A Branch-and-Price-and-Cut Method for Ship Scheduling with Limited Risk

Traditional ship-scheduling models ignore uncertainty, even in highly volatile markets. We present a set-packing model that limits risk using a quadratic variance constraint. After generating first-order linear constraints to represent the variance constraint, we develop a branch-and-price-and-cut algorithm for medium-sized ship-scheduling problems. Computational results are provided, and extensions are discussed. Risk is prevalent in today’s global economy. Threats of terrorism, depleted oil reserves, and war are examples of new sources of instability. Incomes in the United States have become more volatile, bankruptcies are more frequent, and households are shouldering more uncertainty (Gosselin, 2004). As economic fluctuation increases, logistics planners need to find methods of managing risk. We modify here a traditional set-packing problem for ship scheduling by adding a quadratic constraint to limit the variance of profit. The new model is formulated as max cx s.t. Ax ≤ 1 xQx ≤ d x ∈ {0, 1},