An integral LP relaxation for a drayage problem

This paper investigates a drayage problem, where a fleet of trucks must ship container loads from a port to importers and from exporters to the same port, without separating trucks and containers during customer service. We present three formulations for this problem that are valid when each truck carries one container. For the third formulation, we also assume that the arc costs are equal for all trucks, and then we prove that its continuous relaxation admits integer optimal solutions by checking that its constraint matrix is totally unimodular. Under the same hypothesis on costs, even the continuous relaxations of the first two models are proved to admit an integer optimal solution. Finally, the third model is transformed into a circulation problem, that can be solved by efficient network algorithms.     

基于矩阵式遗传算法的进出口集装箱堆场箱位分配策略

为提高集装箱码头堆场系统的运作效率,本文针对集装箱码头进出口堆场的空间分配问题,建立了在“作业面”作业模式下以集卡水平运输距离最短为目标,考虑各箱位作业量均衡的集装箱箱位分配模型,对计划时段内的进出口箱箱位分配进行全局优化．采用矩阵式的实数编码方式的遗传算法对模型进行了求解,使用最优解保存策略保证了最终的优化结果．最后通过仿真算例,验证了本文所建立的箱位分配模型对优化堆场空间资源分配,提高进出口箱流转速度的适用性．     

An efficient mixed integer programming model for pairing containers in inland transportation based on the assignment of orders

The inland transportation takes a significant portion of the total cost that arises from intermodal transportation. In addition, there are many parties (shipping lines, haulage companies, customers) who share this operation as well as many restrictions that increase the complexity of this problem and make it NP-hard. Therefore, it is important to create an efficient strategy to manage this process in a way to ensure all parties are satisfied. This paper investigates the pairing of containers/orders in drayage transportation from the perspective of delivering paired containers on 40-ft truck and/or individual containers on 20-ft truck, between a single port and a list of customer locations. An assignment mixed integer linear programming model is formulated, which solves the problem of how to combine orders in delivery to save the total transportation cost when orders with both single and multiple destinations exist. In opposition to the traditional models relying on the vehicle routing problem with simultaneous pickups and deliveries and time windows formulation, this model falls into the assignment problem category which is more efficient to solve on large size instances. Another merit for the proposed model is that it can be implemented on different variants of the container drayage problem: import only, import–inland and import–inland–export. Results show that in all cases the pairing of containers yields less cost compared to the individual delivery and decreases empty tours. The proposed model can be solved to optimality efficiently (within half hour) for over 300 orders.     

A simulation-based genetic algorithm approach for reducing emissions from import container pick-up operation at container terminal

Emissions from idle truck engines are a main source of pollution at container terminals. In this study, we focus on reducing such emission from waiting trucks as well as the related crane operations with a new truck arrival control method that gives individual truck limited time slots for entry. We develop a method to optimize the time slot assignment for individual trucks, aiming at minimizing total emissions from trucks and cranes at import yards. The method applies discrete event simulation to estimate total truck waiting times and crane moving distance, and then applies a genetic algorithm to minimize the generated emissions from these trucks and cranes. The experiment result shows that the truck arrivals should be controlled based on the stacking of import containers, and that such control is necessary for reducing truck idling emissions at a congested container terminal.     

Alternative algorithms for the optimization of a simulation model of a multimodal container terminal

Multimodal container terminals (MMCTs) are very complex and consequently require synchronization and balancing of container transfers at each node. The problem being investigated is the minimization of ship delays at the port by considering handling and travelling time of containers from the time the ship arrives at port until all the containers from that ship leave the port. When dealing with export containers, the problem would be that of the handling and travelling time of the containers from when they first arrive at the port until the ship carrying the containers departs from the port. Owing to the dynamic nature of the environment, a large number of timely decisions have been reviewed in accordance with the changing conditions of the MMCTs. The model has been run and tested with a small-size problem using CPLEX. A more realistic model is extremely difficult to solve and is in fact proven to be computationally intractable (NP-hard). Metaheuristics have been developed to deal with the intractability so that near-optimal solutions could be obtained in reasonable time.     

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.     

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.     

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.     

