Preemptive scheduling of interval orders is polynomial

In 1979, Papadimitriou and Yannakakis gave a polynomial time algorithm for the scheduling of jobs requiring unit completion times when the precedence constraints form an interval order. The authors solve here the corresponding problem, for preemptive scheduling (a job can be interrupted to work on more important tasks, and completed at a later time, subject to the usual scheduling constraints.) The m-machine preemptive scheduling problem is shown to have a polynomial algorithm, for both unit time and variable execution times as well, when the precedence constraints are given by an interval order.     

Experimental evaluation of simulated annealing algorithms for the time-cost trade-off problem

This paper evaluates variants of a simulated annealing algorithm which solve the total cost minimization problem in activity networks in the case that discrete time-cost execution modes are allowed on the project activities. This problem is a special case of the well known discrete time-cost trade-off problem (DTCTP). Based on a sample of randomly generated activity networks, formal tests of statistical significance are utilized to test both the quality of solutions and the time efficiency of algorithms versus problem factors. A procedure issued from the extreme values statistics is also applied on problem instances in order to determine, on the one hand, the confidence interval estimate of the optimum solution for each algorithm and, on the other hand, when to stop the running of an algorithm.     

Scheduling tasks on a flexible manufacturing machine to minimize tool change delays

This paper considers the problem of scheduling a given set of precedence constraint tasks on a flexible machine equipped with a tool magazine where each task requires exactly one of the tools during its execution. Changing from one tool to another requires a certain amount of time that depends on the pair of tools being exchanged. We present a new algorithmic approach for general task precedence relations when it is desired to sequence the tasks in such a way that the total time required for tool changes is minimized. The proposed algorithm is of polynomial time complexity in case of task precedences of limited width w, i.e. for precedence relations where each subset of independent tasks has not more than w elements. Since the task precedences width w could be arbitrary, we describe two heuristic algorithms and empirically evaluate their effectiveness in finding schedules with minimum total time required for tool changes.     

活动执行时间可提前的多模式反应性项目调度优化

研究不确定活动工期下活动执行时间可提前的多模式反应性项目调度问题。首先对反应性研究现状进行综述;其次建立以最小化反应性总成本为目标的优化模型;随后基于问题特点设计禁忌搜索算法;最后通过具体案例分析关键参数对反应性成本的影响,并得出结论:执行时间提前得到的反应性成本及完工时间明显低于执行时间不可提前的结果;随着项目推进,总成本及影响的活动数量总体上呈减小趋势,但项目完工时间在某些时刻维持不变;对于工期增加较大的活动,将其本身或紧前活动提前启动,或将其转换至活动工期较短的模式可降低反应性成本。研究可为不确定环境下反应性计划制定提供决策支持。     

Project Scheduling under Time Dependent Costs – A Branch and Bound Algorithm

In a given project network, execution of each activity in normal duration requires utilization of certain resources. If faster execution of an activity is desired then additional resources at extra cost would be required. Given a project network, the cost structure for each activity and a planning horizon, the project compression problem is concerned with the determination of optimal schedule (duration) of performing each activity while satisfying given restrictions and minimizing the total cost of project execution. This paper considers the project compression problem with time dependent cost structure for each activity. The planning horizon is divided into several regular time intervals over which the cost structure of an activity may vary. But the cost structure of the activities remains the same (constant) within a time interval. Key events of the project attract penalty for finishing earlier or later than the corresponding target times. The objective is to find an optimal project schedule minimizing the total project cost. We present a mathematical model for this problem, develop some heuristics and an exact branch and bound algorithm. Using simulated problems we provide an insight into the computational performances of heuristics and the branch and bound algorithm.     

Batch Delivery Scheduling on a Single Machine

The problem of partitioning a set of independent and simultaneously available jobs into batches and sequencing them for processing on a single machine is presented. Jobs in the same batch are to be delivered together, upon completion of the last job in the batch. Jobs finished before this time have to wait until delivery. There are a delivery cost depending on the number of batches formed and an earliness cost for jobs finished before delivery. The dynamic programming approach to minimizing the total cost is considered, yielding two pseudopolynomial algorithms when the number of batches has a fixed upper bound. A polynomial algorithm for a special case of the problem is also presented.     

Gossip based asynchronous and randomized distributed task assignment with guaranteed performance on heterogeneous networks

The main contribution of this paper is a novel distributed algorithm based on asynchronous and randomized local interactions, i.e., gossip based, for task assignment on heterogeneous networks. We consider a set of tasks with heterogeneous cost to be assigned to a set of nodes with heterogeneous execution speed and interconnected by a network with unknown topology represented by an undirected graph. Our objective is to minimize the execution time of the set of tasks by the networked system. We propose a local interaction rule which allows the nodes of a network to cooperatively assign tasks among themselves with a guaranteed performance with respect to the optimal assignment exploiting a gossip based randomized interaction scheme. We first characterize the convergence properties of the proposed approach, then we propose an edge selection process and a distributed embedded stop criterion to terminate communications, not only task exchanges, while keeping the performance guarantee. Numerical simulations are finally presented to corroborate the theoretical results.     

