Consider a company that operates a fleet of cargo ships. The company wants to optimize its shipping routes and cargo loadings to maximize profits over a planning horizon of T periods. Each period t corresponds to a specific month, and the company can choose the routes and cargo loadings for each ship in each period.
The company needs more certainty in the form of unpredictable demand for cargo shipping and varying fuel prices. Specifically, the demand for cargo shipping and the fuel prices are modeled as random variables drawn from known probability distributions at the beginning of each period.
The company aims to maximize its expected profits over the planning horizon, subject to some constraints. These constraints include:
Capacity constraints: Each ship has a maximum cargo capacity, and the total cargo loaded on a ship in any period must not exceed this capacity. Demand constraints: The total demand for cargo shipping in each time must be satisfied. Budget constraints: The company has a fixed budget for fuel costs in each period, and the total fuel costs for all ships in that period must not exceed this budget.