Routing and scheduling in project shipping

Tramp shipping companies are committed to transport a set of contracted cargoes and try to derive additional revenue from carrying optional spot cargoes. Here, we present a real life ship routing and scheduling problem for a shipping company operating in project shipping, a special segment of tramp shipping. This segment differs from more traditional tramp segments, as the cargoes are usually transported on a one-time basis. Because of the special nature of the cargoes, complicating requirements regarding stowage onboard the ships and cargo coupling must be considered while determining routes and schedules for the ships in the fleet. A mathematical model is presented and a tabu search heuristic is proposed to solve the problem. Computational results show that the tabu search heuristic provides optimal or near-optimal solutions in a reasonable amount of time, and that it can give significant improvements to manual planning for the shipping company.     

A tabu search heuristic for ship routing and scheduling

The purpose of this paper is to solve a planning problem faced by many shipping companies dealing with the transport of bulk products. These shipping companies are committed to carrying some contract cargoes and will try to derive additional revenue from optional spot cargoes. An efficient tabu search algorithm has been developed to ensure quick decision support for the planners. The solutions generated by the tabu search heuristic are compared with those produced by a previously published multi-start local search heuristic. Computational results show that the tabu search heuristic yields optimal or near-optimal solutions to real-life instances within reasonable time. For large and tigthly constrained cases, the tabu search heuristic provides much better solutions than the multi-start local search heuristic. A version of the tabu search heuristic will be integrated as an improved solver in a prototype decision support system used by several shipping companies.     

Ship routing and scheduling with flexible cargo sizes

Here, we describe a real planning problem in the tramp shipping industry. A tramp shipping company may have a certain amount of contract cargoes that it is committed to carry, and tries to maximize the profit from optional cargoes. For real long-term contracts, the sizes of the cargoes are flexible. However, in previous research within tramp ship routing, the cargo quantities are regarded as fixed. We present an MP-model of the problem and a set partitioning approach to solve the multi-ship pickup and delivery problem with time windows and flexible cargo sizes. The columns are generated a priori and the most profitable ship schedule for each cargo set–ship combination is included in the set partitioning problem. We have tested the method on several real-life cases, and the results show the potential economical effects for the tramp shipping companies by utilizing flexible cargo sizes when generating the schedules.     

A dual-response forwarding approach for containerizing air cargoes under uncertainty,based on stochastic mixed 0-1 programming

This paper proposes a dual-response forwarding approach for renting air containers and simultaneously determining how cargoes are distributed into the containers under uncertain information. Containers have to be booked in advance to obtain a discount rental rate from airlines, as urgent requirement or cancellation of containers on the day of shipping will incur a heavy penalty. We firstly formulate a mixed 0-1 integer model to determine the booking types and quantities of containers for the deterministic problem under accurate information. We then formulate a stochastic mixed 0-1 model to structure a dual-response forwarding system for the uncertain problem where accurate information is not available when booking. The first-stage response is to determine the booking types and quantities of containers. The second-stage response is to prepare for different scenarios that might occur on the day of shipping, including the types and quantities of containers required or returned for each scenario, and also the corresponding cargo loading plan. Computational results show that the stochastic model can provide a cost-efficient, flexible and responsive cargo forwarding system.     

A heuristic approach to stowing general cargo into platform supply vessels

This paper addresses a practical problem encountered in the oil industry, related to the supplying of general cargo to offshore rigs and production units. For a given route assigned to a supply vessel we seek to determine the optimal two-dimensional positioning of deck cargoes such that the overall profit is maximized, while ensuring that several safety and operational constraints are respected. In terms of mathematical modelling, the resulting problem can be seen as a rich variation of the two-dimensional knapsack problem, since some cargoes may wait for a later trip. Furthermore, given that the trip may serve many offshore units and that a substantial number of items must also return from these units, the problem becomes even more complex and can be viewed as a pickup and delivery allocation problem. We propose a probabilistic constructive procedure combined with a local search heuristic to solve this problem. We also report the results of computational experiments with randomly generated instances. These results evidence that our proposed heuristic can effectively help ship planners when dealing with such large-scale allocation problems, with many operational constraints.     

