Yard crane scheduling in port container terminals

Yard cranes are the most popular container handling equipment for loading containers onto or unloading containers from trucks in container yards of land scarce port container terminals. However, such equipment is bulky, and very often generates bottlenecks in the container flow in a terminal because of their slow operations. Hence, it is essential to develop good yard crane work schedules to ensure a high terminal throughput. This paper studies the problem of scheduling a yard crane to perform a given set of loading/unloading jobs with different ready times. The objective is to minimize the sum of job waiting times. A branch and bound algorithm is proposed to solve the scheduling problem optimally. Efficient and effective algorithms are proposed to find lower bounds and upper bounds. The performance of the proposed branch and bound algorithm is evaluated by a set of test problems generated based on real life data. The results show that the algorithm can find the optimal sequence for most problems of realistic sizes.     

A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.     

线性比式和规划问题的输出空间分支定界算法

本文旨在针对线性比式和规划这一NP-Hard非线性规划问题提出新的全局优化算法.首先,通过引入p个辅助变量把原问题等价的转化为一个非线性规划问题,这个非线性规划问题的目标函数是乘积和的形式并给原问题增加了p个新的非线性约束,再通过构造凸凹包络的技巧对等价问题的目标函数和约束条件进行相应的线性放缩,构成等价问题的一个下界线性松弛规划问题,从而提出了一个求解原问题的分支定界算法,并证明了算法的收敛性.最后,通过数值结果比较表明所提出的算法是可行有效的.     

A local branching-based algorithm for the quay crane scheduling problem under unidirectional schedules

The quay crane scheduling problem (QCSP) is at the basis of a major logistic process in maritime container terminals: the process of discharging/loading containers from/on berthed vessels. Several groups of containers, laying in one or more stowage portions of a containership, have to be assigned to multiple cranes and discharge/loading operations have to be optimally sequenced, under some complicating constraints imposed by the practical working rules of quay cranes. The QCSP has been the object of a great deal of research work since the last decade and it is focused in this paper, with the aim of consolidating a promising solution approach based upon the combination of specialized branch & bound (B&B) and heuristic algorithms. A cost-effective solution technique that incorporates the local branching method within a refined B&B algorithm is proposed and its effectiveness is assessed by numerical comparisons against the latest algorithm available in literature.     

A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem

We propose a column generation based exact decomposition algorithm for the problem of scheduling n jobs with an unrestrictively large common due date on m identical parallel machines to minimize total weighted earliness and tardiness. We first formulate the problem as an integer program, then reformulate it, using Dantzig–Wolfe decomposition, as a set partitioning problem with side constraints. Based on this set partitioning formulation, a branch and bound exact solution algorithm is developed for the problem. In the branch and bound tree, each node is the linear relaxation problem of a set partitioning problem with side constraints. This linear relaxation problem is solved by column generation approach where columns represent partial schedules on single machines and are generated by solving two single machine subproblems. Our computational results show that this decomposition algorithm is capable of solving problems with up to 60 jobs in reasonable cpu time.     

Stowage planning in maritime container transportation

We consider a stowage-planning problem of arranging containers on a container ship in the maritime transportation system. Since containers are accessible only from the top of the stack, temporary unloading and reloading of containers, called shifting, is unavoidable if a container required to be unloaded at the current port is stacked under containers to be unloaded at later ports on the route of the ship. The objective of the stowage planning problem is to minimize the time required for shifting and crane movements on a tour of a container ship while maintaining the stability of the ship. For the problem, we develop a heuristic solution method in which the problem is divided into two subproblems, one for assigning container groups into the holds and one for determining a loading pattern of containers assigned to each hold. The former subproblem is solved by a greedy heuristic based on the transportation simplex method, while the latter is solved by a tree search method. These two subproblems are solved iteratively using information obtained from solutions of each other. To see the performance of the suggested algorithm, computational tests are performed on problem instances generated based on information obtained from an ocean container liner. Results show that the suggested algorithm works better than existing algorithms.     

DCA for solving the scheduling of lifting vehicle in an automated port container terminal

The container was introduced as a universal carrier for various goods in the 1960s and soon became a standard worldwide transportation. The competitiveness of a container seaport is marked by different success factors, particularly the time in port for ships. Operational problems of container terminals is divided into several problems, such as assignment of vessels, loading/unloading and storage of the containers, quay cranes scheduling cite, planning yard cranes cite and assignment of storage containers cite. In this work, the study will focus on piloting yard trucks. Two different types of vehicles can be used, namely automated guided vehicles (AGVs) and lifting vehicles (LVs). An AGV receives a container from a quay crane and transports containers over fixed path. LVs are capable of lifting a container from the ground by itself. The model that we consider is formulated as a mixed integer programming problem, and the difficulty arises when the number of binary variables increases. There are a lot of algorithms designed for mixed integer programming problem such as Branch and Bound method, cutting plane algorithm, . . . By using an exact penalty technique we treat this problem as a DC program in the context of continuous optimization. Further, we combine the DCA with the classical Branch and Bound method for finding global solutions.     

