双需求集货送货一体化车辆路径问题的数学模型及算法

本文研究了具有总时间和车容量约束的双需求集货送货一体化车辆路径问题,在综合考虑运输费用和车辆出行固定费用的前提下,建立了该问题的整数线性规划模型,并分别给出了求解该模型的精确算法和基于节约准则的启发式算法。最后通过一个具体实例验证了算法的有效性。     

A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.     

考虑空重箱转换的港口集装箱甩挂运输问题研究

针对港口堆场与内陆腹地客户之间的空重集装箱运输问题,本文结合甩挂运输的特点将客户的进出港需求拆分为相互关联的空箱和重箱任务,实现单个决策期内运输系统中集装箱的状态转换与回收工作。状态转换受集装箱货物装卸时间影响,因此需要合理调度牵引车路线,以满足前置任务约束。针对此类问题的特点,本文建立了空重箱运输任务整合的整数规划模型,并设计了基于集群选择的改进蚁群算法进行求解。最后,通过不同规模的仿真算例与现有数学模型及优化算法对比结果可知,本文所提出的改进蚁群算法在此类问题的最优解搜索中具有良好的稳定性和求解效率。     

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.     

Optimizing a multi-stage production/inventory system by DC programming based approaches

This paper deals with optimizing the cost of set up, transportation and inventory of a multi-stage production system in presence of bottleneck. The considered optimization model is a mixed integer nonlinear program. We propose two methods based on DC (Difference of Convex) programming and DCA (DC Algorithm)—an innovative approach in nonconvex programming framework. The mixed integer nonlinear problem is first reformulated as a DC program and then DCA is developed to solve the resulting problem. In order to globally solve the problem, we combine DCA with a Branch and Bound algorithm (BB-DCA). A convex minorant of the objective function is introduced. DCA is used to compute upper bounds while lower bounds are calculated from a convex relaxation problem. The numerical results compared with those of COUENNE (http://www.coin-or.org/download/binary/Couenne/), a solver for mixed integer nonconvex programming, show the rapidity and the ?-globality of DCA in almost cases, as well as the efficiency of the combined DCA-Branch and Bound algorithm. We also propose a simple heuristic algorithm which is proved by experimental results to be better than an existing heuristic in the literature for this problem.     

基于两阶段启发式算法的物流配送选址-路径问题研究

为了解决配送中心选址与带时间窗的多中心车辆路径优化组合决策问题,利用双层规划法建立了配送中心选址与车辆路径安排的多目标整数规划模型,针对该模型的特点,采用两阶段启发式算法进行了求解。首先,通过基于聚集度的启发式算法对客户进行分类,确定了备选配送中心的服务范围;然后,基于双层规划法,以配送中心选址成本最小作为上层规划目标,以车辆配送成本最小作为下层规划目标,建立了多目标整数规划模型;最后,利用改进的蚁群算法进行了求解。通过分析实例数据和Barreto Benchmark算例的实验结果,验证了该模型的有效性和可行性。     

A heuristic approach to a single stage assembly problem with transportation allocation

Determining assembly scheduling and transportation allocation are two practical problems that industries face, such as the electronics and health products industries. Problems associated with assembly scheduling mainly focus on how to determine the orders’ processing sequence on the assembly line in order to minimize the waiting times before they are flown to their destinations. Problems associated with transportation allocation arise in the system of assigning processed orders to transport modes with the purpose of minimizing penalties from earliness and tardiness. To minimize overall delivery costs, businesses should decide on assembly scheduling and transportation allocation decision simultaneously. However, since simultaneously making these two decisions is not an easy task, most of the works done on them usually deal with these two problems separately. Apart from previous works, this paper establishes a mixed integer programming model that deals with these problems simultaneously. Due to the computational complexity of the problem, this paper develops a hybrid heuristic algorithm to solve this problem, and we evaluate the performance of the presented heuristic algorithm with the well-known GAMS/BARON and Lingo commercial software, which tests the heuristic algorithm on randomly-generated problems. The presented heuristic algorithm is shown to perform well compared with well-known commercial software.     

