Unsupervised learning-based equipment Anomaly Detection (AD) has become increasingly important in facilitating proactive yield and operations management in smart manufacturing. The authors designed a Spectral and Time Autoencoder Learning for Anomaly Detection (STALAD) framework to automate AD on individual sensory data items by integrating normality learning and hypothesis testing. Specifically, STALAD utilizes error sequences, the difference between the given data and the learned normality, to identify anomalies in each item. Although STALAD performs well without resorting much to knowledge about the data, its testing fails to consider relations among sensor measurements, especially the simultaneity of anomaly signals, which may help improve detection sensitivity and/or reduce false alarms. In this paper, we design a novel test scheme of error sequence fusion for anomaly detection (MESFAD), which fuses multiple error sequences to exploit the simultaneity of anomaly signals. The novelty of the MESFAD design has two folds: (i) evenly fusing standardized error sequences as a test statistic that amplifies simultaneous anomaly signals over noises, and (ii) probabilistic approximation model-based setting of the test threshold under a given false alarm rate. Analysis of and experiments on two-item cases show that MESFAD achieves superior sensitivity to STALAD in detecting a shift-type anomaly at the same false alarm rate.

Online knowledge sharing networks (KSNets) have made significant impacts on the economy as well as wellbeing of societies through sharing. One of the most successful KSNets is Wikipedia that allows users to create contents in a collaborative manner and to provide fast and easy access at no cost to users. Recent research, however, has shown that the numbers of “Wikipedians” and new page creations have been declining, reflecting decrease in user contributions and in new contents. To facilitate management for sustainability, this paper aims at quantitatively modeling how the decline in new contents affects the number of Wikipedians and in turn content creations, and predicting decline start time and speed based on available Wikipedia data. The novel modeling approach adopts auto-regression with an extended Bass Diffusion model (AREBDM) embedded to describe the Wikipedia-wide evolutions of the number of Wikipedians and content developments. Model parameters are then extracted by a nonlinear least square method from early Wikipedia data. Simulation predictions match well with actual Wikipedia decline trajectories of later stages. Our analysis shows that the decline of new page creation leads in time the decline of the number of new Wikipedians, and the decline speed increases with the decrease of new contents. Our approach therefore has the potential to predict decline time and speed so that proactive actions can be taken as early as possible.

Sharing of spectrum and radio access networks (RANs) has been a trend for future mobile networks to economically cope with fast growth in wireless data traffic and services. Although technical and regulatory advancements in dynamic spectrum sharing and wireless network virtualization (WNV) have brought new possibility of sharing, it is unclear how individual mobile network operators (MNOs) may benefit from sharing while in competition. In this regard, we propose a novel framework of independent service sharing coordination (ISSC). The framework sets up an independent platform that respectively collects information from all MNOs for coordination and ensures individual confidentiality at the same time. Each MNO plays both seller and buyer of shared resources and has chicken-egg problems between buy and sell decisions. The framework then adopts a Nash game theoretic approach, where the ISSC platform finds individual MNOs' strategies by iterating over demand estimation, resource allocation, price determination, and subscriber number estimation to find the best response for each MNO. Numerical study demonstrates that ISSC may facilitate all-win sharing of spectrum and RANs among competing MNOs, especially when MNOs have a medium level of demands with different spectrum availability and small cell coverages.

Licensed shared access (LSA) is one of the emerging modes of regulation for dynamic spectrum sharing management among incumbent wireless networks and secondary networks such as LTE mobile networks. This proof- of-concept demonstration of LSA exploits the Virtually Shared Spectrum Access (ViSSA) platform among various wireless networks and management entities. The ViSSA platform is an innovative integration of five parts by combining LTE small cells, emulators and management servers: i) a monitoring and management center with a spectrum repository that extends a license-exempt mode compliant geo-location database (GLDB/SR); ii) emulated incumbents that may register to GLDB/SR or directly access their spectrum; iii) a few LTE small cell networks of secondary accesses, each network having an LSA controller to communicate between GLDB/SR and its own network management; iv) feature-based sensing of incumbent signals emulated by a USRP; and v) implementation of LSRAI- and http-based communications among i) - iv) via Internet. On-site exhibition of ViSSA platform will demonstrate the novel LSA management of database-guided and sensing-based evacuation yielding to the incumbent. Demonstrations of re-activation of secondary LTE small cells in other available spectrum bands show the feasibility of completing evacuation and re-activation in 60 to 70 seconds.

