FMS scheduling as cooperative problem solving

This paper describes an FMS scheduling method that treats an FMS as a group of problem-solving agents cooperating to perform manufacturing jobs. The main thrusts of such a method include the ability to handle the dynamically changing production conditions, its taking into account the communication method, the improved reliability, and the use of distributed control. The paper emphasizes research issues associated with various aspects of the cooperative problem-solving method, including: (1) dynamic task assignments, (2) the coordination mechanism, and (3) knowledge-based scheduling as problem solving. A simulation study which compares the performance of the cooperative problem solving approach with that of the more traditional scheduling approaches is also reported.     

ARMMS: Analogical reasoning model management system for multicriteria vehicle scheduling

The transportation industry problem of scheduling vehicles combines the spatial characteristics of routing with time domain considerations of activity schedules. The problem is complex because of the numerous interacting constraints in the spatial and time domains. Further, some of the constraints are flexible and some arise in real-time. The scheduling problem is often presented with multiple objectives that are not all economic in nature and which can be contradictory to one another. In response to these needs, this paper describes an analogical reasoning model management system, called ARMMS, designed in the domain of vehicle scheduling. ARMMS consists of knowledge bases and data bases, a truth maintenance system, a user interface, an inference engine, a learning mechanism, and a model library. Given a scheduling problem, ARMMS searches its memory for solutions. If no solution is available, ARMMS falls back on an analogical problem solving approach in which similar experience can be recalled, and solutions to new, but similar, problems can be constructed. If no similar experience exists, ARMMS intelligently selects an appropriate algorithmic model from its model library, based on the input parameters and problem type, to solve the given problem. By combining experts' knowledge, analogical problem-solving approaches, and algorithmic methods, ARMMS provides an efficient problem-solving approach for vehicle scheduling and routing. ARMMS is also a feasible base for the development of intelligent model management systems.     

Application of neural-network methods for prediction of the job execution characteristics in multiprocessor computing systems

In recent years, the architecture of multiprocessor computing systems has become more and more complex and needs in large amounts of computations rapidly increase, together with the number of users of multiprocessor systems. Because of a large number of factors acting on the user job inside such a system, analytical approaches to solution of the job scheduling problem are very complex and expensive. This paper considers a neural-network approach to scheduling the computations in multiprocessor systems (which uses a method that predicts certain characteristics of the job execution procedure) and estimates the applicability of this approach in real conditions. Ways for increasing the accuracy of prediction are proposed.     

小批量随机块坐标下降算法

针对机器学习中广泛存在的一类问题：结构化随机优化问题（其中“结构化”是指问题的可行域具有块状结构,且目标函数的非光滑正则化部分在变量块之间是可分离的）,我们研究了小批量随机块坐标下降算法（mSBD）。按照求解非复合问题和复合问题分别给出了基本的mSBD和它的变体,对于非复合问题,分析了算法在没有一致有界梯度方差假设情况下的收敛性质。而对于复合问题,在不需要通常的Lipschitz梯度连续性假设条件下得到了算法的收敛性。最后通过数值实验验证了mSBD的有效性。     

Resource-constrained job scheduling with recyclable resources

In resource-constrained project scheduling problems, resources are typically classified as being either renewable, non-renewable, or doubly-constrained. A new resource classification, recyclable, is introduced. Notation and a generalized problem formulation are developed for resource-constrained job scheduling problems where resources are recyclable. This foundation is then used for studying the single-machine scheduling problem with tooling constraints. For a given set of jobs, the problem is to find the job sequence, tool type quantities, and tool recycling schedule such that the sum of job completion times and quantity of tools allocated are both minimized. Two solution approaches are developed, and examples are used to compare and contrast the approaches. The results indicate that the ‘traditional’ job scheduling approach (i.e. schedule jobs first, then tools) can lead to sub-optimal solutions. Furthermore, by scheduling jobs and tools simultaneously, it may be possible to attain a given level of performance with fewer tools.     

