Optimal operating strategy for a long-haul liner service route

This paper proposes an optimal operating strategy problem arising in liner shipping industry that aims to determine service frequency, containership fleet deployment plan, and sailing speed for a long-haul liner service route. The problem is formulated as a mixed-integer nonlinear programming model that cannot be solved efficiently by the existing solution algorithms. In view of some unique characteristics of the liner shipping operations, this paper proposes an efficient and exact branch-and-bound based ε-optimal algorithm. In particular, a mixed-integer nonlinear model is first developed for a given service frequency and ship type; two linearization techniques are subsequently presented to approximate this model with a mixed-integer linear program; and the branch-and-bound approach controls the approximation error below a specified tolerance. This paper further demonstrates that the branch-and-bound based ε-optimal algorithm obtains a globally optimal solution with the predetermined relative optimality tolerance ε in a finite number of iterations. The case study based on an existing long-haul liner service route shows the effectiveness and efficiency of the proposed solution 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.     

排放控制区限制下邮轮航线及速度优化

近年来,邮轮行业发展突飞猛进,但随之而来的航运污染问题也不容小觑。国际海事组织设立了排放控制区(Emission Control Area,简称ECA)以限制船舶硫排放,包括邮轮在内的所有船舶在ECA内均需使用昂贵的低硫油,这就使得船舶航行方案需要进行重新规划。本文提出了一个有到港时间限制的邮轮航线和速度优化模型,优化船舶在ECA内外的航线及速度,以最小化总燃油成本。同时引用西北大西洋沿岸一条代表性的邮轮航线,通过计算决策出合理的航行方案,并评估ECA对航运的影响,证明模型的有效性和实用性。     

Reducing fuel emissions by optimizing speed on shipping routes

Fuel consumption and emissions on a shipping route are typically a cubic function of speed. Given a shipping route consisting of a sequence of ports with a time window for the start of service, substantial savings can be achieved by optimizing the speed of each leg. This problem is cast as a non-linear continuous program, which can be solved by a non-linear programming solver. We propose an alternative solution methodology, in which the arrival times are discretized and the problem is solved as a shortest path problem on a directed acyclic graph. Extensive computational results confirm the superiority of the shortest path approach and the potential for fuel savings on shipping routes.     

Supply chain scheduling: Sequence coordination

A critical issue in supply chain management is coordinating the decisions made by decision makers at different stages, for example a supplier and one or several manufacturers. We model this issue by assuming that both the supplier and each manufacturer have an ideal schedule, determined by their own costs and constraints. An interchange cost is incurred by the supplier or a manufacturer whenever the relative order of two jobs in its actual schedule is different from that in its ideal schedule. An intermediate storage buffer is available to resequence the jobs between the two stages. We consider the problems of finding an optimal supplier's schedule, an optimal manufacturer's schedule, and optimal schedules for both. The objective functions we consider are the minimization of total interchange cost, and of total interchange plus buffer storage cost. We describe efficient algorithms for all the supplier's and manufacturers’ problems, as well as for a special case of the joint scheduling problem. The running time of these algorithms is polynomial in both the number of jobs and the number of manufacturers. Finally, we identify conditions under which cooperation between the supplier and a manufacturer reduces their total cost.     

基于可变航速的支线集装箱船舶调度优化模型与算法

随着航运市场的竞争不断加剧和集装箱船舶大型化的发展,越来越多的航运企业选择轴-辐式航运网络模式。支线船舶调度问题作为轴-辐式航运网络的重要组成部分受到研究者的高度关注。本文研究了可变航速和经济航速两种情境下的支线船舶调度问题,同时考虑枢纽港和喂给港的取送箱时间窗限制,以航运企业运营成本最小化为目标函数建立非线性混合整数规划模型。首先使用专业的规划求解器进行小规模算例的求解,验证了模型的准确性。同时运用改进的遗传算法对大规模支线船舶优化调度模型进行求解。为了提高求解效果,进一步设计了多智能体进化算法进行求解。数值结果表明,可变航速的运营成本低于经济航速的运营成本;在算法效率方面,改进遗传算法收敛速度较快,多智能体进化算法则可以提高求解精度。     

