考虑潮汐影响的离散型泊位和岸桥集成调度

泊位和岸桥是集装箱港口最紧缺的资源,二者的调度问题存在很强的内在关联。针对大型船需乘潮进出港的离散型泊位,为提高集装箱码头运作效率和客户满意度,将泊位分配、岸桥指派和岸桥调度集成为一体。首先,考虑潮汐的影响以及岸桥作业中可动态调度的现实,以计划期内所有抵港船舶的岸桥作业成本和滞期成本之和最少为目标,建立一个混合整数规划模型,然后设计了一个嵌入启发式规则的遗传算法对其进行求解。最后,算例结果中给出了每艘船舶在确切时刻对应的具体岸桥和每个岸桥的动态作业时间窗,并通过与单独优化的方案对比,验证了集成方案的有效性。     

汽车滚装码头泊位调度优化模型与算法研究

本文研究滚装码头混合泊位分配和劳动力分配的联合调度优化问题。首先,考虑潮汐时间窗约束、装卸劳动力约束、泊位缆桩分布约束以及泊位不规则布局因素,建立以最小化船舶总服务时间为目标的混合整数规划模型。其次,采用内外嵌套算法设计策略,提出求解该类问题的组合算法。其中,外层是多种群并行进化的遗传算法,生成多种船舶计划顺序,内层为基于规则的启发式算法,用于计算给定计划顺序的目标函数值。然后,基于实际运营数据,生成多组不同规模的算例进行全面数值实验,结果表明所提出的算法可在10分钟内求解包含50艘船、100个泊段的算例。最后,开展基于真实滚装码头运营实例的案例分析,对所提模型和算法在实际码头调度问题中的适用性与高效性进行验证。     

Minimizing makespan on a single burn-in oven in semiconductor manufacturing

This paper considers a scheduling problem for a single burn-in oven in semiconductor manufacturing industry where the oven is a batch processing machine and each batch processing time is represented by the largest processing time among those of all the jobs contained in the batch. The objective measure of the problem is the maximum completion time (makespan) of all jobs. This paper investigates a static case in which all jobs are available to process at time zero, and also analyzes a dynamic case with different job-release times, for which a branch-and-bound algorithm and several heuristics are exploited. The worst case error performance ratios of the heuristics are also derived.     

Optimal berth allocation and time-invariant quay crane assignment in container terminals

Due to the dramatic increase in the world’s container traffic, the efficient management of operations in seaport container terminals has become a crucial issue. In this work, we focus on the integrated planning of the following problems faced at container terminals: berth allocation, quay crane assignment (number), and quay crane assignment (specific). First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment (number) problems called BACAP. Then we extend it by incorporating the quay crane assignment (specific) problem as well, which is named BACASP. Computational experiments performed on problem instances of various sizes indicate that the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality. Unfortunately, this is not the case for BACASP. Therefore, to be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a post-processing algorithm. In case this condition is not satisfied, we make use of a cutting plane algorithm which solves BACAP repeatedly by adding cuts generated from the optimal solutions until the aforementioned condition holds. This method proves to be viable and enables us to solve large BACASP instances as well. To the best of our knowledge, these are the largest instances that can be solved to optimality for this difficult problem, which makes our work applicable to realistic problems.     

Managing variances in manufacturing system design

The goal of this paper is to investigate how uncertainties in demand and production should be incorporated into manufacturing system design problems. We examine two problems in manufacturing system design: the resource allocation problem and the product grouping problem. In the resource allocation problem, we consider the issue of how to cope with uncertainties when we utilize two types of resources: actual processing capacity and stored capacity (inventory). A closed form solution of the optimal allocation scheme for each type of capacity is developed, and its performance is compared to that of the conventional scheme where capacity allocation and inventory control decisions are made sequentially. In the product grouping problem, we consider the issue of how we design production lines when each line is dedicated to a certain set of products. We formulate a mathematical program in which we simultaneously determine the number of production lines and the composition of each line. Two heuristics are developed for the problem.     