Exploitation of underutilized spectrum is an effective approach to meet the explosive demand for wireless communications. When heterogeneous secondary networks (HSNs) are allowed to operate in the same underutilized spectrum, their coexistence becomes a critical issue. This paper considers a coexistence network that involves one spectrum provider (SP) sharing unused spectrum resources to multiple HSNs. To coordinate interference-free spectrum sharing among these HSNs, this paper adopts an auction-based approach and designs an Unilateral Vickrey-Clarke-Groves (VCG)-based Auction for HSNs (UVAH). UVAH has three novel designs that make it a practical and efficient solution. Firstly, effective partition of auction regions takes into account the SP's non-uniform amount of supply units in a target area. Secondly, based on the partition, UVAH provides HSNs with a highly expressive package bidding format to freely specify the amount of demand units and operating regions. Lastly virtual bidders by regions are introduced so as to resolve the revenue deficiency problem of VCG while retaining the property of truthfulness. With these three designs, UVAH maximizes the social welfare of the coexistence network without sacrificing the overall spectrum utilization. Numerical analysis shows that, compared to the existing solutions, UVAH improves spectrum utilization, spectrum revenue and HSN satisfaction by 9.96%, 17.26% and 121.73%, respectively.

Teaching material sharing networks (TMSNs) are a class of co-creating social networks (CSNets) which have made significant impacts on human civilization, where a network member is both content user and contributor. To understand and manage a TMSN, Chen and Chang, 2013, has developed a generalized Bass diffusion model (GBDM) embedded Discrete Time Markov chain (DTMC) to describe its growth dynamics of membership and content volume from the introduction to saturation stage. This paper is focused on modeling the dynamics of decline, which has two root causes of member leaving in lack of new teacher material (TM) uploads, defined as perceived innovations (PIs), and no retention once a member leaves. Our novel modeling methodology extends GBDM to describing the growth of leaving probability with the lack of new PIs and adds to DTMC a sink state to capture the no retention phenomenon. Key innovation of the GBDM extension lies in the embedding in its innovation coefficient term with an auto-regression (AR) model of PIs with time-discounting coefficients on new TM upload quantities over a number of recent time periods. Continuously low PI values over a few periods will lead to a high coefficient value of GBDM and hence high leaving probability. Simulation study verifies that teacher's leaving probability is high with small time-discounting coefficients of AR model which means small PI. The AR model captures the small PI will lead to the network decline. Furthermore, sustained monthly TM upload above a threshold is a critical to decline mitigation. To increase TM uploads per month, incentives design to attract member sharing are discussed, and it is helpful for application to co-creation network management.

Exploitation of short-interval spectrum availability offers an opportunity to better utilize spectrum for wireless communications. One significant class of short-interval secondary spectrum (SiSS) markets involves a primary license holder (PLH) renting out homogeneous spectrum units to a few competing Mobile Virtual Network Operators (MVNOs). This paper presents a design of SiSS market framework with brokerage services that mitigate information asymmetry and host auctions. The novel SiSS auction design is single-round and Vickrey-Clarke-Groves (VCG) auction-based and integrates two innovations. The first is a highly expressive bidding format that allows maximum bidding options to MVNOs in single submission. The second is a virtual bidder by the broker, whose bids are based on PLH's specification of per-unit reserve price, to avoid MVNOs' consideration of undesirable bidding strategies and guarantee that per-unit payment be no less than the reserve price. Such a design exploits the truthfulness of VCG and further achieves individual rationality and budget balance. Numerical experimentation shows that SiSS auction generates in average 31.3% higher per-unit revenue than VCG. For a SiSS market of 200 MVNOs and 500 spectrum units, computation time of clearing auction is within 15 seconds. These designs suit for SiSS applications in time efficiency and economic considerations.