Mathematical expressions for the transit time of merchandise through a liner shipping network

Recent publications on the design of liner shipping networks are limited in their treatment of the level of service (LoS) experienced by shippers. We propose the use of inventory holding costs—a function of merchandise transit time—as a proxy for LoS. We assume the existence of a two-tier optimization model, where fleet deployment, vessel routing, and vessel speed are determined in the higher tier. Merchandise flows and transshipment quantities are determined in the lower tier. We partition the total merchandise transit time into time spent in open waters, time spent during port calls, and time spent dwelling in the terminal yard. Using the notions of service frequency and service phase, we develop mathematical expressions for the three aforementioned quantities within the lower tier of the optimization model. We arrive at a bilinear expression for overall inventory holding costs that is suitable for liner shipping network design.     

Impact analysis of maritime cabotage legislations on liner hub-and-spoke shipping network design

Maritime cabotage is a legislation published by a particular coastal country, which is used to conduct the cargo transportation between its two domestic ports. This paper proposes a two-phase mathematical programming model to formulate the liner hub-and-spoke shipping network design problem subject to the maritime cabotage legislations, i.e., the hub location and feeder allocation problem for phase I and the ship route design with ship fleet deployment problem for phase II. The problem in phase I is formulated as a mixed-integer linear programming model. By developing a hub port expanding technique, the problem in phase II is formulated as a vehicle routing problem with pickup and delivery. A Lagrangian relaxation based solution method is proposed to solve it. Numerical implementations based on the Asia–Europe–Oceania shipping services are carried out to account for the impact analysis of the maritime cabotage legislations on liner hub-and-spoke shipping network design problem.     

Static target search path planning optimization with heterogeneous agents

Disruptions in airline operations can result in infeasibilities in aircraft and passenger schedules. Airlines typically recover aircraft schedules and disruptions in passenger itineraries sequentially. However, passengers are severely affected by disruptions and recovery decisions. In this paper, we present a mathematical formulation for the integrated aircraft and passenger recovery problem that considers aircraft and passenger related costs simultaneously. Using the superimposition of aircraft and passenger itinerary networks, passengers are explicitly modeled in order to use realistic passenger related costs. In addition to the common routing recovery actions, we integrate several passenger recovery actions and cruise speed control in our solution approach. Cruise speed control is a very beneficial action for mitigating delays. On the other hand, it adds complexity to the problem due to the nonlinearity in fuel cost function. The problem is formulated as a mixed integer nonlinear programming (MINLP) model. We show that the problem can be reformulated as conic quadratic mixed integer programming (CQMIP) problem which can be solved with commercial optimization software such as IBM ILOG CPLEX. Our computational experiments have shown that we could handle several simultaneous disruptions optimally on a four-hub network of a major U.S. airline within less than a minute on the average. We conclude that proposed approach is able to find optimal tradeoff between operating and passenger-related costs in real time.     

Early detection of vessel delays using combined historical and real-time information

In ocean transportation, detecting vessel delays in advance or in real time is important for fourth-party logistics (4PL) in order to fulfill the expectations of customers and to help customers reduce delay costs. However, the early detection of vessel delays faces the challenges of numerous uncertainties, including weather conditions, port congestion, booking issues, and route selection. Recently, 4PLs have adopted advanced tracking technologies such as satellite-based automatic identification systems (S-AISs) that produce a vast amount of real-time vessel tracking information, thus providing new opportunities to enhance the early detection of vessel delays. This paper proposes a data-driven method for the early detection of vessel delays: in our new framework of refined case-based reasoning (CBR), real-time S-AIS vessel tracking data are utilized in combination with historical shipping data. The proposed method also provides a process of analyzing the causes of delays by matching the tracking patterns of real-time shipments with those of historical shipping data. Real data examples from a logistics company demonstrate the effectiveness of the proposed method.     

