Abstract:The quay crane scheduling problem consists of determining a sequence of unloading and loading movements for cranes assigned to a vessel in order to minimize the vessel completion time as well as the crane idle times. Idle times originate from interferences between cranes since these roll on the same rails and a minimum safety distance must be maintained between them. The productivity of container terminals is often measured in terms of the time necessary to load and unload vessels by quay cranes, which are the most important and expensive equipment used in ports. We formulate the quay crane scheduling problem as a vehicle routing problem with side constraints, including precedence relationships between vertices. For small size instances our formulation can be solved by CPLEX. For larger ones we have developed a branch-and-cut algorithm incorporating several families of valid inequalities, which exploit the precedence constraints between vertices.

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We introduce a new approach to minimizing a function defined as the pointwise maximum over finitely many convex real functions (next referred to as the “component functions”), with the aim of working on the basis of “incomplete knowledge” of the objective function. A descent algorithm is proposed, which need not require at the current point the evaluation of the actual value of the objective function, namely, of all the component functions, thus extending to min-max problems the philosophy of the incremental approaches, widely adopted in the nonlinear least squares literature. Given the nonsmooth nature of the problem, we resort to the well-established machinery of “bundle methods.” We provide global convergence analysis of our method, and in addition, we study a subgradient aggregation scheme aimed at simplifying the problem of finding a tentative step. This paper is completed by the numerical results obtained on a set of standard test problems.

The paper describes a model for the optimal management of periodic deliveries of a given commodity. The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling and routing policies of the vehicles in order to minimize over the planning horizon the maximum number of vehicles simultaneously employed, i.e., the fleet size. Heuristic algorithms are proposed and computational experience is reported.

We describe an extension of the classical cutting plane algorithm to tackle the unconstrained minimization of a nonconvex, not necessarily differentiable function of several variables. The method is based on the construction of both a lower and an upper polyhedral approximation to the objective function and it is related to the use of the concept of proximal trajectory. Convergence to a stationary point is proved for locally Lipschitz functions.