Co-creation is an active, creative and social process to generate value for customers based on collaboration between suppliers and consumers. Teaching material sharing networks (TMSNs) are a class of co-creation networks. There is a positive feedback loop between individual teachers' creation of teaching materials (TMs) and richness of TM content shared, and TMSN members thus co-create TMs. In this paper, we focus on modeling co-creation in a TMSN and analyzing its effect on individual behaviors and network evolution. Our novel approach consists of three parts: (i) investigation of how TM creation increases with respect to the richness of content shared, where the new creation rate is marginally decreasing, (ii) generalization of Bass Diffusion Model (BDM) by replacing its constant innovation factor coefficient with a content richness-dependent log function to capture the positive feedback loop of innovation and the marginally decreasing feedback gain, and (iii) comparison between GBDM and BDM by using simulation to analyze how the inclusion of co-creation in modeling makes differences in individual behavior and network dynamics of a TMSN. Comparisons show that by capturing co-creation, the GBDM results in slower growth in membership and TM richness at the start-up stage, and then an earlier rise time of growth at a much faster growth rate than those by BDM. Numerical experimentation of GBDM demonstrates its potential for application to TMSN management.

In building emergency evacuation, the perception of hazards can stress crowds, evoke their competitive behaviors, and trigger disorder and blocking as they pass through narrow passages (e.g., a small exit). This is a serious concern threatening evacuees' survivability and egress efficiency. How to optimize crowd guidance while considering such effects is an important problem. Based on advanced microscopic pedestrian models and simulations, this paper establishes a new macroscopic network-flow model where fire, smoke, and psychological factors can evoke a crowd's desire to escape—the desired flow rate. Disorder and blocking occur when the desired flow rate exceeds the passage capacity, resulting in a drastic decrease of crowd movement in a nonlinear and random fashion. To effectively guide crowds, a divide-and-conquer approach is developed based on groups to reduce computational complexity and to reflect psychological findings. Egress routes for individual groups are optimized by using a novel combination of stochastic dynamic programming and the rollout scheme. These routes are then coordinated so that limited passage capacities are shared to meet the total need for joint movement. Numerical testing and simulation demonstrate that, compared with a strategy of merely using nearest exits, our solution can evacuate more people more rapidly by preventing or mitigating potential disorder and blocking at bottleneck passages.

Teaching material sharing networks (TMSN) may enrich teachers teaching capacity and quality through sharing. To effectively manage a network and its evolution, managers have to characterize members' behaviors such as joining/leaving the network (membership) and uploading/downloading teaching materials (sharing) and network state dynamics of membership, teaching material (TM) quantity and quality. The challenge presented in this paper is to design a methodology for modeling individual behaviors and network dynamics to predict network evolution based on empirical data of the network. SCTNet, a TMSN among elementary school teachers, serves as an exemplary network for designing the modeling methodology. Novelty of the design has three folds. i) Probabilistic individual behaviors are modeled to capture the individual difference. In particular, the features of probabilities with respect to states from data are slow start, fast growth, and saturation, thus the Bass diffusion model is adopted to model how the probabilities are affected by network states ii) How network states evolve over time with respect to the current states and individual behavior probabilities is then described by a set of Bass-Model embedded difference equations. iii) Because of limited empirical data for modeling, a Quasi-bootstrap based nonlinear least square (NLS) method is used to estimate Bass model parameters of the behavior probabilities along with the network evolution. User behaviors and network dynamics thus obtained were validated via an agent-based simulation (ABS), and the results observe that the accuracy of membership evolution reproduced by ABS matches the empirical data of SCTNet by more than 95%. This proven modeling accuracy shed the light for a better TMSN network management.

Group elevator scheduling has long been recognized as an important problem for building transportation efficiency, since unsatisfactory elevator service is one of the major complaints of building tenants. It now has a new significance driven by homeland security concerns. The problem, however, is difficult because of complicated elevator dynamics, uncertain traffic in various patterns, and the combinatorial nature of discrete optimization. With the advent of technologies, one important trend is to use advance information collected from devices such as destination entry, radio frequency identification, and sensor networks to reduce uncertainties and improve efficiency. How to effectively utilize such information remains an open and challenging issue. This paper presents the optimized scheduling of a group of elevators with destination entry and future traffic information for normal operations and coordinated emergency evacuation. Key problem characteristics are abstracted to establish a two-level separable formulation. A decomposition and coordination approach is then developed, where subproblems are solved by ordinal optimization-based local search, and top ranked nodes are selectively optimized by using dynamic programming. The approach is then extended to handle up-peak with little or no future traffic information, elevator parking for low intensity traffic, and coordinated emergency evacuation. Numerical testing results demonstrate near-optimal solution quality, computational efficiency, the value of future traffic information, and the potential of using elevators for emergency evacuation.

