Fleet sizing with time and voyage-chartered vessels for an oil shipping company under demand uncertainty

The fleet sizing problem is one of the main concerns for an industry shipping company under various uncertainty of market conditions. This paper addresses the problem in a single period with uncertain shipment demand for an oil shipping company, who transports the refined petroleum products among multiple origin–destination (OD) pairs. Besides the self-owned vessels, the time-chartered and voyage-chartered vessels are considered by the company as two types of rental vessels from the potential outsourcing market. The company aims to determine the numbers of vessels with different capacity levels and different rental types, deploy them among all OD pairs to minimize the total expected cost including the rent costs of time-chartered and voyage-chartered vessels and the holding cost of time-chartered vessels. Several stochastic programming models are proposed to investigate three scenarios: the aggregative shipment demand and an available fleet with continuously separable vessel capacity in the outsourcing market, the aggregative shipment demand and an available fleet with inseparable vessel capacity, and the OD shipment demand matrix and an available fleet with inseparable vessel capacity. Assuming economies of scale in rental duration, vessel capacity, and voyage distance, we conduct theoretical analysis to deduce the necessary conditions and solution properties for optimal resolutions to the fleet sizing problems. The real-world numerical examples based on China National Petroleum Corporation are adopted to illustrate the proposed models and theoretical results.