A Mathematical Programming Approach for a Vessel Scheduling-Transportation Problem with Multiple Sources and Destinations, and Normal Daily Demand Distributions

Abstract

The principal focus of this research effort is to investigate a stochastic vessel scheduling problem to transport a product (crude oil) from multiple sources to various destinations. In this vessel operation, a vessel is fully loaded at a source and is fully unloaded at a destination. In this research effort, we focus on the case when the daily demands at the destinations are normally distributed, based on which different penalties are imposed on the shortages/excesses in daily storage levels at the destinations. The anticipated total cost of such fleet operation is composed of the total vessels' operational expenses, expected total penalties resulting from violating specified lower and upper bounds at the destinations, and chartering expenses. We aim to employ a mathematical modeling approach to simultaneously optimize the fleet schedules and maintain desirable daily storage levels to meet the stochastic demand requirements at the destinations with acceptable reliability levels. The proposed problem is formulated as a stochastic optimization model to minimize the expected total cost of the studied vessel operation. Our computational results are presented for a set of test problems to a) demonstrate the efficacy of the proposed modeling approach and b) examine the effect of the variations in demands and the probabilities of satisfying demands on the overall vessel operation and cost components.