Using concave envelopes to globally solve the nonlinear sum of ratios problem

This article presents a branch and bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm works by globally solving a sum of ratios problem that is equivalent to problem (P). In the algorithm, upper bounds are computed by maximizing concave envelopes of a sum of ratios function over intersections of the feasible region of the equivalent problem with rectangular sets. The rectangular sets are systematically subdivided as the branch and bound search proceeds. Two versions of the algorithm, with convergence results, are presented. Computational advantages of these algorithms are indicated, and some computational results are given that were obtained by globally solving some sample problems with one of these algorithms.     

A linear programming-based optimization algorithm for solving nonlinear programming problems

In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush–Kuhn–Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.     

An interval branch and bound algorithm for bound constrained optimization problems

In this paper, we propose modifications to a prototypical branch and bound algorithm for nonlinear optimization so that the algorithm efficiently handles constrained problems with constant bound constraints. The modifications involve treating subregions of the boundary identically to interior regions during the branch and bound process, but using reduced gradients for the interval Newton method. The modifications also involve preconditioners for the interval Gauss-Seidel method which are optimal in the sense that their application selectively gives a coordinate bound of minimum width, a coordinate bound whose left endpoint is as large as possible, or a coordinate bound whose right endpoint is as small as possible. We give experimental results on a selection of problems with different properties.     

Modelling and Optimal Receding-horizon Control of Maritime Container Terminals

The main objective of this paper consists in modelling, optimizing, and controlling container transfer operations inside intermodal terminals. More specifically, maritime container terminals are here considered, involving three kinds of transportation modes, i.e., maritime, rail, and road transport. Generally speaking, an intermodal port terminal can be seen as a system of container flows with two interfaces, towards the hinterland and towards the sea, respectively. Moreover, inside a terminal, unloading operations of inbound containers, container storage, and loading operations of outbound containers are carried out. A simple model for maritime container terminals is proposed in this paper. In the model, a system of queues represents the standing of containers and their movements inside the terminal. The dynamic evolutions of these queues are described by discrete-time equations, where the state variables represent the queue lengths and the control variables take into account the utilization of terminal resources such as load/unload handling rates. On the basis of the proposed model, an optimization problem is defined that consists in minimizing the transfer delays of containers in the terminal. The problem is stated as an optimal control problem whose solution is sought by adopting a receding-horizon strategy.      

A polyhedral approach to a production planning problem

Production planning in manufacturing industries is concerned with the determination of the production quantities (lot sizes) of some items over a time horizon, in order to satisfy the demand with minimum cost, subject to some production constraints. In general, production planning problems become harder when different types of constraints are present, such as capacity constraints, minimum lot sizes, changeover times, among others. Models incorporating some of these constraints yield, in general, NP-hard problems. We consider a single-machine, multi-item lot-sizing problem, with those difficult characteristics. There is a natural mixed integer programming formulation for this problem. However, the bounds given by linear relaxation are in general weak, so solving this problem by LP based branch and bound is inefficient. In order to improve the LP bounds, we strengthen the formulation by adding cutting planes. Several families of valid inequalities for the set of feasible solutions are derived, and the corresponding separation problems are addressed. The result is a branch and cut algorithm, which is able to solve some real life instances with 5 items and up to 36 periods. This revised version was published online in June 2006 with corrections to the Cover Date.     

An extended branch and bound algorithm for linear bilevel programming

For linear bilevel programming, the branch and bound algorithm is the most successful algorithm to deal with the complementary constraints arising from Kuhn–Tucker conditions. However, one principle challenge is that it could not well handle a linear bilevel programming problem when the constraint functions at the upper-level are of arbitrary linear form. This paper proposes an extended branch and bound algorithm to solve this problem. The results have demonstrated that the extended branch and bound algorithm can solve a wider class of linear bilevel problems can than current capabilities permit.     

Global optimization for the sum of generalized polynomial fractional functions

In this paper, a branch and bound approach is proposed for global optimization problem (P) of the sum of generalized polynomial fractional functions under generalized polynomial constraints, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. By utilizing an equivalent problem and some linear underestimating approximations, a linear relaxation programming problem of the equivalent form is obtained. Consequently, the initial non-convex nonlinear problem (P) is reduced to a sequence of linear programming problems through successively refining the feasible region of linear relaxation problem. The proposed algorithm is convergent to the global minimum of the primal problem by means of the solutions to a series of linear programming problems. Numerical results show that the proposed algorithm is feasible and can successfully be used to solve the present problem (P).     