A heuristic algorithm for the truckload and less-than-truckload problem

The delivery of goods from a warehouse to local customers is an important and practical problem of a logistics manager. In reality, we are facing the fluctuation of demand. When the total demand is greater than the whole capacity of owned trucks, the logistics managers may consider using an outsider carrier.Logistics managers can make a selection between a truckload (a private truck) and a less-than-truckload carrier (an outsider carrier). Selecting the right mode to transport a shipment may bring significant cost savings to the company.In this paper, we address the problem of routing a fixed number of trucks with limited capacity from a central warehouse to customers with known demand. The objective of this paper is developing a heuristic algorithm to route the private trucks and to make a selection of less-than-truckload carriers by minimizing a total cost function. Both the mathematical model and the heuristic algorithm are developed. Finally, some computational results and suggestions for future research are presented.     

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.     

不确定箱量下内河集装箱班轮航线动态配载决策

内河集装箱班轮运输中海关抽检可导致外贸箱箱量不断发生变化,班轮航线配载需要动态决策。基于滚动调度策略,将当前港口的配载决策按随机事件划分为多个阶段,以最小化班轮堆栈占用数量和相邻阶段间配载计划偏差为目标,构建单港口单阶段的配载决策模型,进而滚动实现班轮航线动态配载决策。基于大邻域搜索思想设计一种包含整数规划、破坏器与修复器的精确启发式算法,实现港口多阶段滚动配载。基于真实场景的算例研究表明,在优化堆栈占用数量方面,模型与算法之间差异不大,但在考虑相邻阶段间配载计划偏差时,算法的求解结果要优于模型。因此,模型与算法可用来辅助实现不确定箱量下内河集装箱班轮航线动态配载决策,且算法表现更优,可实现配载计划对不确定箱量的鲁棒吸收。     

基于贪婪禁忌搜索算法的垂岸式堆场出口箱装船翻箱研究

基于垂岸式自动化集装箱码头不同装船周期出口集装箱堆场多贝位混合堆存、场桥大车在贝位间频繁移动取箱装船特点,考虑装船发箱时场桥移动等操作时间及翻箱取箱次数对出口箱装船效率和连续性影响,建立多贝位出口箱装船堆场翻箱模型,提出两阶段贪婪禁忌搜索算法,将翻箱规则嵌入算法中,有效限制算法时间和解空间增长速度。通过算例,将提出的翻箱规则与现有常见翻箱规则进行对比,验证模型及算法的有效性与实用性。结果表明,提出的模型和算法可以在合理的求解时间内输出较优的翻箱方案,减少装船时场桥发箱作业时间,提高装船作业效率。     

A matheuristic for the truck and trailer routing problem

In the truck and trailer routing problems (TTRPs) a fleet of trucks and trailers serves a set of customers. Some customers with accessibility constraints must be served just by truck, while others can be served either by truck or by a complete vehicle (a truck pulling a trailer). We propose a simple, yet effective, two-phase matheuristic that uses the routes of the local optima of a hybrid GRASP × ILS as columns in a set-partitioning formulation of the TTRP. Using this matheuristic we solved both the classical TTRP with fixed fleet and the new variant with unlimited fleet. This matheuristic outperforms state-of-the-art methods both in terms of solution quality and computing time. While the best variant of the matheuristic found new best-known solutions for several test instances from the literature, the fastest variant of the matheuristic achieved results of comparable quality to those of all previous method from the literature with an average speed-up of at least 2.5.     

Allocation of empty containers between multi-ports

Owing to imbalances in international trade activities, shipping companies accumulate a large number of unnecessary empty containers in the import-dominant ports, whilst request a large number of empty containers in export-dominant ports. The logistics challenge to shipping companies is to better manage and control their containers, which consist of company-owned containers and leased containers. The multi-port empty container allocation problem is concerned with the allocation of empty containers from supply ports to demand ports. In this paper, optimal pairs of critical policies, (U, D) for one port, which are importing empty containers up to U when the number of empty containers in the port is less than U, or exporting empty containers down to D when the number of empty containers is larger than D, doing nothing otherwise, are adapted to multi-port case so that decision-makers can make decisions about allocating the right amounts of empty containers to the right ports at the right time. This allocation problem has been formulated and the heuristic methods are designed according to that the average cost using (u, d) policy at one port is convex in u and d. Furthermore, the examples show that, using the heuristic algorithm, the result in the inland line case is quite close to the lower bound, even the distance is not so close in the global line case.     

