Storage yards at container terminals serve as temporary buffers for inbound and outbound containers. Rubber tyred gantry cranes (RTGCs) are the most frequently used equipment in yards for container handling. The efficiency of yard operations heavily depends on the productivity of these RTGCs. As the workload distribution in the yard changes over time, dynamic deployment of RTGCs among storage blocks (container stacking areas) is an important issue of terminal operations management. This paper addresses the crane deployment problem. Given the forecasted workload of each block in each period of a day, the objective is to find the times and routes of crane movements among blocks so that the total delayed workload in the yard is minimized. The problem is formulated as a mixed integer programming (MIP) model and solved by Lagrangean relaxation. To improve the performance of this approach, we augment the Lagrangean relaxation model by adding additional constraints and modify the solution procedure accordingly. Computational experiments show that the modified Lagrangean relaxation method generates excellent solutions in short time.

Dynamic crane deployment in container storage yards

This paper describes experiences with mixed integer linear programming (MILP) based approaches on the short-term hydro scheduling (STHS) function. The STHS is used to determine the optimal or near-optimal schedules for the dispatchable hydro units in a hydro-dominant system for a user-definable study period at each time step while respecting all system and hydraulic constraints. The problem can be modeled in detail for a hydro system that contains both conventional and pumped-storage units. Discrete and dynamic constraints such as unit startup/shutdown and minimum-up/minimum-down time limits are also included in the model for hydro unit commitment (HUC). The STHS problem is solved with a state-of-the-art package which includes an algebraic modeling language and a MILP solver. The usefulness of the proposed solution algorithm is illustrated by testing the problem with actual hydraulic system data. Numerical experiences show that the solution technique is computationally efficient, simple, and suitable for decision support of short-term hydro operations planning. In addition, the proposed approaches can be easily extended for scheduling applications in a deregulated environment.

Experiences with Mixed Integer Linear Programming-Based Approaches in Short-Term Hydro Scheduling

The short-term unit commitment (UC) problem in hydrothermal power generation is a large-scale, mixed-integer nonlinear program, which is difficult to solve efficiently, especially for large-scale instances. It is possible to approximate the nonlinear objective function of the problem by means of piecewise-linear functions, so that UC can be approximated by an mixed-integer linear program (MILP); applying the available efficient general-purpose MILP solvers to the resulting formulations, good quality solutions can be obtained in a relatively short amount of time. We build on this approach, presenting a novel way to approximating the nonlinear objective function based on a recently developed class of valid inequalities for the problem, called ldquoperspective cuts.rdquo At least for many realistic instances of a general basic formulation of UC, an MILP-based heuristic obtains comparable or slightly better solutions in less time when employing the new approach rather than the standard piecewise linearizations, while being not more difficult to implement and use. Furthermore, ldquodynamicrdquo formulations, whereby the approximation is iteratively improved, provide even better results if the approximation is appropriately controlled.

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Tighter Approximated MILP Formulations for Unit Commitment Problems

Tighter approximated MILP formulations for Unit Commitment Problems

Fast evolutionary programming techniques are applied for the solution of a short-term hydrothermal scheduling problem. Evolutionary programming (EP)-based algorithms with Gaussian and other mutation techniques have been developed and tested on a multi-reservoir cascaded hydroelectric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results show that all of the EP algorithms are capable of finding very nearly global solutions within a reasonable time but an EP algorithm with better of Gaussian and Cauchy mutations appears to be the best amongst all EPs in terms of convergence speed, solution time, and minimum cost.

Fast Evolutionary Progranuning Techniques for Short-Term Hydrothermal Scheduling

In this paper, a mixed-integer hydroelectric power model for short-term generation planning is presented, The advantage of this model is that the schedules only include points with good efficiency The planning problem is decomposed into a subproblem for each hydroelectric power plant In order to obtain smooth schedules, the model includes start-up costs for hydro aggregates The main mathematical methods used in this work are Lagrange relaxation, dynamic programming and network programming The model is illustrated by a numerical example from a part of the Swedish power system

D. Sjelvgren

Papers

Mixed-integer programming applied to short-term planning of a hydro-thermal system