A branch‐and‐cut algorithm for the quay crane scheduling problem in a container terminal

Abstract

Abstract:The quay crane scheduling problem consists of determining a sequence of unloading and loading movements for cranes assigned to a vessel in order to minimize the vessel completion time as well as the crane idle times. Idle times originate from interferences between cranes since these roll on the same rails and a minimum safety distance must be maintained between them. The productivity of container terminals is often measured in terms of the time necessary to load and unload vessels by quay cranes, which are the most important and expensive equipment used in ports. We formulate the quay crane scheduling problem as a vehicle routing problem with side constraints, including precedence relationships between vertices. For small size instances our formulation can be solved by CPLEX. For larger ones we have developed a branch-and-cut algorithm incorporating several families of valid inequalities, which exploit the precedence constraints between vertices.

Combined quay crane assignment and quay crane scheduling with crane inter-vessel movement and non-interference constraints

“…They used Branchand-Bound (B&B) in conjunction with the Greedy Randomized Adaptive Search Procedure (GRASP) (Feo, 1995), to overcome the difficulties of B&B on its own. (Moccia et al, 2006), formulated QCSP as a vehicle routing problem with additional constraints like the precedence relationships between tasks. CPLEX was used to solve small scale instances and the Branch-and-Cut (B&C) algorithm to solve large scale instances.…”

Crane Scheduling in Steelmaking Plants via Priority Propagation and a Memetic Algorithm

“…Since the serial number of tasks is decided according to the non-decreasing order of the release times, all tasks allocated to the same crane can be performed in accordance with the serial number. Taking the code {2,1,3,2,2,1,2,3,3,1,2} as an example, when 11 tasks are assigned to 3 cranes, task (2,6,10) are allocated to crane 1, tasks (1,4,5,7,11) to crane 2, and task (3,8,9) to crane 3. The key to obtain a feasible solution is to decode the chromosome with priority propagation based collision avoidance mechanism.…”

“…For crane scheduling problem, the cranes can be divided into several sub-sets due to the special circumstances: quay cranes [1][2][3][4][5], yard cranes [6][7][8][9][10], hoist cranes [11][12][13] and cranes in steel-making continuous-casting process [14] and so on. For quay cranes, Kim and Park [1] formulated a mixed integer linear programming model.…”

“…For quay cranes, Kim and Park [1] formulated a mixed integer linear programming model. Moccia et al [2] revised the model proposed by Kim and Park (2004) and proposed a branch and cut…”

A reclaimer scheduling problem arising in coal stockyard management

“…A greedy randomized adaptive search procedure (GRASP) is developed to handle instances where the branch-and-bound algorithm takes too much time. Moccia et al (2006) have strengthened the MIP formulation of Kim and Park (2004) by deriving sets of valid inequalities. They propose a branch-and-cut algorithm to solve the problem to optimality.…”