Parallel machine scheduling problems with a single server

In this paper, we consider the problem of scheduling jobs on parallel machines with setup times. The setup has to be performed by a single server. The objective is to minimize the schedule length (makespan), as well as the forced idle time. The makespan problem is known to be NP-hard even for the case of two identical parallel machines. This paper presents a pseudopolynomial algorithm for the case of two machines when all setup times are equal to one. We also show that the more general problem with an arbitrary number of machines is unary NP-hard and analyze some list scheduling heuristics for this problem. The problem of minimizing the forced idle time is known to be unary NP-hard for the case of two machines and arbitrary setup and processing times. We prove unary NP-hardness of this problem even for the case of constant setup times. Moreover, some polynomially solvable cases are given.     

Robust berth scheduling with uncertain vessel delay and handling time

In container terminals, the actual arrival time and handling time of a vessel often deviate from the scheduled ones. Being the input to yard space allocation and crane planning, berth allocation is one of the most important activities in container terminals. Any change of berth plan may lead to significant changes of other operations, deteriorating the reliability and efficiency of terminal operations. In this paper, we study a robust berth allocation problem (RBAP) which explicitly considers the uncertainty of vessel arrival delay and handling time. Time buffers are inserted between the vessels occupying the same berthing location to give room for uncertain delays. Using total departure delay of vessels as the service measure and the length of buffer time as the robustness measure, we formulate RBAP to balance the service level and plan robustness. Based on the properties of the optimal solution, we develop a robust berth scheduling algorithm (RBSA) that integrates simulated annealing and branch-and-bound algorithm. To evaluate our model and algorithm design, we conduct computational study to show the effectiveness of the proposed RBSA algorithm, and use simulation to validate the robustness and service level of the RBAP formulation.     

Dynamic uncapacitated lot sizing with random demand under a fillrate constraint

This paper deals with the single-item dynamic uncapacitated lot sizing problem with random demand. We propose a model based on the “static uncertainty” strategy of Bookbinder and Tan (1988). In contrast to these authors, we use exact expressions for the inventory costs and we apply a fillrate constraint. We present an exact solution method and modify several well-known dynamic lot sizing heuristics such that they can be applied for the case of dynamic stochastic demands. A numerical experiment shows that there are significant differences in the performance of the heuristics whereat the ranking of the heuristics is different from that reported for the case of deterministic demand.     

A branch-and-price algorithm to solve the integrated berth allocation and yard assignment problem in bulk ports

In this research, two crucial optimization problems of berth allocation and yard assignment in the context of bulk ports are studied. We discuss how these problems are interrelated and can be combined and solved as a single large scale optimization problem. More importantly we highlight the differences in operations between bulk ports and container terminals which highlights the need to devise specific solutions for bulk ports. The objective is to minimize the total service time of vessels berthing at the port. We propose an exact solution algorithm based on a branch and price framework to solve the integrated problem. In the proposed model, the master problem is formulated as a set-partitioning problem, and subproblems to identify columns with negative reduced costs are solved using mixed integer programming. To obtain sub-optimal solutions quickly, a metaheuristic approach based on critical-shaking neighborhood search is presented. The proposed algorithms are tested and validated through numerical experiments based on instances inspired from real bulk port data. The results indicate that the algorithms can be successfully used to solve instances containing up to 40 vessels within reasonable computational time.     

Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times

In this paper we study the problem of scheduling n jobs on a single machine with availability constraints. The objective is to minimize total weighted job completion times. We show that the problem is NP-hard in the strong sense. Then we consider two intractable special cases, namely, proportional weight case, and single availability constraint case. We propose two heuristics for these cases and analyze their worst-case error bounds.     

Stochastic cyclic scheduling problem in synchronous assembly and production lines

In this paper we address the stochastic cyclic scheduling problem in synchronous assembly and production lines. Synchronous lines are widely used in the production and assembly of various goods such as automobiles or household appliances. We consider cycle time minimisation (or throughput rate maximisation) as the objective of the scheduling problem with the assumption that the processing times are independent random variables. We first discuss the two-station case and present a lower bounding scheme and an approximate solution procedure for the scheduling problem. For the general case of the problem, two heuristic solution procedures are presented. An extension of the two-station lower bound to the general case of the problem is also discussed. The performance of the proposed heuristics on randomly generated problems is documented, and the impact of scheduling decisions on problems with different levels of variability in processing times are analysed. We also analyse the problem of sequence determination when the available information is limited to the expected values of individual processing times.     