Modelling of containerized air cargo forwarding problems under uncertainty

This paper examines air container renting and cargo loading problems experienced by freight forwarding companies. Containers have to be booked in advance, in order to obtain discounted rental rates from airlines; renting or returning containers on the day of shipping will incur a heavy penalty. We first propose a mixed-integer model for the certain problem, in which shipment information is known with certainty, when booking. We then present a two-stage recourse model to handle the uncertainty problem, in which accurate shipment information cannot be obtained when booking, and all cargoes have to be shipped without delay. The first-stage decision is made at the booking stage, to book specific numbers of different types of containers. The second-stage decision is made on the day of shipping, depending on the extent to which the uncertainty has been realized. The decisions include number of additional containers of different types that are required to be rented, or the number of containers to be returned, under the scenario that might occur on the day of shipping. We then extend the recourse model into a robust model for dealing with the situation in which cargoes are allowed to be shipped later. The robust model provides a quantitative method to measure the trade-off between risk and cost. A series of experiments demonstrate the effectiveness of the robust model in dealing with risk and uncertainty.     

A combined ship scheduling and allocation problem

We present a bulk ship scheduling problem that is a combined multi-ship pickup and delivery problem with time windows (m-PDPTW) and multi-allocation problem. In contrast to other ship scheduling problems found in the literature, each ship in the fleet is equipped with a flexible cargo hold that can be partitioned into several smaller holds in a given number of ways. Therefore, multiple products can be carried simultaneously by the same ship. The scheduling of the ships constitutes the m-PDPTW, while the partition of the ships' flexible cargo holds and the allocation of cargoes to the smaller holds make the multi-allocation problem. A set partitioning approach consisting of two phases is proposed for the combined ship scheduling and allocation problem. In the first phase, a number of candidate schedules (including allocation of cargoes to the ships' cargo holds) is generated for each ship. In the second phase, we minimise transportation costs by solving a set partitioning problem where the columns are the candidate schedules generated in phase one. The computational results show that the proposed approach works, and optimal solutions are obtained on several cases of a real ship planning problem.     

A heuristic for sea-freight container selection,cargo allocation and cargo orientation

A model is proposed to generate solutions for container selection, for the allocation of cargo to containers, and for cargo orientation within a container. The model is in the form of a mixed integer program with the objective of minimizing the total shipping cost. The practical requirements of loading priority and weight distribution along the main dimension of the container are incorporated into the model. A heuristic solution strategy is proposed and used to control the computation time by pre-setting the search increments. Three case examples are presented. The first and third examples show that the proposed model can produce a better solution than the manual schedulers. The second example is taken from the literature and is compared with the solution generated by the proposed model, demonstrating that the practical considerations incorporated into the model do not necessarily lead to increased shipping costs.     

Methods for strategic liner shipping network design

In this paper the combined fleet-design, ship-scheduling and cargo-routing problem with limited availability of ships in liner shipping is considered. A composite solution approach is proposed in which the ports are first aggregated into port clusters to reduce the problem size. When the cargo flows are disaggregated, a feeder service network is introduced to ship the cargo within a port cluster. The solution method is tested on a problem instance containing 58 ports on the Asia–Europe trade lane of Maersk. The best obtained profit gives an improvement of more than 10% compared to the reference network based on the Maersk network.     

