Question

The port operations staff in Izmir Port tries to make loading schedule of a ship that will arrive on Monday. There are 6 container yards in the port. The containers first must be picked up from each yard to shipment lane by a dedicated forklift. Secondly containers must be loaded on board from shipment lane by a specific crane. The required times (in minutes) for each operation is as follows; Yards Forklift Crane 1 15 45 2 55 60 3 26 75 4 9 50 5 22 20 6 19 10 Determine how the loading of container at each yard should be scheduled in order to minimize the total makespan. Please draw the Gantt chart to show the optimal schedule and calculate the makespan.

Answer 1

One of the ways to solve this is to use Johnson’s rule. It is a heuristic method of assigning n number of jobs in 2 machines when the task of machine 1 should be followed by machine 2.

The approach to this is to assign the smallest available time into its respective machine. Next, provide the second smallest task to its respective machine.

Step 1. Yards 4 has the smallest task. That is the forklift task and thus we will assign it to the forklift end.

Forklift

4

Crane

Step 2. Yards 6 has the second smallest task. That is by crane and thus it will be on the crane’s end

Forklift

4

6

Crane

Step 3. Yards 1 has the next smallest task by forklift. It’s assigned on the forklift end

Forklift

4

1

6

Crane

Step 4. Yards 5 is assigned to crane.

Forklift

4

1

5

6

Crane

Step 5. Yards 3 is assigned to forklift.

Forklift

4

1

3

5

6

Crane

Step 6. Yards 2 is remaining and is assigned in the 4^th position.

Forklift

4

1

3

2

5

6

Crane

This makes the sequence as 413256 in the order of forklift – crane operation.

The gantt chart is shown below.

The makespan is 269