A crane scheduling method for port container terminals

Abstract

This paper discusses the problem of scheduling quay cranes (QCs), the most important equipment in port terminals. A mixed-integer programming model, which considers various constraints related to the operation of QCs, was formulated. This study proposes a branch and bound (B & B) method to obtain the optimal solution of the QC scheduling problem and a heuristic search algorithm, called greedy randomized adaptive search procedure (GRASP), to overcome the computational difficulty of the B & B method. The performance of GRASP is compared with that of the B & B method.

Introduction

The productivity of a container terminal can be measured in terms of the productivity of two types of operations. One type is ship operations, in which containers are discharged from and loaded onto a ship. The other is receiving and delivery operations, in which containers are transferred to and from outside trucks. The planning process of ship operations consists of berth planning, quay crane (QC) scheduling (in practice, called work scheduling), and discharge and load sequencing. During the process of berth planning, the berthing time and the berthing position of a containership on a wharf are determined. A QC schedule specifies the service sequence of bays in a ship by each QC and the time schedule for the services. Input data for QC scheduling consists of a stowage plan of a ship, the ready time of each QC, and a yard map that shows the storage locations of containers bound for the ship. Finally, during discharge and load sequencing, the discharge and load sequence of individual containers are determined based on a QC schedule. This paper addresses the QC scheduling problem, which is pertinent to the second stage of ship operation planning.

Several studies have been conducted to improve the efficiency of ship operations in port container terminals. The subject of these studies includes the following: berth planning (Brown et al., 1995; Lim, 1998), in which berthing positions and berthing times of vessel are determined; load sequencing (Cho, 1982; Cojeen and Dyke, 1976; Gifford, 1981), in which the loading sequence of individual containers are determined; and transtainer routing (Kim and Kim, 1999; Narasimhan and Palekar, 2002), in which the travel route of each transtainer and the number of outbound containers to pick up at each yard-bay are determined. In addition, Cheung et al. (2002) and Zhang et al. (2002) proposed methods for deploying yard cranes, methods in which the times and routes of yard crane movements among blocks are determined.

Daganzo (1989) was the first who discussed the QC scheduling problem. He suggested an algorithm for determining the number of cranes to assign to ship-bays of multiple vessels. Peterkofsky and Daganzo (1990) also provided an algorithm for determining the departure times of multiple vessels and the number of cranes to assign to individual holds of vessels at a specific time segment. They also attempted to minimize the delay costs. The studies by Daganzo (1989) and Peterkofsky and Daganzo (1990) assumed one task per ship-bay, a task which needs crane operations during a specific length of time, and did not consider the interference among QCs or precedence relationships among tasks. In contrast, this study assumes that there may be multiple tasks involved in a ship-bay, and thus this study divides a task into smaller sizes, compared to Daganzo (1989) and Peterkofsky and Daganzo (1990).

This study further assumes that the berthing and departure times of a vessel and the operation starting times of QCs assigned to that vessel are given. This study attempts to determine the schedule of each QC assigned to a vessel, with the goal of completing all of the ship operations of a vessel as rapidly as possible.

The next section introduces the ship operation and defines the QC scheduling problem. Section 3 provides a mathematical formulation for the QC scheduling problem. Section 4 proposes a branch and bound (B & B) algorithm for solving the mathematical formulation. Section 5 applies the heuristic algorithm GRASP to the QC scheduling problem. Section 6 discusses the results of a numerical experiment, and Section 7 provides a conclusion.