Automating the planning of container loading for Atlas Copco: Coping with real-life stacking and stability constraints

The Atlas Copco^☆ distribution center in Allen, TX, supplies spare parts and consumables to mining and construction companies across the world. For some customers, packages are shipped in sea containers. Planning how to load the containers is difficult due to several factors: heterogeneity of the packages with respect to size, weight, stackability, positioning and orientation; the set of packages differs vastly between shipments; it is crucial to avoid cargo damage. Load plan quality is ultimately judged by shipping operators.This container loading problem is thus rich with respect to practical considerations. These are posed by the operators and include cargo and container stability as well as stacking and positioning constraints. To avoid cargo damage, the stacking restrictions are modeled in detail. For solving the problem, we developed a two-level metaheuristic approach and implemented it in a decision support system. The upper level is a genetic algorithm which tunes the objective function for a lower level greedy-type constructive placement heuristic, to optimize the quality of the load plan obtained.The decision support system shows load plans on the forklift laptops and has been used for over two years. Management has recognized benefits including reduction of labour usage, lead time, and cargo damage risk.     

A single-resource revenue management problem with random resource consumptions

We study a single-resource multi-class revenue management problem where the resource consumption for each class is random and only revealed at departure. The model is motivated by cargo revenue management problems in the airline and other shipping industries. We study how random resource consumption distribution affects the optimal expected profit and identify a preference acceptance order on classes. For a special case where the resource consumption for each class follows the same distribution, we fully characterize the optimal control policy. We then propose two easily computable heuristics: (i) a class-independent heuristic through parameter scaling, and (ii) a decomposition heuristic that decomposes the dynamic programming formulation into a collection of one-dimensional problems. We conduct extensive numerical experiments to investigate the performance of the two heuristics and compared them with several widely studied heuristic policies. Our results show that both heuristics work very well, with class-independent heuristic slightly better between the two. In particular, they consistently outperform heuristics that ignore demand and/or resource consumption uncertainty. Our results demonstrate the importance of considering random resource consumption as another problem dimension in revenue management applications.     

面向靠桥率及道口冲突率的航班-机位指派问题优化模型及其启发式算法研究

在给定航班时刻表条件下,对于进出港航班的机位分配,除了必须满足航班、飞机和机位之间的技术性要求之外,还要考虑尽量提高整个机场的机位利用率,且方便旅客出入港及时、安全和便捷.文章以飞机机型、所属航空公司、客运/货运航班、国内/国际航班等匹配条件为约束条件,以航班-机位分配完成率、靠桥率、道口非冲突率为目标,建立了一个航班...     

A multi-commodity, capacitated pickup and delivery problem: The single and two-vehicle cases

We explore dynamic programming solutions for a multi-commodity, capacitated pickup and delivery problem. Cargo flows are given by an origin/destination matrix which is not necessarily symmetric. This problem is a generalization of several known pickup and delivery problems, as regards both problem structure and objective function. Solution approaches are developed for the single-vehicle and two-vehicle cases. The fact that for each cargo that goes from a node i to another node j there may be a cargo going in the opposite direction provides the motivation for the two-vehicle case, because one may conceivably consider solutions where no cargoes that travel in opposite directions between node pairs are carried by the same vehicle. Yet, it is shown that such scenarios are generally sub-optimal. As expected, the computational effort of the single vehicle algorithm is exponential in the number of cargoes. For the two-vehicle case, said effort is of an order of magnitude that is not higher than that of the single-vehicle case. Some rudimentary examples are presented or both the single-vehicle and two-vehicle cases so as to better illustrate the method.     

Routing,ship size,and sailing frequency decision-making for a maritime hub-and-spoke container network

This study formulates a two-objective model to determine the optimal liner routing, ship size, and sailing frequency for container carriers by minimizing shipping costs and inventory costs. First, shipping and inventory cost functions are formulated using an analytical method. Then, based on a trade-off between shipping costs and inventory costs, Pareto optimal solutions of the two-objective model are determined. Not only can the optimal ship size and sailing frequency be determined for any route, but also the routing decision on whether to route containers through a hub or directly to their destination can be made in objective value space. Finally, the theoretical findings are applied to a case study, with highly reasonable results. The results show that the optimal routing, ship size, and sailing frequency with respect to each level of inventory costs and shipping costs can be determined using the proposed model. The optimal routing decision tends to be shipping the cargo through a hub as the hub charge is decreased or its efficiency improved. In addition, the proposed model not only provides a tool to analyze the trade-off between shipping costs and inventory costs, but it also provides flexibility on the decision-making for container carriers.     