Scheduling orders for multiple product types to minimize total weighted completion time

We consider the problem of scheduling orders for multiple different product types in an environment with m dedicated machines in parallel. The objective is to minimize the total weighted completion time. Each product type is produced by one and only one of the m dedicated machines; that is, each machine is dedicated to a specific product type. Each order has a weight and may also have a release date. Each order asks for certain amounts of various different product types. The different products for an order can be produced concurrently. Preemptions are not allowed. Even when all orders are available at time 0, the problem has been shown to be strongly NP-hard for any fixed number (?2) of machines. This paper focuses on the design and analysis of efficient heuristics for the case without release dates. Occasionally, however, we extend our results to the case with release dates. The heuristics considered include some that have already been proposed in the literature as well as several new ones. They include various static and dynamic priority rules as well as two more sophisticated LP-based algorithms. We analyze the performance bounds of the priority rules and of the algorithms and present also an in-depth comparative analysis of the various rules and algorithms. The conclusions from this empirical analysis provide insights into the trade-offs with regard to solution quality, speed, and memory space.     

单向航道船舶进港次序与泊位分配协同优化

为提高单向航道离散泊位港口的服务水平,研究船舶进港次序和泊位分配的协同优化。考虑船舶进出港及泊位作业的实际约束,以计划期内所有船舶的锚地、泊位等待成本、滞期成本和偏离成本之和最小为目标,构建了一个混合整数规划模型,结合问题特征设计了引入禁忌搜索算法的和声搜索算法进行求解。算例结果给出了计划期内每艘船舶的进港次序和靠泊泊位,并通过与单独优化方案的对比和不同规模算例求解效果的分析,验证了模型和算法的有效性;分析进出港时段变动对船舶作业成本的影响,确定不同船舶抵港规模下的最佳进出港时段长度,为单向航道港口时长设置提供借鉴。     

A Multi-Period Renewal equipment problem

This paper looks at a Multi-Period Renewal equipment problem (MPR). It is inspired by a specific real-life situation where a set of hardware items is to be managed and their replacement dates determined, given a budget over a time horizon comprising a set of periods. The particular characteristic of this problem is the possibility of carrying forward any unused budget from one period to the next, which corresponds to the multi-periodicity aspect in the model. We begin with the industrial context and deduce the corresponding knapsack model that is the subject of this paper. Links to certain variants of the knapsack problem are next examined. We provide a study of complexity of the problem, for some of its special cases, and for its continuous relaxation. In particular, it is established that its continuous relaxation and a special case can be solved in (strongly) polynomial time, that three other special cases can be solved in pseudo-polynomial time, while the problem itself is strongly NP-hard when the number of periods is unbounded. Next, two heuristics are proposed for solving the MPR problem. Experimental results and comparisons with the Martello&Toth and Dantzig heuristics, adapted to our problem, are provided.     

Berth allocation planning in the public berth system by genetic algorithms

This paper addresses the problem of determining a dynamic berth assignment to ships in the public berth system. While the public berth system may not be suitable for most container ports in major countries, it is desired for higher cost-effectiveness in Japan’s ports. The berth allocation to calling ships is a key factor for efficient public berthing. However, it is not calculated in polynomially-bounded time. To obtain a good solution with considerably small computational effort, we developed a heuristic procedure based on the genetic algorithm. We conducted a large amount of computational experiments which showed that the proposed algorithm is adaptable to real world applications.     