Short-term liner ship fleet planning with container transshipment and uncertain container shipment demand

This paper proposes a short-term liner ship fleet planning problem by taking into account container transshipment and uncertain container shipment demand. Given a liner shipping service network comprising a number of ship routes, the problem is to determine the numbers and types of ships required in the fleet and assign each of these ships to a particular ship route to maximize the expected value of the total profit over a short-term planning horizon. These decisions have to be made prior to knowing the exact container shipment demand, which is affected by some unpredictable and uncontrollable factors. This paper thus formulates this realistic short-term planning problem as a two-stage stochastic integer programming model. A solution algorithm, integrating the sample average approximation with a dual decomposition and Lagrangian relaxation approach, is then proposed. Finally, a numerical example is used to evaluate the performance of the proposed model and solution algorithm.     

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.     

带固定轴线成本的轴辐式网络设计问题

带固定轴线成本的轴辐式网络设计问题广泛应用于第三方物流、邮政和航空运输等领域. 现有研究主要考虑了枢纽站的节点成本, 本研究则强调合并运输的固定轴线成本. 固定轴线成本的必要性在于：轴辐式网络中的轴线运输需要借助更大型的运输工具, 因此必须支付固定成本. 建立了该问题的混合整数规划模型, 探讨了最优解特征, 并构造了求解问题的拉格朗日松驰算法, 实验显示算法具有非常好的求解效率与求解质量. 同时, 还讨论了一个重要的扩展问题：增加O-D流的绕道约束, 绕道约束常常应用于快递运输和应急物流等领域. 在局部修改原算法的基础上提供了扩展问题的求解方案.     

An algebraic geometry algorithm for scheduling in presence of setups and correlated demands

We study here a problem of schedulingn job types onm parallel machines, when setups are required and the demands for the products are correlated random variables. We model this problem as a chance constrained integer program.Methods of solution currently available—in integer programming and stochastic programming—are not sufficient to solve this model exactly. We develop and introduce here a new approach, based on a geometric interpretation of some recent results in Gröbner basis theory, to provide a solution method applicable to a general class of chance constrained integer programming problems.Out algorithm is conceptually simple and easy to implement. Starting from a (possibly) infeasible solution, we move from one lattice point to another in a monotone manner regularly querying a membership oracle for feasibility until the optimal solution is found. We illustrate this methodology by solving a problem based on a real system.Corresponding author.     

铁路客运网络列车开行方案优化模型的列生成算法

列车开行方案的设计是铁路旅客运输组织规划中的一个重要环节。本文首先给出了一个综合考虑铁路旅客运输的经济效益和公共服务性的优化模型,以铁路旅客运输的公共效益最大化为目标,对整个铁路客运网络上不同始发-终到和不同停站方式的列车开行方案进行优化。然后提出了一个求解此模型的启发式列生成算法,该算法与标准列生成算法相比,可以减少迭代次数并缩短收敛时间。最后给出一组利用随机生成的网络和需求进行求解的算例,验证本算法可以在较短时间内求解较大规模的铁路网络列车开行方案优化问题,并能有效缩小问题规模。     

A mathematical model of inter-terminal transportation

We present a novel integer programming model for analyzing inter-terminal transportation (ITT) in new and expanding sea ports. ITT is the movement of containers between terminals (sea, rail or otherwise) within a port. ITT represents a significant source of delay for containers being transshipped, which costs ports money and affects a port’s reputation. Our model assists ports in analyzing the impact of new infrastructure, the placement of terminals, and ITT vehicle investments. We provide analysis of ITT at two ports, the port of Hamburg, Germany and the Maasvlakte 1 & 2 area of the port of Rotterdam, The Netherlands, in which we solve a vehicle flow combined with a multi-commodity container flow on a congestion based time–space graph to optimality. We introduce a two-step solution procedure that computes a relaxation of the overall ITT problem in order to find solutions faster. Our graph contains special structures to model the long term loading and unloading of vehicles, and our model is general enough to model a number of important real-world aspects of ITT, such as traffic congestion, penalized late container delivery, multiple ITT transportation modes, and port infrastructure modifications. We show that our model can scale to real-world sizes and provide ports with important information for their long term decision making.     