The multiple container loading cost minimization problem

In the shipping and transportation industry, there are several types of standard containers with different dimensions and different associated costs. In this paper, we examine the multiple container loading cost minimization problem (MCLCMP), where the objective is to load products of various types into containers of various sizes so as to minimize the total cost. We transform the MCLCMP into an extended set cover problem that is formulated using linear integer programming and solve it with a heuristic to generate columns. Experiments on standard bin-packing instances show our approach is superior to prior approaches. Additionally, since the optimal solutions for existing test data is unknown, we propose a technique to generate test data with known optimal solutions for MCLCMP.     

Algorithms for common due-date assignment and sequencing on a single machine with sequence-dependent setup times

This paper focuses on the single machine sequencing and common due-date assignment problem for the objective of minimizing the sum of the penalties associated with earliness, tardiness and due-date assignment. Unlike the previous research articles on this class of scheduling problem, we consider sequence-dependent setup times that make the problem much more difficult. To solve the problem, a branch and bound algorithm, which incorporates the method to obtain lower and upper bounds as well as a dominance property to reduce the search space, is suggested that gives the optimal solutions for small-sized instances. Heuristic algorithms are suggested to obtain solutions for large-sized problems within a reasonable computation time. The performances of both the optimal and heuristic algorithms, in computational experiments on randomly generated test instances, are reported.     

Modeling formulation and a new heuristic for the railroad blocking problem

The railroad blocking problem is an important issue at the tactical level of railroad freight transportation. This problem consists of determining paths between the origins and destinations of each shipment to minimize the operating and user costs while satisfying the railroad supply and demand restrictions. A mixed-integer program (MIP) is developed to find the optimal paths, and a new heuristic is developed to solve the proposed model. This heuristic decomposes the model into two sub-problems of manageable size and then provides feasible solutions. We discuss the performance of the proposed heuristic for a set of instances with up to 90 stations. A comparison with the CPLEX MIP solver shows that the heuristic gives the exact solution for 10 out of 15 instances. For the remaining instances, the heuristic obtained solutions within a tolerance of 0.03–0.84%. Furthermore, compared with the CPLEX MIP solver, the heuristic reduced the run time by an average of 85% for all 15 instances. Finally, we present the computational results of the heuristic applied to Iranian railroads.     

A branch-and-price approach to the feeder network design problem

In this paper we consider the problem of designing a container liner shipping feeder network. The designer has to choose which port to serve during many rotations that start and end at a central hub. Many operational characteristics are considered, such as variable leg-by-leg speeds and cargo transit times. Realistic instances are generated from the LinerLib benchmark suite. The problem is solved with a branch-and-price algorithm, which can solve most instances to optimality within one hour. The results also provide insights on the cost structure and desirable features of optimal routes. These insights were obtained by means of an analysis where scenarios are generated varying internal and external conditions, such as fuel costs and port demands.     

A Lagrangian relaxation-based heuristic for the vehicle routing with full container load

We address a problem of vehicle routing that arises in picking up and delivering full container load from/to an intermodal terminal. The substantial cost and time savings are expected by efficient linkage between pickup and delivery tasks, if the time of tasks and the suitability of containers for cargo allow. As this problem is NP-hard, we develop a subgradient heuristic based on a Lagrangian relaxation which enables us to identify a near optimal solution. The heuristic consists of two sub-problems: the classical assignment problem and the generalized assignment problem. As generalized assignment problem is also NP-hard, we employ an efficient solution procedure for a bin packing based problem, which replaces the generalized assignment problem. The heuristic procedure is tested on a wide variety of problem examples. The test results demonstrate that the procedure developed here can efficiently solve large instances of the problem.     

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.