A minmax regret approach to the critical path method with task interval times

The execution of a given project, with a number of interrelated tasks due to precedence constraints, represents a challenge when one must to control the available resources and the compromised due dates. In this paper, we analyse this problem under uncertain individual task completing times, specifically, we will assume that a given range, for the admissible values of each individual completing time, is available. Taking into account that the precedence relations between tasks must be preserved, each realization of the admissible execution times for the set of tasks will define a new scenario determining the ending time for the project and the subset of critical tasks.     

Iterated local search for workforce scheduling and routing problems

The integration of scheduling workers to perform tasks with the traditional vehicle routing problem gives rise to the workforce scheduling and routing problems (WSRP). In the WSRP, a number of service technicians with different skills, and tasks at different locations with pre-defined time windows and skill requirements are given. It is required to find an assignment and ordering of technicians to tasks, where each task is performed within its time window by a technician with the required skill, for which the total cost of the routing is minimized. This paper describes an iterated local search (ILS) algorithm for the WSRP. The performance of the proposed algorithm is evaluated on benchmark instances against an off-the-shelf optimizer and an existing adaptive large neighbourhood search algorithm. The proposed ILS algorithm is also applied to solve the skill vehicle routing problem, which can be viewed as a special case of the WSRP. The computational results indicate that the proposed algorithm can produce high-quality solutions in short computation times.     

Single machine scheduling subject to precedence delays

A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by precedence delays, i.e., a task can start its execution only after any of its predecessors has completed and the delay between the two tasks has elapsed. In the case of unit execution times and integer lengths of delays, the problem is shown to be NP-hard in the strong sense. In the case of integer execution times and unit length of delays, the problem is polynomial, and an O(n²) optimal algorithm is provided. Both preemptive and non-preemptive cases are considered.     

Multi-depot vehicle scheduling problems with time windows and waiting costs

The multi-depot vehicle scheduling problem with time windows (MDVSPTW) consists of scheduling a fleet of vehicles to cover a set of tasks at minimum cost. Each task is restricted to begin within a prescribed time interval and vehicles are supplied by different depots. The problem is formulated as an integer nonlinear multi-commodity network flow model with time variables and is solved using a column generation approach embedded in a branch-and-bound framework. This paper breaks new ground by considering costs on exact waiting times between two consecutive tasks instead of minimal waiting times. This new and more realistic cost structure gives rise to a nonlinear objective function in the model. Optimal and heuristic versions of the algorithm have been extensively tested on randomly generated urban bus scheduling problem (UBSP) and freight transport scheduling problem (FTSP). The results show that such a general solution methodology outperforms specialized algorithms when minimal waiting costs are used, and can efficiently treat the case with exact waiting costs.     

Scheduling UET task systems with concurrency on two parallel identical processors

Problems with unit execution time tasks and two identical parallel processors have received a great deal of attention in scheduling theory. In contrast to the conventional models, where each task requires only one processor, we consider a situation when a task may require both processors simultaneously. For problems without precedence constraints we present several polynomial time algorithms which complement recent results of Lee and Cai. We also show that the introduction of precedence constraints leads to NP-hardness results for maximum lateness and mean flow time objective functions. For the maximum lateness problem, a family of algorithms, based upon the idea of modified due dates, is considered. The worst case behaviour of these algorithms is analysed, and it is shown that the same upper bound is tight for each algorithm of this family.     

A variable neighbourhood search algorithm for the constrained task allocation problem

A variable neighbourhood search algorithm that employs new neighbourhoods is proposed for solving a task allocation problem whose main characteristics are: (i) each task requires a certain amount of resources and each processor has a capacity constraint which limits the total resource of the tasks that are assigned to it; (ii) the cost of solution includes fixed costs when using processors, task assignment costs, and communication costs between tasks assigned to different processors. A computational study shows that the algorithm performs well in terms of time and solution quality relative to other local search procedures that have been proposed.     

On the computational behavior of a polynomial-time network flow algorithm

A variation on the Edmonds-Karp scaling approach to the minimum cost network flow problem is examined. This algorithm, which scales costs rather than right-hand sides, also runs in polynomial time. Large-scale computational experiments indicate that the computational behavior of such scaling algorithms may be much better than had been presumed. Within several distributions of square, dense, capacitated transportation problems, a cost scaling code, SCALE, exhibits linear growth in average execution time with the number of edges, while two network simplex codes, RNET and GNET, exhibit greater than linear growth.Our experiments reveal that median and mean execution times are predictable with surprising accuracy for all of the three codes and all three distributions from which test problems were generated. Moreover, for fixed problem size, individual execution times appear to behave as though they are approximately lognormally distributed with constant variance. The experiments also reveal sensitivity of the parameters in the models, and in the models themselves, to variations in the distribution of problems. This argues for caution in the interpretation of such computational studies beyond the realm in which the computations were performed.This work has been supported in part by NSF grants ENG-7910807, ECS-8313853, DMS-8706133, and DDM-8813054, and by AFOSR, NSF, and ONR under NSF grant DMS-8920550 to Cornell University, and by a Sloan Foundation research fellowship held by the first author.     