Optimal size-based opportunistic scheduler for wireless systems

Modern wireless cellular systems are able to utilize the opportunistic scheduling gain originating from the variability in the users’ channel conditions. By favoring users with good instantaneous channel conditions, the service capacity of the system can be increased with the number of users. On the other hand, for service systems with fixed service capacity, the system performance can be optimized by utilizing the size information. Combining the advantages of size-based scheduling with opportunistic scheduling gain has proven to be a challenging task. In this paper, we consider scheduling of data traffic (finite-size elastic flows) in wireless cellular systems. Assuming that the channel conditions for different users are independent and identically distributed, we show how to optimally combine opportunistic and size-based scheduling in the transient setting with all flows available at time 0. More specifically, by utilizing the time scale separation assumption, we develop a recursive algorithm that produces the optimal long-run service rate vectors within the corresponding capacity regions. We also prove that the optimal operating policy applies the SRPT-FM principle, i.e., the shortest flow is served with the highest rate of the optimal rate vector, the second shortest with the second highest rate, etc. Moreover, we determine explicitly how to implement the optimal rate vectors in the actual time slot level opportunistic scheduler. In addition to the transient setting, we explore the dynamic case with randomly arriving flows under illustrative channel scenarios by simulations. Interestingly, the scheduling policy that is optimal for the transient setting can be improved in the dynamic case under high traffic load by applying a rate-based priority scheduler that breaks the ties based on the SRPT principle.     

Incorporating geo-metallurgical information into mine production scheduling

Economic characterization of mining parcels depends upon geo-metallurgical properties, which vary throughout orebody. Mine production scheduling should aim to obtain maximum utility from orebody in such a way as to ensure mine–mill reconciliation. As heterogeneity of geo-metallurgical variables increases, the scheduling will be a very complicated task. Geo-metallurgical and financial data used in the mine production scheduling are based on simulation and/or estimation generated from sparse drilling and unknown future events. Therefore, the scheduling process involves a significant degree of uncertainty. In order to deal with the uncertainty stemmed from geo-metallurgical and financial variables, two approaches are recommended in this paper. Firstly, mine production scheduling is formulated as a problem of stochastic programming with recourse. The extraction periods of mining blocks are treated as the first-stage variables and the block destinations represents a recourse vector. It is observed that the solution is implicitly robust. Secondly, the scheduling is expressed as a maximin problem to extract more uniform metal quantity in periods to coincide with mill requirements instead of maximization of net present value because the blending constraint in the traditional approach forces more uniform production. In the case where there is correlation between grade and geo-metallurgical variables, this model generates reasonably good results.     

Expert systems in production scheduling

One area of computer-related studies that has recently been receiving considerable publicity is the development of expert systems. The more noteworthy applications of this approach to problem-solving are still in engineering and the natural sciences, but a growing number of applications to problems in business management are beginning to appear. This paper reviews recent research and discusses the applicability of an ‘expert system’ approach to problems in production scheduling.     

Job scheduling with forbidden setups and two objectives using genetic algorithms and penalties

One of the most important tasks in service and manufacturing systems is how to schedule arriving jobs such that some criteria will be satisfied. Up to now there have been defined a great variety of scheduling problems as well as corresponding models and solution approaches. Most models suffer from such more or less restrictive assumptions like single machine, unique processing times, zero set-up times or a single criterion. On the other hand some classical approaches like linear or dynamic programming are practicable for small-size problems only. Therefore over the past years we can observe an increasing application of heuristic search methods. But scheduling problems with multiple machines, forbidden setups and multiple objectives are scarcely considered. In our paper we apply a Genetic Algorithm to such a problem which was found at a continuous casting plant. Because of the forbidden setups the probability for a random generated schedule to be feasible is nearly zero. To resolve this problem we use three kinds of penalties, a global, a local and a combined approach. For performance investigations of these penalty types we applied our approaches to a real world test instance with 96 jobs, three machines and two objectives. We tested five different penalty levels with 51 independent runs to evaluate the impact of the penalties.     

Airline Crew Scheduling: State-of-the-Art

The airline industry is faced with some of the largest scheduling problems of any industry. The crew scheduling problem involves the optimal allocation of crews to flights. Over the last two decades the magnitude and complexity of crew scheduling problems have grown enormously and airlines are relying more on automated mathematical procedures as a practical necessity. In this paper we survey different approaches studied and discuss the state-of-the-art in solution methodology for the airline crew scheduling problem. We conclude with a discussion about promising areas for further work to make it possible to get very good solutions for the crew scheduling problem.     

A school bus scheduling problem

This paper introduces a school bus scheduling problem wherein trips for each school are given. A trip consists of a sequence of bus stops and their designated school. Each school has its fixed time window within which trips should be completed. A school bus can serve multiple trips for multiple schools. The school bus scheduling problem seeks to optimize bus schedules to serve all the given trips considering the school time windows. We first model the problem as a vehicle routing problem with time windows (VRPTW) by treating a trip as a virtual stop. Two assignment problem based exact approaches are then proposed for special cases and a heuristic algorithm is proposed for more general cases. Benchmark problems and computational experiments are presented. Computational experiments show the effectiveness of the proposed approaches.     