Decision support system for container terminal planning

In this paper we describe a decision support system for capacity planning of container terminals. Typical elements of a container terminal are a quay, cranes,a stack yard and trucks for transport of containers between the quay and the stack yard and vice versa. For each of these elements we can devise models to describe the performance. The decision support system combined a heuristic analysis of these models to a global model to study the interaction between the elements of a container terminal.     

Multiple Container Packing: A Case Study of Pipe Packing

While the problem of packing single containers and pallets has been thoroughly investigated very little attention has been given to the efficient packing of multiple container loads. Normally in practice a multiple container load is packed by a single container algorithm used in a greedy fashion. This paper introduces the issues involved in multiple container loading. It lays out three different strategies for solving the problem: sequential packing using a single container heuristic, pre-allocating items to the containers and choosing container loads using simultaneous packing models. The principal simultaneous models are pattern selection IP models. We present an application of packing pipes in shipping containers using two pattern selection IP models, a pattern selection heuristic, a sequential greedy algorithm and a pre-allocation method. The experimental results use randomly generated data sets. We discuss several useful insights into the methods and show that for this application the pattern selection methods perform best.     

Shipping Container Logistics and Allocation

A major shipping company in Hong Kong is faced with several logistical and allocation problems. It needs to find a better way to allocate empty containers that are transported from the Middle East to ports in the Far East, subject to vessel schedules and capacities. It needs to know what to do when the supply of empty containers is less than the demand, and it needs to determine the mix of container types that the company should maintain in the long run. To deal with these challenges, a simulation model of the shipping company's operational activities was developed. Heuristic search was employed to identify the policies that yield the lowest operating cost in terms of leasing, storage, pick-up, drop-off and other charges. What makes the problem difficult is that the forecasts of future export movement as well as the demand for empty containers change continually and the company is faced with the possibility of lost sales if containers are not available when requested by customers. This study provided insights that resulted in substantial savings to the shipping company while increasing customers' satisfaction.     

海运服务链中的运力定价和空箱调运责任研究

本文研究了单个承运商和两个货运代理在双向港口间提供往返货运服务的航运服务链。由于港口间货运需求的内在不平衡,货运公司在多港口间的空箱调运会产生巨大的空箱调运费用。分别构建了承运商承担和承运商与货运代理共同承担空箱调运的数学模型,通过数学模型和数值算例分析了不同市场条件下的空箱调运责任和运力定价策略。研究发现承运商和货运代理是否采用定价策略来平衡需求取决于双向港口间货运市场的潜在需求差异。同时,承运商与货运代理的空箱调运分摊为非此即彼策略,当空箱调运成本大于某阈值时,承运商独自承担空箱调运责任;反之,货运代理承担空箱调运责任。而且货运代理承担模式增加整个海运链的利润,但进一步加剧空箱的不平衡状况。     

A network flow model for the optimal allocation of both foldable and standard containers

This paper considers a multi-port and multi-period container planning problem of shipping companies that use both standard and foldable containers. A company must decide which number of empty containers of each type to purchase and reposition at each port within a defined period to minimize the total purchasing, repositioning, and storage costs.We develop a model to optimally allocate both foldable and standard containers. We show that a single commodity minimum cost network flow algorithm solves the problem by proving that a two commodity flow problem can be modeled as a single commodity flow problem.     

集装箱码头堆场翻箱与外集卡提箱顺序同步优化方法

针对集装箱码头提箱作业过程中,由于外集卡的提箱顺序与目标箱在堆场的堆存位置不匹配导致大量翻箱这一难题,以码头的作业成本和外集卡的延误成本之和最小为目标,建立堆场翻箱与外集卡提箱顺序同步优化模型,优化外集卡的提箱顺序、龙门吊的任务分配以及翻箱方案。设计基于动态规划的启发式算法求解模型,并利用算例对模型与算法的有效性进行了验证。结果表明:与目前码头普遍采用的提箱方式相比,通过调整外集卡提箱顺序并同时优化翻箱方案以及龙门吊的任务分配可以降低堆场翻箱率,减少龙门吊的移动成本,从而节省提箱作业的总成本。