Promoting cooperation in selfish computational grids

In distributed computing, the recent paradigm shift from centrally-owned clusters to organizationally distributed computational grids introduces a number of new challenges in resource management and scheduling. In this work, we study the problem of Selfish Load Balancing which extends the well-known load balancing (LB) problem to scenarios in which each processor is concerned only with the performance of its local jobs. We propose a simple mathematical model for such systems and a novel function for computing the cost of the execution of foreign jobs. Then, we use the game-theoretic framework to analyze the model in order to compute the expected result of LB performed in a grid formed by two clusters. We show that, firstly, LB is a socially-optimal strategy, and secondly, for similarly loaded clusters, it is sufficient to collaborate during longer time periods in order to make LB the dominant strategy for each cluster. However, we show that if we allow clusters to make decisions depending on their current queue length, LB will never be performed. Then, we propose a LB algorithm which balances the load more equitably, even in the presence of overloaded clusters. Our algorithms do not use any external forms of compensation (such as money). The load is balanced only by considering the parameters of execution of jobs. This analysis is assessed experimentally by simulation, involving scenarios with multiple clusters and heterogeneous load.     

工时依赖于开工时间的单台机排序问题

此文考察工时依赖于开工时间的排序问题．文章证明：(1)即使准奋时间完全相同，判断工时与开工时间相关的单台机排序问题是否有可行解也是NP完全的．(2)即使只存在两个不同的截止期，判断工时与开工时间相关的单台机排序问题是否有可行解仍然是NP完全的．(3)当所有工件有相同截止期时，问题是否有可行解可在多项式时间内判定．     

Balancing and scheduling tasks in assembly lines with sequence-dependent setup times

The classical Simple Assembly Line Balancing Problem (SALBP) has been widely enriched over the past few years with many realistic approaches and much effort has been made to reduce the distance between the academic theory and the industrial reality. Despite this effort, the scheduling of the execution of tasks assigned to every workstation following the balancing of the assembly line has been scarcely reported in the scientific literature. This is supposed to be an operational concern that the worker should solve himself, but in several real environments, setups between tasks exist and optimal or near-optimal tasks schedules should be provided inside each workstation. The problem presented in this paper adds sequence-dependent setup time considerations to the classical SALBP in the following way: whenever a task is assigned next to another at the same workstation, a setup time must be added to compute the global workstation time. After formulating a mathematical model for this innovative problem and showing the high combinatorial nature of the problem, eight different heuristic rules and a GRASP algorithm are designed and tested for solving the problem in reasonable computational time.     

Preemptive Scheduling with Two Minimax Criteria

Two preemptive single-machine bicriteria scheduling problems with release dates and deadlines are considered in this paper. Each criterion is formulated as a maximum cost. In the first problem the cost of both criteria depends on the completion time of the tasks. This problem can be solved by enumerating all the Pareto optimal points with an approach proposed by Hoogeveen (1996) for the nonpreemptive problem without release dates. In the second problem, the costs of one criterion are dependent on the completion times of the tasks and the costs of the other criterion are dependent on the start times. This problem is more difficult but an efficient algorithm is proposed for a sub-problem with heads, tails, release dates and deadlines that appears in the job-shop scheduling problem.     

Solving a robotic assembly line balancing problem using efficient hybrid methods

In this paper we are studying a robotic assembly line balancing problem. The goal is to maximize the efficiency of the line and to balance the different tasks between the robots by defining the suitable tasks and components to assign to each robot. We are interested in a robotic line which consists of seizing the products on a moving conveyor and placing them on different location points. The performances evaluations of the system are done using a discret event simulation model. This latter has been developed with C++ language. As in our industrial application we are bounded by the execution time, we propose some resolution methods which define the suitable component and point positions in order to define the strategy of pick and place for each robot. These methods are based on the ant colony optimization, particle swarm optimization and genetic algorithms. To enhance the quality of the developed algorithms and to avoid local optima, we have coupled these algorithms with guided local search. After that, an exact method based on full enumeration is also developed to assess the quality of the developed methods. Then, we try to select the best algorithm which is able to get the best solutions with a small execution time. This is the main advantage of our methods compared to exact methods. This fact represents a great interest taking in consideration that the selected methods are used to manage the functioning of real industrial robotic assembly lines. Numerical results show that the selected algorithm performs optimally for the tested instances in a reasonable computation time and satisfies the industrial constraint.     

广义优先关系约束下Max-npv项目调度问题及其遗传算法

以往Max-npv项目调度问题的研究都假定活动之间的关系为单一结束-开始类型,现实中活动之间关系复杂多变,因此,将广义优先关系引入Max-npv项目调度问题中,构建了广义优先关系约束下的Max-npv项目调度模型。针对该优化模型设计了一种双层遗传算法,外层遗传算法负责任务执行模式的优化,内层遗传算法负责任务调度的优化。在内层遗传算法中,采用任务开始时间之差作为新的编码方式,大大简化了交叉变异算子,针对网络图中的环状结构设计了修复算子,确保了编码的有效性。通过一个算例对算法进行了测试,实验结果验证了算法的有效性。