An empirical data-based design methodology is proposed for Internet-access management to improve congestion, uneven usage and fairness, especially during peak hours, over a free-of-charge or flat-rate network. The design methodology combines time-of-day pricing (TDP) with quota-based priority control (QPC). Core to the design methodology are the innovations in characterising user demand and quota-allocation behaviour with respect to time and pricing. In-depth analyses of empirical data reveal distinctive behaviour patterns of myopic and prudent quota allocations over time and both patterns indicate high preference for peak-hour access. The user models adopt general utility functions and capture how pricing affects user behaviour as prudent or myopic. Preference parameters of users' utility over time are then estimated by collecting easily measurable user volumes. The TDP design problem is formulated and solved as a Stackelberg game. Tested on the empirical data of a 5000-user network, the TDP design leads to significant improvements in peak-hour usage and fairness, peak shaving and load balancing over pure QPC. The methodology requires only two simple and short-period data collections from an operational network and takes about 1 min of CPU time for TDP calculation. Results demonstrate the effectiveness of our design methodology when applied to Internet-access environments with frequent changes.

Semiconductor wafer fab operations are characterized by complex and reentrant production processes over many heterogeneous machine groups with stringent performance requirements. Efficient composition of good scheduling policies from combinatorial options of wafer release and machine dispatching rules has posed a significant challenge to competitive fab operations. In this paper, we design a fast simulation-based methodology by an innovative integration of ordinal optimization (OO) and design of experiments (DOEs) to efficiently select a good scheduling policy for fab operations. Instead of finding the exact performance among scheduling policies, our approach compares their relative orders of performance to a specified level of confidence. Our new approach consists of three stages: performance estimation model construction using DOE, policy option screening process, and final simulation evaluation with intelligent computing budget allocation. The exponential convergence of OO is integrated into all the three stages to significantly improve computational efficiency. Simulation results of applications to scheduling wafer fabrications not only screen out good scheduling policies but also provide insights about how factors such as wafer release and the dispatching of each machine group may affect production cycle times and smoothness under a reentrant process flow. Most of the OO-based DOE simulations require 2-3 orders of magnitude less computation time than those of a traditional approach. Such a high speedup enables decision makers to explore much larger problems.Note to Practitioners- This paper designs a fast simulation-based methodology to compose a good scheduling policy from various dispatching rules of fab operations. The methodology innovatively applies DOE to estimate performance of dispatching rule combinations (policies) over various machines groups in a fab, screens out good enough policy options by using OO over the performance estimation, and allocates computation time intelligently to simulate potentially good options. Our study shows that OO-based DOE simulations require 2-3 orders of magnitude less computation time than those of a traditional approach. The high speedup enables fab managers to identify good scheduling policies from the many combinations of wafer release and dispatching rules.

In a building, effective operations of transportation systems including elevators, escalators, and stairs are vital. Among them, group elevator scheduling has long been recognized as an important issue for transportation efficiency. The problem, however, is difficult because of the large state space, various traffic profiles, and uncertainties. With the progress in information technology and sensor networks, one potential way is to use advanced traffic information to reduce uncertainties and optimize the performance. How to effectively utilize such information remains an open and challenging issue. This paper presents the optimized scheduling of a group of elevators with advanced traffic information for normal operations and coordinated emergency evacuation. A look-ahead time window is first introduced to model advanced information. Key characteristics of group elevator scheduling are abstracted to establish an innovative formulation. The objective function is transformed into an additive form to facilitate the decomposition of the problem into individual car subproblems. Subproblems are independently solved by using a local search method in conjunction with dynamic programming with a novel definition of stages, states, decisions, and costs to optimize single car dispatching. With surrogate optimization, local search is “good enough” to set multiplier updating directions. Individual cars are then coordinated through the updating of multipliers by using surrogate optimization for near-optimal solutions. Numerical testing results demonstrate that near-optimal solutions are obtained for problems of moderate sizes under selected traffic patterns. The results also show the value of advanced information through testing different window sizes and rescheduling intervals.

This paper presents the research and development of the hybridization of a mathematical programming approach with a promising evolution on the daily imaging scheduling problem for the newest generation of low-orbit, earth observation satellite, FORMOSAT-2. This NP-hard satellite scheduling problem belongs to a class of single-machine scheduling problems with salient features of job-assembly characteristic, sequence-dependent setup effect, and constraint of operating time window. We construct innovative hybrid techniques that incorporate the best of Lagrangian relaxation and Tabu search solution approaches to solve this scheduling problem. Numerical results demonstrate that the proposed hybrid algorithms are effective and efficient in applications to the real problems.