Beam search heuristic to solve stochastic integer problems under probabilistic constraints

This paper proposes a Beam Search heuristic strategy to solve stochastic integer programming problems under probabilistic constraints. Beam Search is an adaptation of the classical Branch and Bound method in which at any level of the search tree only the most promising nodes are kept for further exploration, whereas the remaining are pruned out permanently. The proposed algorithm has been compared with the Branch and Bound method. The numerical results collected on the probabilistic set covering problem show that the Beam Search technique is very efficient and appears to be a promising tool to solve difficult stochastic integer problems under probabilistic constraints.     

Management of periodic demands in distribution systems

The problem of the optimal scheduling of periodic demands for a given facility or commodity is presented and some properties of an integer programming model are discussed. Algorithms (both of implicit enumeration type and heuristic) are also given.     

考虑泊位疏浚的连续型泊位和动态岸桥联合调度

针对集装箱码头泊位需要定期维护的实际特征,研究了泊位疏浚情况下连续型泊位和动态岸桥联合调度问题。首先,建立了一个以船舶周转时间最小为目标的整数线性规划模型;其次,针对问题特性设计了三种启发式算法。为了分析泊位疏浚对码头工作的影响并验证模型正确性和算法有效性,分别对未考虑泊位疏浚和考虑泊位疏浚两种调度情形,进行了小规模与大规模问题输入的多组测试。三种算法在小规模输入上均取得了相同于CPLEX的精确解,从而验证了算法的有效性;进一步通过对比分析这些算法在大规模输入中的运行结果,验证其有效性能。     

Integrated scheduling of crane handling and truck transportation in a maritime container terminal

This paper studies the interactions between crane handling and truck transportation in a maritime container terminal by addressing them simultaneously. Yard trucks are shared among different ships, which helps to reduce empty truck trips in the terminal area. The problem is formulated as a constraint programming model and a three-stage algorithm is developed. At the first stage, crane schedules are generated by a heuristic method. At the second stage, the multiple-truck routing problem is solved based on the precedence relations of the transportation tasks derived from the first stage. At the last stage a complete solution is constructed by using a disjunctive graph. The three procedures are linked by an iterative structure, which facilitates the search for a good solution. The computational results indicate that the three-stage algorithm is effective for finding high-quality solutions and can efficiently solve large problems.     

带覆盖需求约束的设施选址问题

带覆盖需求约束的设施选址问题(FLPWCDL)研究:客户必须在规定的响应半径内被服务,并要求服务站能够覆盖规定的需求数量,如何选择合适的服务站,使总成本(建站成本+路线成本)最小.FLPWCDL广泛应用于应急服务、物流、便利店等服务站的选址.建立了问题的混合整数规划模型,并构造了求解FLPWCDL的Benders分解算法,计算实验显示Benders分解算法具有非常高的求解效率与求解质量.     

Integer Programming to Minimize Labour Costs

The main purpose of this paper is to demonstrate a real-world application of pure integer programming to find the optimum solution to a labour cost problem. The length of a daily working shift is defined as an integer variable and several shift strategies are analysed to determine the optimum length and shift combinations that satisfy a predicted demand at minimum cost. The state-space model has been used to predict the stochastic behaviour of monthly demands for beer and soft drink. Savings of about 7% of the annual sales have been obtained as a result of implementing the integer programming approach. A numerical example shows that the solution obtained by rounding off the continuous optimal solution does not match with the integer optimal solution. It was also noted that if a rounded-off solution is feasible, then it provides an initial integer solution for the branch-and-bound algorithm that may reduce the computational time.     

考虑订单合并和货物转运的多式联运路径优化研究

为了获得运输的规模经济效应,本文研究了一种考虑订单合并和货物转运的零担多式联运路径优化问题。首先,以总运输成本为目标函数,以网络中的运输工具容量、可以提供的运输工具最大数量、运输工具服务的关闭时间以及订单时间窗为约束,构建混合整数规划模型,在模型中允许多个订单进行合并运输并考虑运输过程中的转运成本。其次,由于多式联运路径优化问题是典型的NP-hard问题,为了快速求解该模型,开发了一种可以快速为该问题提供近似最优解和下界的列生成启发式算法。最后,生成并测试了大量算例,结果表明所开发的列生成启发式算法可以在较短的时间内提供高质量的近似最优解。文章所构建的模型和开发的列生成启发式算法可以为零担自营多式联运物流企业提供高效的决策支持。