Noncompliant oligopolistic firms and marketable pollution permits: Statics and dynamics

In this paper, we consider the modeling, analysis, and computation of solutions to both static and dynamic models of multiproduct, multipollutant noncompliant oligopolistic firms who engage in a market for pollution permits. In the case of the static model, we utilize variational inequality theory for the formulation of the governing equilibrium conditions as well as the qualitative analysis of the equilibrium pattern, including sensitivity analysis. We then propose a dynamic model, using the theory of projected dynamical systems, whose set of stationary points coincides with the set of solutions to the variational inequality problem. We propose an algorithm, which is a discretization in time of the dynamic adjustment process, and provide convergence results using the stability analysis results that are also provided herein. Finally, we apply the algorithm to several numerical examples to compute the profit-maximized quantities of the oligopolistic firms' products and the quantities of emissions, along with the equilibrium allocation of licenses and their prices, as well as the possible noncompliant overflows and underflows. This is the first time that these methodologies have been utilized in conjunction to study a problem drawn from environmental policy modeling and analysis.     

具有预知信息的集装箱码头泊位与岸桥联合调度在线模型

探讨了预知服务需求信息能力下的集装箱码头泊位与岸桥联合调度 over-list 在线模型. 在每个船舶服务请求释放时, 决策者预知后续 k(k \geq 2)个请求的信息,目标为最小化所有请求的最大完工时间. 针对由3个离散泊位组成的混合型泊位与4个岸桥, 以及只有大小两种服务请求的情形, 给出了预知任意 k \geq 2个请求下的竞争比下界; 同时, 对于k=2的特定情形, 给出了具有最优竞争比7/6 的在线策略. 数值实验进一步表明了所设计策略的良好执行性能.     

基于泊位偏好与岸桥干扰的泊位和岸桥分配

泊位和岸桥是集装箱港口资源中最紧缺的资源,合理的泊位分配和岸桥调度可以提高集装箱港口的资源利用率和港口的运作效率和效益。针对泊位偏离和岸桥工作损失两个因素,文章建立了集装箱港口泊位和岸桥的混合整数线性规划模型;运用采集自宁波某典型集装箱港口的数据,用Gurobi优化软件和两阶段启发式算法对模型进行了求解;对计算结果进行了经济性分析。计算结果表明:该港口的岸线资源利用率为46%时,1000m~1600m基本没被利用;18台岸桥要比16台岸桥的目标值更优,求解时间更短,而且18台岸桥的平均利用率为80%,为此,建议该港口再增加两台岸桥。同时发现:随着船舶规模的增加,Gurobi优化求解的时间增长较快,而两阶段启发式算法仍能在很短时间内求得准优解。     

煤炭码头船货匹配下泊位动态分配多目标优化模型及算法

本文针对输出型煤炭码头船货匹配下泊位动态分配问题,构建了堆场-取装线-泊位-船舶联合分配优化数学模型,并设计了采用仿真推演策略解码的遗传算法求解。首先,综合考虑船舶、泊位、堆场、取装线、煤种、航道开放时间和装船作业规则等要素,以船舶在港时间最短和作业效率最大为目标建立了相应的多约束多目标优化模型。然后,综合多目标优化、遗传算法以及仿真推演技术,设计了相应的遗传算法求解,包括:组合式编码、采用仿真推演策略的解码方法,追加了具有合法性检查的染色体生成算法,设计了采用多种策略的遗传操作等。最后实例表明,本算法的执行效率高而且优化效果好。     

Modeling of financial supply chain

The research work on supply-chain management has primarily focused on the study of materials flow and very little work has been done on the study of upstream flow of money. In this paper we study the flow of money in a supply chain from the viewpoint of a supply chain partner who receives money from the downstream partners and makes payments to the upstream partners. The objective is to schedule all payments within the constraints of the receipt of the money. A penalty is to be paid if payments are not made within the specified time. Any unused money in a given period can be invested to earn an interest. The problem is computationally complex and non-intuitive because of its dynamic nature. The incoming and outgoing monetary flows never stop and are sometimes unpredictable. For tractability purposes we first develop an integer programming model to represent the static problem, where monetary in-flows and out-flows are known before hand. We demonstrate that even the static problem is NP-Complete. First we develop a heuristic to solve this static problem. Next, the insights derived from the static problem analysis are used to develop two heuristics to solve the various level of dynamism of the problem. The performances of all these heuristics are measured and presented.