Many industries rely on maintenance networks to maintain their key assets, and a key characteristic of such maintenance services is the wide use of rotable parts. In view of today's time-based competition, efficiently managing the rotable inventory becomes imperative for a maintenance network to achieve short turn-around-times and low costs. This, however, is difficult in view of complicated and uncertain maintenance processes, and hybrid inventory replenishments from both new and refurbished parts. As the information on demands and replenishments is highly dependent on maintenance processes, and can be obtained, utilizing this information opens a new way to improve the inventory operational efficiency. This paper presents a new approach for rotable inventory control with the demand and replenishment information. Key characteristics of maintenance processes and hybrid replenishments are abstracted to form a novel model within the context of stochastic optimal control, where the demand and replenishment information is incorporated in the system state. Comparing to traditional approaches with a large-size augmented state, an aggregated state variable is defined based on inventory dynamics to reduce the number of required state components. A solution methodology based on stochastic dynamic programming (SDP) is developed, with stage-wise costs obtained in terms of aggregated state variables. Steady state solutions are computed offline, and are stored as inventory policies to be implemented by table lookup. Simulation results demonstrate the effectiveness of the approach on reducing inventory costs with the demand and replenishment information.

In a fab with heterogeneous machine groups, the number of scheduling policies grows in a combinatorial way because each machine group has its specific dispatching rules. In this paper, we design a fast simulation methodology by an innovative combination of the notions of ordinal optimization (OO) and design of experiments (DOE) to efficiently select a good scheduling policy for fab operation, Instead of finding the exact performance among scheduling policies, our approach compares their relative orders of performance to a specified level of confidence. The DOE method is exploited to largely reduce the number of scheduling policies to be evaluated by the OO-based simulation. Simulation results of applications to scheduling wafer fabrications show that most of the OO-based DOE simulations require 2 to 3 orders of magnitude less computation time than those of traditional approach, and the speedup is up to 7,000 times in certain cases.

This paper describes the design of a two-level hierarchical production scheduling engine, which captures the industrial practice of mass production semiconductor fabrication factories (fabs). The two levels of the hierarchy consist of a mid-term scheduler and a short-term scheduler, and are aimed at achieving coordination between the fab-wide objectives and local shop-floor operations. The mid-term scheduler maximizes weighted production flow to reduce the fab-wide cycle time and ensure on-time delivery by properly setting daily production target volumes and reference work-in-process (WIP) levels for individual part types and stages. Mid-term scheduling results are further broken down into more detailed schedules by the short-term scheduler. In addition to the same set of operational constraints in mid-term scheduling, the short-term scheduler includes the consideration of batching effects. It maximizes weighted production flow while tracking the daily production targets and the reference WIP levels specified by mid-term scheduling. The schedulers adopt a solution methodology with three ingredients; the Lagrange relaxation approach, network flow optimization, and Frank-Wolfe method. The scheduling tool is reasonably efficient in computation.

We exploit the speed of an ordinal optimization (OO)-based simulation tool designed by Hsieh et al. (1999) to investigate dynamic selection of scheduling rules for semiconductor wafer fabrication (FAB). Although a scheduling rule is a combination of loading wafer release and dispatching rules, this paper specifically focuses on dispatching when significant amount of wafers-in-process are held due to engineering causes and when major machine failures occur. Four prominent dispatching rules combined with the wafer release policy of workload regulation constitute a basic set of rule options. The dispatching rule may be weekly selected based on FAB states over a four-week horizon. A total of 756 rule options are then evaluated and ranked by the OO-based simulation tool under the performance index of mean cycle time and throughput rate. Results demonstrate the value of dynamic rule selection for uncertainty handling, the insightful selection of good rules and the needs for further research.

Computational efficiency is one of the major challenges of applying simulation to short-term operation scheduling of semiconductor wafer fabrication factories (fabs), which are characterized by re-entrant process flows, stringent production control requirements and fast changing technology and business environments. The paper explores the application of the ordinal optimization (OO)-based simulation technique to efficiently selecting good rules for scheduling wafer fabrications. An efficient simulation tool, which makes use of OO and optimal computing budget allocation techniques, is developed. Experiments with the OO-based simulation tool are conducted for static selection of good rules under different factors such as initial state, performance index and time horizon. Results indicate that one to two orders of computation time reduction over traditional simulations can be achieved and that what rules are good varies with factors of initial state, performance index and time horizon. These results motivate our further investigation about applications to dynamic selection of dispatching rules upon the occurrence of two significant uncertain events: holding of significant amount of wafers-in-process due to engineering causes and major machine failures. Results demonstrate the value of dynamic rule selection for uncertainty handling, the insightful selection of good rules and the needs for future research.

