Quay Length Optimization Using a Stochastic Knapsack Model

Vessels arriving at a port wait for an available berth at the quay to load/unload. The ability to provide a berthing space for a vessel without delay is a major managerial concern. Thus, there is an optimal resource-allocation problem, in which the resource is the length of the quay allocated dynamically over the vessels according to an arrival process. Unfortunately, quay length cannot be changed arbitrarily because of the construction and operating costs, which are increasing functions of the quay length. This paper’s concern is the determination of the optimal quay length, and this problem is formulated using a variant of the stochastic knapsack problem. This method is primarily intended to estimate the length of a single quay. After introducing the mathematical formulation for the model, it is applied to a number of case studies built based on the real data obtained for several ports. Next, a sensitivity analysis of the model is presented with a wide range of arrival and service parameters drawn from real-life data. The paper concludes with a practical approach to estimating the quay lengths roughly.