Nonlinear integer programming for optimal allocation in stratified sampling

A stratified random sampling plan is one in which the elements of the population are first divided into nonoverlapping groups, and then a simple random sample is selected from each group. In this paper, we focus on determining the optimal sample size of each group. We show that various versions of this problem can be transformed into a particular nonlinear program with a convex objective function, a single linear constraint, and bounded variables. Two branch and bound algorithms are presented for solving the problem. The first algorithm solves the transformed subproblems in the branch and bound tree using a variable pegging procedure. The second algorithm solves the subproblems by performing a search to identify the optimal Lagrange multiplier of the single constraint. We also present linearization and dynamic programming methods that can be used for solving the stratified sampling problem. Computational testing indicates that the pegging branch and bound algorithm is fastest for some classes of problems, and the linearization method is fastest for other classes of problems.     

A distributed exact algorithm for the multiple resource constrained sequencing problem

Sequencing problems arise in the context of process scheduling both in isolation and as subproblems for general scenarios. Such sequencing problems can often be posed as an extension of the Traveling Salesman Problem. We present an exact parallel branch and bound algorithm for solving the Multiple Resource Constrained Traveling Salesman Problem (MRCTSP), which provides a platform for addressing a variety of process sequencing problems. The algorithm is based on a linear programming relaxation that incorporates two families of inequalities via cutting plane techniques. Computational results show that the lower bounds provided by this method are strong for the types of problem generators that we considered as well as for some industrially derived sequencing instances. The branch and bound algorithm is parallelized using the processor workshop model on a network of workstations connected via Ethernet. Results are presented for instances with up to 75 cities, 3 resource constraints, and 8 workstations.     

A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique

This paper is concerned with the development of an algorithm to solve continuous polynomial programming problems for which the objective function and the constraints are specified polynomials. A linear programming relaxation is derived for the problem based on a Reformulation Linearization Technique (RLT), which generates nonlinear (polynomial) implied constraints to be included in the original problem, and subsequently linearizes the resulting problem by defining new variables, one for each distinct polynomial term. This construct is then used to obtain lower bounds in the context of a proposed branch and bound scheme, which is proven to converge to a global optimal solution. A numerical example is presented to illustrate the proposed algorithm.     

An optimization-based heuristic for the robotic cell problem

This study investigates an optimization-based heuristic for the robotic cell problem. This problem arises in automated cells and is a complex flow shop problem with a single transportation robot and a blocking constraint. We propose an approximate decomposition algorithm. The proposed approach breaks the problem into two scheduling problems that are solved sequentially: a flow shop problem with additional constraints (blocking and transportation times) and a single machine problem with precedence constraints, time lags, and setup times. For each of these problems, we propose an exact branch-and-bound algorithm. Also, we describe a genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that the proposed optimization-based approach delivers high-quality solutions and consistently outperforms the genetic algorithm. However, the genetic algorithm delivers reasonably good solutions while requiring significantly shorter CPU times.     

沿海港口集装箱空箱调运策略优化模型

我国沿海港口进出口箱分布非常不均衡,由此产生了集装箱空箱调运现象,合理的空箱调运策略能够有效地降低航运成本。本文研究了沿海港口间的空箱调运问题。在传统确定目的港策略的基础上,提出了一种新的空箱调运策略,不确定目的港策略。针对两种不同调运策略分别建立了以总调运费用最小为目标的规划模型。并以中国沿海港口空箱调运为例,运用遗传算法,在不同的空箱供需情况下,对两种调运策略费用进行了优化求解。结果表明,供需平衡模式下,固定目的港策略略有优势;在供需不平衡模式中,不确定目的港策略优势更加明显。此研究能够为港口间空箱调运提供辅助决策。     

A Parallel Interior Point Method and Its Application to Facility Location Problems

We present a parallel interior point algorithm to solve block structured linear programs. This algorithm can solve block diagonal linear programs with both side constraints (common rows) and side variables (common columns). The performance of the algorithm is investigated on uncapacitated, capacitated and stochastic facility location problems. The facility location problems are formulated as mixed integer linear programs. Each subproblem of the branch and bound phase of the MIP is solved using the parallel interior point method. We compare the total time taken by the parallel interior point method with the simplex method to solve the complete problems, as well as the various costs of reoptimisation of the non-root nodes of the branch and bound. Computational results on two parallel computers (Fujitsu AP1000 and IBM SP2) are also presented in this paper.