizing the delay penalties for the jobs. If still some jobs cannot be inserted into the idle time span, they are appended after the last job of the final schedule. Figure 2 illustrates this idea in detail. 

Figure 2. Illustration of schedule repair heuristic 

In Figure 2, the x axial denotes time. The blocks denote the scheduled jobs. During time t to t+DU, the jobs predetermined to be processed are denoted using shaded blocks. The delayed jobs are to be inserted into the idle times among the job groups in the BSSH schedule as denoted by the arc in the figure using the following heuristic. 

The schedule repair heuristic (SRH): 

1. Sequence the jobs scheduled between t and t+D U by Longest-Processing Time (LPT) first rule.
2. Insert disturbed jobs into the idle time spans between order groups. Suppose there are N_{d} disturbed jobs and are sequenced by LPT rule. Let the BSSH schedule has S idle time spans from time t+D U till the end of the planning period. The detailed steps are:

2.1. i=1, j=1

2.2. \text{If Length} [\operatorname{span}(I)] > \operatorname{ProcessingTime}[j o b(j)], insert job j into span i . Else, go to 2.5.

2.3. \text{Length} [\operatorname{span}(i)]=\operatorname{Length}[\operatorname{span}(i)] - \text{ProcessingTime[job (j)]}.

2.4. j=j+1. If j > N_{d}, go to 2.7. Else, go to 2.2.

2.5. i=i+1 . If i \leq S, go to 2.2. Else, go to 2.6.

2.6. Append the remaining N_{d}-j jobs after the last job of the BSSH schedule.

2.7. Stop.

By computational experiments, it is shown that SRH can achieve good results. For detailed content, it can be referred to Li et al.