2 . 10 A simulation based approach to optimize berth throughput

Berth ~hed.ulin9 is a critical functi?" at marine container terminals and determining the best berth schedule depends on several factors including the type and function of the port, size of the port, location, nearby competition, and type of contractual ~greement between the terminal and the carriers. In this paper we formulate the berth scheduling problem as a bi-objective mixed· Integer problem with the objective to ma)(lmlZe customer satisfaction and reliability of the berth schedule under the assumption that vessel handling times are stochastic parameters following a discrete and known probability distribution. A combination of an exact a~or~hm, a Genetic Algorithms based heuristic and a simulation post·Pareto analysis is proposed as the solution approach to the resulting problem. Based on a number of experiments ~ is concluded that the proposed berth scheduling policy outperforms the berth scheduling policy where reliability is not considered . 1.0 INTRODUCTION In this paper, we deal with the discrete space and dynamic vessel arrival berth scheduling problem (DDBSP), which can be formulated as the machine scheduling problem (1, 2]. The DDBSP received and continues to receive increased attention from the research community as it is a problem that marine container terminal operators deal with on a daily basis [3]. In this paper we formulate the DDBSP as a biobjective mixed-integer problem with the objective to maximize berth throughput and maximize the reliability of the berth schedule, under the assumption that the vessel handling times are stochastic parameters with a known discrete probability distributions. Berth throughput is taken under consideration by the minimization of the total service time for all the vessels. In order to maximize the reliability of the berth schedule, a risk measure is proposed that is dependent on the vessel-to-berth assignment and the distributions of the vessels' handling times. The remainder of this paper is organized as follows: The next section describes the problem and motivation for considering stochasticity in the vessel handling times, and presents the model formulation. The third section presents the solution algorithm and the fourth section a small number of numerical examples to evaluate the proposed approach. The final section summarizes findings and suggest future research directions. 2.0 MODEL FORMULATION As has been supported by the literature [4) the competitiveness of a container terminal depends on various factors. It has also been well established by researchers and practitioners that decisions in container terminals are interrelated [5]. More specifically , decisions regarding the SSP are closely related and affect(ed) by the decisions regarding the scheduling and productivity of the quay cranes and the internal transport movers [3, 5]. Combining these problems into one single problem cannot be handled efficiently and the number of assumptions adopted (when researchers tried to partially combine them) portrays an approximation of reality (5]. For that reason the majority of research, to our knowledge, has focused in isolating each problem and assumed deterministic inputs from its related counterpart problems (for example in the berth scheduling problem the assignment of the quay cranes on each vessel is assumed as an input). To that end, the majority of SSP models have not accounted for the stochastic nature of the vessel handling times; a stochasticity that https://ntrs.nasa.gov/search.jsp?R=2011001212