Integration of production planning and scheduling using an expert system and a genetic algorithm

In the traditional approaches, processes of planning and scheduling are done sequentially, where the process plan is determined before the actual scheduling is performed. This simple approach ignores the relationship between the scheduling and planning. Practical scheduling systems need to be able to react to significant real-time events within an acceptable response time and revise schedules appropriately. Therefore, the author proposes a new methodology with artificial intelligence to support production planning and scheduling in supply net. In this approach, the production planning problem is first solved, and then the scheduling problem is considered with the constraint of the solution. The approach is implemented as a combination of expert system and genetic algorithm. The research indicates that the new system yields better results in real-life supply net than using a traditional method. The results of experiments provide that the proposed genetic algorithm produces schedules with makespan that is average 21% better than the methods based on dispatching rules.     

A metacognitive-based instruction for Primary Four students to approach non-routine mathematical word problems

Many Primary Four students (fourth graders) in Singapore have difficulties initiating or persevering in the problem-solving process even though the curriculum has focused on problem solving since 1992. This study served to examine the role of metacognition in self-regulated problem solving. The study, a quasi-experimental pretest–posttest design involving a convenience sample of 63 students from two intact mixed-ability Primary Four classes, examined the impact of using a metacognitive scheme that focuses on the understanding and planning stages of Pòlya’s four-stage approach on students’ mathematical problem-solving behavior, performance and attitudes. The findings revealed that the metacognitive-based scheme had a positive impact on students’ understanding of the problem posed, solution planning, confidence in and personal control of problem-solving behavior and emotions. It had also helped them to initiate and persevere in the problem-solving process to achieve a higher level of problem-solving success. Limitations and instructional implications are discussed.     

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.     

Local search algorithms for the multiprocessor flow shop scheduling problem

The multiprocessor flow shop scheduling problem is a generalization of the ordinary flow shop scheduling problem. The problem consists of both assigning operations to machines and scheduling the operations assigned to the same machine. We review the literature on local search methods for flow shop and job shop scheduling and adapt them to the multiprocessor flow shop scheduling problem. Other local search approaches we consider are variable-depth search and simulated annealing. We show that tabu search and variable-depth search with a neighborhood originated by Nowicki and Smutnicki outperform the other algorithms.     

Integrated production scheduling and distribution planning in dairy supply chain by hybrid modelling

In this paper we address the production scheduling and distribution planning problem in a yoghurt production line of the multi-product dairy plants. A mixed integer linear programming model is developed for the considered problem. The objective function aims to maximize the benefit by considering the shelf life dependent pricing component and costs such as processing, setup, storage, overtime, backlogging, and transportation costs. Key features of the model include sequence dependent setup times, minimum and maximum lot sizes, overtime, shelf life requirements, machine speeds, dedicated production lines, typically arising in the dairy industry. The model obtains the optimal production plan for each product type, on each production line, in each period together with the delivery plan. The hybrid modelling approach is adopted to explore the dynamic behavior of the real world system. In the hybrid approach, operation time is considered as a dynamic factor and it is adjusted by the results of the simulation and optimization model iteratively. Thus, more realistic solutions are obtained for the scheduling problem in yoghurt industry by using the iterative hybrid optimization-simulation procedure. The efficiency and applicability of the proposed model and approach are demonstrated in a case study for a leading dairy manufacturing company in Turkey.     

Efficient neighborhood search for the one-machine earliness–tardiness scheduling problem

This paper addresses the one-machine scheduling problem where the objective is to minimize a sum of costs such as earliness–tardiness costs. Since the sequencing problem is NP-hard, local search is very useful for finding good solutions. Unlike scheduling problems with regular cost functions, the scheduling (or timing) problem is not trivial when the sequence is fixed. Therefore, the local search approaches must deal with both job interchanges in the sequence and the timing of the sequenced jobs. We present a new approach that efficiently searches in a large neighborhood and always returns a solution for which the timing is optimal.     

Dual decomposition of a single-machine scheduling problem

We design a fast ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints. We show that designing such an algorithm is relatively simple if a scheduling problem is formulated in terms of the job completion times rather than as an 0–1 linear program. Also, we show that upon termination of such an ascent direction algorithm we get a dual decomposition of the original problem, which can be exploited to develop approximative and enumerative approaches for it. Computational results exhibit that in our application the ascent direction leads to good Lagrangian lower and upper bounds.