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

• Input:

  Yards	Forklift	Crane
  1	15	45
  2	55	60
  3	26	75
  4	9	50
  5	22	20
  6	19	10

  Johnson's rule is used to find the schedule that minimizes the total makespan.

  Johnson's rule = Select the Yard having the shortest processing time, if that is for Operation 1 (Forklift), then schedule the Yard first, if that is for Operation 2 (Crane), then schedule the Yard last. Yards which are scheduled, are removed from further consideration. Repeat the process until all Yards are scheduled.

  The shortest time is 9, of Yard 4 for Forklift. So, Yard 4 is scheduled the first.

  Of the remaining yards, the shortest time is 10, of Yard 6 for Crane. So, Yard 6 is scheduled the last.

  Of the remaining yards, the shortest time is 15, of Yard 1 for Forklift. So, Yard 1 is scheduled the second.

  Of the remaining yards, the shortest time is 20, of Yard 5 for Crane. So, Yard 5 is scheduled the second last.

  Of the remaining yards, the shortest time is 26, of Yard 3 for Forklift. So, Yard 3 is scheduled the third.

  Remaining Yard 2 is scheduled the fourth.

  Resulting sequence is: 4,1,3,2,5,6

  Original Makespan (without using Johnson's rule) is : 285

  

  Minimum makespan after scheduling by Johnson's rule is: 269

  

  Gantt Chart is as follows:

  

  Makespan = 269