Distribution-free vessel deployment for liner shipping

One important problem faced by the liner shipping industry is the fleet deployment problem. In this problem, the number and type of vessels to be assigned to the various shipping routes need to be determined, in such a way that profit is maximized, while at the same time ensuring that (most of the time) sufficient vessel capacity exists to meet shipping demand. Thus far, the standard assumption has been that complete probability distributions can be readily specified to model the uncertainty in shipping demand. In this paper, it is argued that such distributions are hard, if not impossible, to obtain in practice. To relax this oftentimes restrictive assumption, a new distribution-free optimization model is proposed that only requires the specification of the mean, standard deviation and an upper bound on the shipping demand. The proposed model possesses a number of attractive properties: (1) It can be seen as a generalization of an existing variation of the liner fleet deployment model. (2) It remains a mixed integer linear program and (3) The model has a very intuitive interpretation. A numerical case study is provided to illustrate the model.     

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.     

Improving airline operational performance through schedule perturbation

Schedule development is typically the first phase of the airline planning process. We present a framework for perturbing scheduled departure and arrival times after a crew schedule has been found. We characterize perturbations that keep a schedule legal while not increasing the planned cost of the crew schedule. We show that when random delays occur in operations, the expected cost can be reduced and the on-time performance improved. Computational results are reported for two real fleets and a large number of crew schedules. AMS Classification: 90B06     

A model of JIT make-to-stock inventory with stochastic demand

We consider a firm that manages its internal manufacturing operations according to a just-in-time (JIT) system but maintains an inventory of finished goods as a buffer against random demands from external customers. We formulate a model in which finished goods are replenished by a small fixed quantity each time period. In the interest of schedule stability, the size of the replenishment quantity must remain fixed for a predetermined interval of time periods. We analyse the single-interval problem in depth, showing how to compute a cost-minimising value of the replenishment quantity for a given interval length, and characterising the optimal cost, inventory levels and service as functions of the interval length and initial inventory. The model displays significant cost and service penalties for schedule stability. A dynamic version of the problem is also formulated, and shown to be convex in nature with relatively easily computed optima.     

Computationally Efficient Solution of a Multiproduct,Two-Stage Distribution—Location Problem

A two-stage distribution planning problem, in which customers are to be served with different commodities from a number of plants, through a number of intermediate warehouses is addressed. The possible locations for the warehouses are given. For each location, there is an associated fixed cost for opening the warehouse concerned, as well as an operating cost and a maximum capacity. The demand of each customer for each commodity is known, as are the shipping costs from a plant to a possible warehouse and thereafter to a customer. It is required to choose the locations for opening warehouses and to find the shipping schedule such that the total cost is minimized. The problem is modelled as a mixed-integer programming problem and solved by branch and bound. The lower bounds are calculated through solving a minimum-cost, multicommodity network flow problem with capacity constraints. Results of extensive computational experiments are given.     

Scheduling rooted forests with communication delays

We show that a greedy algorithm for scheduling unit time jobs on two machines with unit communication delays produces an optimal schedule when the precedence constraints are given by a rooted forest. We also give a min/max relationship for the length of such a schedule. The min/max result (for forests and two machines) shows that the addition of unit communication delays increases the optimal schedule length by at most one.The author thanks Ivan Rival for bringing this problem to his attention. Partially supported by a grant from the Reidler Foundation.     

自由作业的供应链排序研究

研究一类集成工件加工和发送的供应链排序模型,即研究如何安排工件在自由作业机器上加工,把加工完毕的工件分批发送给下游客户,使得含生产排序费用和发送费用的目标函数最优.这里,分别取工件最大送到时间和平均送到时间为生产排序费用;而发送费用是由固定费用和与运输路径有关的变化费用组成.利用排序理论和动态规划方法,构造了自由作业供应链排序问题的多项式时间近似算法,并分析算法的性能比.     

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.