Container Scheduling: Complexity and Algorithms

We consider the transport of containers through a fleet of ships. Each ship has a capacity constraint limiting the total number of containers it can carry and each ship visits a given set of ports following a predetermined route. Each container has a release date at its origination port, and a due date at its destination port. A container has a size 1 or size 2; size 1 represents a 1 TEU (20‐foot equivalent unit) and size 2 represents 2 TEUs. The delivery time of a container is defined as the time when the ship that carries the container arrives at its destination port. We consider the problem of minimizing the maximum tardiness over all containers. We consider three scenarios with regard to the routes of the ships, namely, the ships having (i) identical, (ii) nested, and (iii) arbitrary routes. For each scenario, we consider different settings for origination ports, release dates, sizes of containers, and number of ports; we determine the computational complexity of various cases. We also provide a simple heuristic for some cases, with its worst case analysis. Finally, we discuss the relationship of our problems with other scheduling problems that are known to be open.     

基于混合流水作业组织的集装箱码头装卸作业集成调度优化

集装箱码头集疏运资源调度的对象是由岸桥、集卡、场桥所构成的多阶段一体化的集装箱装、卸、运操作系统,将该系统的调度优化基于多阶段混合流水线调度问题建立混合整数规划模型,同时考虑集装箱码头现实作业中预定义顺序、避免岸桥交叉作业、以及取决于作业顺序的切换时间等现实约束,针对问题自身的特点设计了两阶段启发式算法,得出各阶段设备的指派结果及作业顺序。通过与基于现行调度规则的调度方案以及与目标函数理论下界值的对比实验,显示了所提出的集成调度模型及求解算法能够有效降低船舶在港时间并实现集卡资源的共享,为集装箱码头集疏运资源的集成调度提供了新的思路。     

考虑实时预倒箱的出口箱堆场多场桥调度优化

在出口集装箱堆场的实际作业过程中，倒箱是制约场桥作业效率的瓶颈之一。为提高出口箱堆场的作业效能，减少船舶装船作业时间，采用实时预倒来降低倒箱的影响，研究出口箱堆场多场桥调度优化问题。考虑待提箱作业次序固定、场桥间保持安全距离及不可跨越的现实约束，兼顾内集卡的等待上限，侧重场桥作业过程中的实时预倒箱，构建了以带惩罚因子的内集卡总等待时间最少为目标的混合整数线性规划模型。基于问题自身的特点设计了混合和声模拟退火算法，得出了各场桥的行走路径与实时预倒箱方案。在算例实验中，通过与不考虑实时预倒箱的方案、FCFS方案以及下界进行对比，验证了考虑实时预倒箱的场桥调度模型及算法的有效性，为集装箱码头出口箱堆场的场桥调度提供参考。     

Scheduling material handling vehicles in a container terminal

Increasing global trade has created the need for efficient container ports. The goal of the port is to move containers as quickly as possible and at the least possible cost. Goods that are delayed at the port are inevitably tardy when delivered to the customer, and thus sanctioned by late charges. Two key activities in the port are (i) unloading of containers from truck and then storage in the export area, and (ii) removal of containers from import storage and then loading onto the trucks. Since containers are large and heavy, specialized material handling vehicles are required for transporting them within the terminal. The focus of this paper is on port terminals where straddle carriers are primarily used to move containers. Container terminals typically have well developed computer and communication networks. Through these networks a terminal scheduler will control and schedule the movement of the straddle carrier fleet in real time. The objective of the terminal scheduler is to minimize the empty travel of straddle carriers, while at the same time minimizing any delays in servicing customers. This paper presents a straddle scheduling procedure that can be used by a terminal scheduler to control the movement of straddle carriers. At its core, the procedure is driven by an assignment algorithm that dynamically matches straddle carriers and trucks, as each becomes available. The procedures were developed and tested in collaboration with the largest container terminal operator in the Port of New York and New Jersey. Using a simulation model of the real system, the superiority of the proposed procedure over two alternative scheduling strategies is illustrated.     

EDUCATION

The power of an integer programming approach—and more particularly a 0,1 programming approach—to resource allocation problems is not widely appreciated. Recent developments in mathematical programming and in problem formulation enable decision makers to deal explicitly with the special conditions which characterize real world problems in capital budgeting, scheduling, and facilities planning. In this paper, somewhat tutorial in nature, we seek to demonstrate formulation and solution of an equipment selection resource allocation problem with several special conditions. The problem can be solved on any reasonably equipped computer system. Sensitivity studies are also performed and discussed.     

Just-in-time scheduling with controllable processing times on parallel machines

We study scheduling problems with controllable processing times on parallel machines. Our objectives are to maximize the weighted number of jobs that are completed exactly at their due date and to minimize the total resource allocation cost. We consider four different models for treating the two criteria. We prove that three of these problems are NP\mathcal{NP} -hard even on a single machine, but somewhat surprisingly, the problem of maximizing an integrated objective function can be solved in polynomial time even for the general case of a fixed number of unrelated parallel machines. For the three NP\mathcal{NP} -hard versions of the problem, with a fixed number of machines and a discrete resource type, we provide a pseudo-polynomial time optimization algorithm, which is converted to a fully polynomial time approximation scheme.     