This paper presents a Lagrangian relaxation-based approach for production scheduling of flexible flow shops (PSFFS) where sequence-dependent setup effects are significant. PSPFS is first formulated as a separable integer programming problem with synchronization constraints between production and machine usage. Lagrangian relaxation is then applied, and the scheduling is decomposed into part production and machine scheduling. In these subproblems, there are network flow structures in the equality constraints describing machine status change and production flow balance. Our iterative algorithm applies a minimum cost network flow algorithm to individual subproblems and adopts an efficient surrogate subgradient method to optimize Lagrangian multipliers. A machine availability-searching heuristic finally adjusts the solution to satisfy all synchronization constraints by exploiting the network structure, economic interpretation of Lagrangian multipliers, and the slack time policy. Numerical results of 16 cases, each having 20 test problems, demonstrate that differences between the schedules obtained by our approach and the true optima are on average within 15%, CPU times spent are all less than 17 min on a Pentium-II personal computer. Among the problem dimension factors, the number of part types has the most significant effect on both optimality and computation efficiency. Application of the methodology to daily scheduling of a realistic integrated circuit testing facility of 30 machines takes about 6 min of CPU time to generate a near-optimal solution.

This paper presents an efficient, optimization model-based approach for scheduling the production of discrete-part, make-to-order type of flexible flow shops, where setup effects are negligible. A nominal scheduling algorithm based on Lagrangian relaxation and minimum cost linear network flow is first developed for scheduling under nominal conditions. Fast rescheduling algorithms that exploit the economic interpretation of the Lagrange multipliers and the network structure of production flows are then proposed for timely adjusting the nominal schedule to cope with disturbances. Numerical results on realistic examples demonstrate that our methodology is quite effective; it generates near-optimal schedules, provides relatively smooth adjustment for small disturbances, and is computationally efficient.>

This paper develops a new method for synthesizing deadlock avoidance controllers (DACs) that realize job and machine dispatching policies of a flexible manufacturing system (FMS) into deadlock free control actions. Such controllers not only keep the FMS capable of repeating any of its operations, but also achieve a high resource utilization under any given dispatching policy. Our methodology is based on an untimed Petri net formalism. It consists of four ingredients: 1) a bottom-up approach for synthesizing a controlled production Petri net (CPPN) model of a FMS; 2) a necessary and sufficient liveness condition based on decomposition of the CPPN into controlled production subnets and the concept of minimal resource requirements; 3) a sufficient procedure to test whether the liveness condition is kept after a control action is executed; and 4) an algorithm that combines the test procedure with the given dispatching policy to generate valid and utilization maximizing control actions. We assess that this method is of polynomial time complexity and show that it results in a much larger class of controls than that of an existing deadlock avoidance scheme.>

The authors present an integrated framework for order and production scheduling of a discrete-part, make-to-order flow shop. They first formulate the integrated problem and then decompose it by applying Lagrangian relaxation into subproblems of order scheduling, production scheduling, and overtime capacity allocation, which match the operational functions in a manufacturing organization, and form a dual problem to optimize the Lagrange multipliers for relaxation. which are interpreted as marginal costs. The solution algorithm has a structure that clearly captures the interrelationship among subproblems and provides a framework for integration. Exploiting such a framework. effective rescheduling algorithms for handling new order insertion and capacity loss are developed.>

The authors present an efficient, optimization model-based approach for scheduling the production of discrete-part, make-to-order type of flexible flow shops, where setup effects are negligible. A nominal scheduling algorithm based on Lagrangian relaxation and minimum cost linear network flow is developed for scheduling under nominal conditions. Fast rescheduling algorithms that exploit the economic interpretation of Lagrange multipliers and the network structure of production flows are proposed for timely adjustment of the nominal schedule to cope with disturbances. Numerical results on realistic examples demonstrated that the methodology was quite effective. It generated near-optimal schedules, provided relatively smooth adjustments and was computationally efficient.>