Tighter MIP models for Barge Container Ship Routing

This paper addresses the problem of optimal planning of a liner service for a barge container shipping company. Given estimated weekly demands between pairs of ports, our goal is to determine the subset of ports to be called and the amount of containers to be shipped between each pair of ports, so as to maximize the profit of the shipping company. In order to save possible leasing or storage costs of empty containers at the respective ports, our approach takes into account the repositioning of empty containers. The line has to follow the outbound–inbound principle, starting from the port at the river mouth. We propose a novel integrated approach in which the shipping company can simultaneously optimize the route (along with repositioning of empty containers), the choice of the final port, length of the turnaround time and the size of its fleet. To solve this problem, a new mixed integer programming model is proposed. On the publicly available set of benchmark instances for barge container routing, we demonstrate that this model provides very tight dual bounds and significantly outperforms the existing approaches from the literature for splittable demands.We also show how to further improve this model by projecting out arc variables for modeling the shipping of empty containers. Our numerical study indicates that the latter model improves the computing times for the challenging case of unsplittable demands. We also study the impact of the turnaround time optimization on the total profit of the company.     

MRP in a job shop environment using a resource constrained project scheduling model

One of the most difficult tasks in a job shop manufacturing environment is to balance schedule and capacity in an ongoing basis. MRP systems are commonly used for scheduling, although their inability to deal with capacity constraints adequately is a severe drawback. In this study, we show that material requirements planning can be done more effectively in a job shop environment using a resource constrained project scheduling model. The proposed model augments MRP models by incorporating capacity constraints and using variable lead time lengths. The efficacy of this approach is tested on MRP systems by comparing the inventory carrying costs and resource allocation of the solutions obtained by the proposed model to those obtained by using a traditional MRP model. In general, it is concluded that the proposed model provides improved schedules with considerable reductions in inventory carrying costs.     

A continuous-time supply-driven inventory-constrained routing problem

We address an inventory routing problem (IRP) in which routing and inventory decisions are dictated by supply rather than demand. Moreover, inventory is held in containers that act as both a storage container and a movable transport unit. This problem emanates from logistics related to biogas transportation in which biogas is transported in containers from many suppliers to a single facility. We present a novel and compact formulation for the supply-driven IRP which addresses the routing decisions in continuous-time in which inventory levels within the containers are continuous. Valid inequalities are included and realistic instances are solved to optimality. For all experiments, we found that the total transportation time is minimized when the storage capacity at each supplier is larger than or equal to the vehicle capacity. These routes are characterized by tours in which mostly single suppliers are visited. In 95% of the instances, the average content level of the exchanged containers exceeded 99.6%.     

考虑空箱调运的集装箱海运收益管理能力分配优化模型

文章基于收益管理的思想对面临不确定需求的海运集装箱能力分配问题进行了定量研究。首先描述了集装箱海运收益管理问题与航空客运收益管理的差异,接着建立了考虑和不考虑空箱调运的海运集装箱能力分配随机规划模型,并应用稳健优化方法对模型进行求解,最后通过数值仿真,说明了模型和求解方法对于海运集装箱运输企业的收益管理问题具有重要的应用价值。     

A FRAMEWORK FOR MACHINE SCHEDULING PROBLEMS WITH CONTROLLABLE PROCESSING TIMES

This is a study of single and parallel machine scheduling problems with controllable processing time for each job. The processing time for job j depends on the position of the job in the schedule and is a function of the number of resource units allocated to its processing. Processing time functions and processing cost functions are allowed to be nonlinear. The scheduling problems considered here have important applications in industry and include many of the existing scheduling models as special cases. For the single machine problem, the objective is minimization of total compression costs plus a scheduling measure. The scheduling measures include makespan, total flow time, total differences in completion times, total differences in waiting times, and total earliness and tardiness with a common due date for all jobs. Except when the total earliness and tardiness measure is involved, each case the problem is solved efficiently. Under an assumption typically satisfied in just-in-time systems, the problem with total earliness and tardiness measure is also solved efficiently. Finally, for a large class of processing time functions; parallel machine problems with total flow time and total earliness and tardiness measures are solved efficiently. In each case we reduce the problem to a transportation problem.     

Market Good Flexibility in Capacity Auctions

We consider the allocation of limited production capacity among several competing agents through auctions. Our focus is on the contribution of flexibility in market good design to effective capacity allocation. The application studied is a capacity allocation problem involving several agents, each with a job, and a facility owner. Each agent generates revenue by purchasing capacity and scheduling its job at the facility. Ascending auctions with various market good designs are compared. We introduce a new market good that provides greater flexibility than those previously considered in the literature. We allow ask prices to depend both on agents’ utility functions and on the number of bids at the previous round of the auction, in order to model and resolve resource conflicts. We develop both optimal and heuristic solution procedures for the winner determination problem. Our computational study shows that flexibility in market good design typically increases system value within auctions. A further increase is achieved if each agent is allowed to bid for multiple market goods at each round. On average, the multiple flexible market goods auction provides over 95% of the system value found by centralized planning.     

Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads

We study minmax due-date based on common flow-allowance assignment and scheduling problems on a single machine, and extend known results in scheduling theory by considering convex resource allocation. The total cost function of a given job consists of its earliness, tardiness and flow-allowance cost components. Thus, the common flow-allowance and the actual jobs’ processing times are decision variables, implying that the due-dates and actual processing times can be controlled by allocating additional resource to the job operations. Consequently, our goal is to optimize a cost function by seeking the optimal job sequence, the optimal job-dependent due-dates along with the actual processing times. In all addressed problems we aim to minimize the maximal cost among all the jobs subject to a constraint on the resource consumption. We start by analyzing and solving the problem with position-independent workloads and then proceed to position-dependent workloads. Finally, the results are generalized to the method of common due-window. For all studied problems closed form solutions are provided, leading to polynomial time solutions.

     

一种基于闭排队网络的集装箱码头设备配置优化模型

将集装箱码头龙门吊装卸工艺抽象为闭排队网络模型,采用估算均值法计算了顾客到达和服务时间分布为一般情况的闭排队网络系统性能指标.仿真结果表明,闭排队网络模型计算结果可以为集装箱码头设备配置提供一定的决策支持.     

单资源调度中误工问题的作业时间压缩算法

本文采用作业时间可压缩的方法来解决单资源调度中的误工问题。在安排任务处理顺序的过程中,当某个任务发生误工时,我们基于关键路径反向搜索的方法,给出了一个启发式算法,求得需要压缩的任务集,使这个误工任务的延误时间尽可能的减少,并使需要压缩的任务数目最少,最后证明了算法的有效性,并给出了一个算例。     

一种策略层项目计划的双目标优化方法

针对产品开发项目管理的实际情况,对策略层计划优化方法进行研究。以工作包的工作量估算为基础,以资源投入水平和工期最小化为目标,考虑各种约束条件,提出一种策略层项目计划问题的混合整数规划问题模型。以非支配遗传算法NSGA-II为基础框架,设计了一种改进的双目标遗传算法。该算法针对问题的特点,提出了基于资源平滑的解码算法。参考NSGA-III的关键特征,对拥挤密度计算方法进行改进。通过企业实际项目案例,验证了算法的性能和所提出的策略层项目计划方法的有效性。     

Fundamental Insights into Part Family Scheduling: The Single Machine Case

A simulation study was conducted to investigate the behavior of family scheduling procedures in a dynamic dispatching environment. Two scheduling rules that incorporate setup avoidance mechanisms (FCFS-F and SPT-F) and two that do not (FCFS and SPT) were applied to a single machine. The scheduling environment was varied by controlling several important factors: the machine utilization, the number of setup configurations (families), the size of the family setup times relative to the job run times, the frequency by which members of the part families were released for processing, and the distribution of job interarrival and job run times. The major results from the study are the following: (1) The degree of stability in the system is the most influential factor with respect to mean flow time and flow time variance. Under low variance service and interarrival time distributions, the impact of scheduling rule selection is minor. (2) Conversely, under unstable scheduling situations, family scheduling procedures can have a substantial impact. (3) Clear interaction effects are noticed between all factors. The environment most conducive to family scheduling is characterized by high resource utilization, low setup-to-run time ratio, few part families, and erratic job arrivals. (4) Under conditions favorable to family scheduling, setup avoiding procedures can be used to increase output while at the same time reduce the mean and variance of flow time. (5) The shortest processing time rule (SPT) performs well with respect to mean flow time when relative setup times are small. Overall, however, SPT-F generates the lowest mean flow time while FCFS-F produces the lowest flow time variance. This study shows that scheduling procedures that consider setups in their structure can outperform rules that do not under many different operating conditions. However, the magnitude of this advantage very much depends on the scheduling environment. The results also highlight the fact that it may be better to try to reshape the manufacturing environment than worry about selecting the correct scheduling rule. If the environment cannot be stabilized, then the choice of a setup avoiding procedure, allocation of families to machines, and setup reduction become important issues.     

A TUTORIAL ON BOTTLENECK DYNAMICS: A HEURISTIC SCHEDULING METHODOLOGY

We give a tutorial on bottleneck dynamics. Bottleneck dynamics is a scheduling framework that uses approximate dual resource prices to make decentralized decisions. The basic idea is to establish a price for a resource as a function of the set of jobs that need to be processed by the resource. Tasks are then sequenced according to a cost/benefit ratio. Starting with one resource sequencing problems, we describe how priorities for jobs can be developed and how they translate into resource prices. We then describe how resource prices can be approximated in a multiresource situation and how lead times which are critical for these approximations can be accurately computed. We also describe a number of studies that have shown bottleneck dynamics to be an effective approach in several different problem areas.