Optimal Schedule Research Articles

Scheduling a Single-Arm Two-Cluster Tool With a Process Module Failure Subject to Wafer Residency Time Constraints

Multi-cluster tools are widely adopted in semiconductor manufacturing. When a process module (PM) at a step fails, a multi-cluster tool cannot complete the process recipe of work-in-process wafers and must be forced to enter a closedown process to be empty. To increase the throughput of a wafer fab, it is economically significant to shorten the failure-closedown process. However, due to the wafer residency time constraints, it is highly challenging to respond to a PM failure and find a corresponding optimal schedule. By assuming no parallel PM at a step, this work is the first to study this important issue for scheduling multi-cluster tools. We analyze the task sequences and synchronization conditions for robot activities to avoid deadlock in a shared buffer module. Upon these analyses, for process-dominant multi-cluster tools whose optimal steady-state schedule is known, algorithms are proposed to synthesize the proper sequences for robots in case of PM failures, then, a nonlinear program model is proposed to find an optimal schedule for the corresponding closedown process or decide no feasible solutions. The proposed model can uniformly deal with different scenarios of PM failures. Examples are given to illustrate the application of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In a wafer fab, there are hundreds, even thousands, of cluster tools. It is common that a failure of a processing module happens in a cluster tool. How to intelligently respond to such a random failure in a multi-cluster tool is an important issue in real-world production. This paper studies the scheduling problem of a multi-cluster tool in case of a failure at a PM. For a multi-cluster tool in case of a failure module, the proposed method can significantly reduce the loss of work-in-process wafers and shorten the closedown process.

On the time complexity of achieving optimal throughput in time division multiple access communication networks

&lt;abstract&gt;&lt;p&gt;The fundamental problem of finding transmission schedules for achieving optimal throughput in time division multiple access (TDMA) communication networks is known to be NP-hard. Let $ \mathcal{N} $ be a scheduled $ k $-time slot TDMA network with $ n $ stations and $ m $ links. We showed that an optimal link schedule for $ \mathcal{N} $ can be computed recursively with a recursion tree of logarithmic depth $ \mathcal{O}(\ln m) $ in expectation. Additionally, we showed that optimal link schedules for those TDMA networks, with recursion trees of depth meeting the expectation, can be found in time $ \mathcal{O}(m^{2+\ln k}) $. Likewise, we discuss analogous results for computing optimal station schedules of TDMA networks.&lt;/p&gt;&lt;/abstract&gt;

Allocation of non-uniform complex of resources in production systems. Scheduling and correction of deadlines

The problem of planning a job complex with the use of resources of various types − renewable (performers who can differ with the productivity) and several types of non-renewable is considered. We allow interruptions, and switching from one performer to another and performing one work simultaneously by several performers. The available number of performers at different times is not constant, and their productivity may vary. A developed polynomial algorithm finds the optimal allocation of resources and builds the optimal schedule of jobs. A pseudopolynomial algorithm for finding the optimal allocation of resources of minimal cost has been developed. These algorithms based on building a flow network model and modifying the packing procedure. An algorithm for the optimal allocation of resources and the construction of an optimal schedule for the case of a heterogeneous set of works is proposed.

Optimization of the Cost of Repetitive Construction Projects Using Computerized Iteration Method

This study introduces an iterative scheduling method that combines two approaches for managing repetitive construction projects: the Critical Path Method (CPM) and the Repetitive Scheduling Method (RSM). The primary objective of this study is to demonstrate how optimization techniques can be applied to minimize the cost of construction projects within a defined range, spanning from the shortest to the longest possible project durations. In the shortest project duration (as determined by CPM), all activities are allocated idle times based on precedence constraints, while in the longest duration (as determined by RSM), there is no idle time allocated. To calculate the optimal schedule, a computerized iterative method specifically designed for this purpose considers all possible combinations of activities with and without idle time. The optimum schedule is the one that minimizes the total project cost. The study reveals that by using an Excel spreadsheet, it is feasible to deterministically optimize the cost of repetitive construction projects, achieving the minimum cost. This minimization process can also be implemented as a Python application. Notably, this proposed system provides multiple optimal solutions, enabling managers to select the most suitable one. This advantage distin-guishes it from conventional methods, such as genetic algorithms and other optimization techniques. However, there are some limitations when applying this application, one of which is the maximum capacity available to run the application.

Safety and early efficacy of involved-field SBRT for nodal oligo-recurrent prostate cancer.

Following treatment for localized prostate cancer, a subset of men will develop recurrent disease in the abdominopelvic nodes. For radiation therapy (RT), the optimal treatment volume, fractionation schedule, and dose remain unanswered questions. We report early outcomes for patients treated with involved-field stereotactic body radiation therapy (SBRT) (IF-SBRT) for nodal oligo-recurrent (NOR) prostate cancer. Between January 2018 and October 2023, 67 patients with a median age of 75 with NOR prostate cancer treated with 74 courses of IF-SBRT at Georgetown were eligible for this analysis. NOR was defined as any volume of disease that could be safely treated within an IF. All patients were treated with five-fraction IF-SBRT (27.5-35 Gy). The IF treatment volume was defined as the nodal basin containing the gross disease as well as the immediately adjacent basins. Disease progression was defined as a prostate-specific antigen (PSA) rise above the pretreatment baseline or initiation of a second treatment. Local control and progression-free survival were calculated using the Kaplan-Meier method. Detection of pre-SBRT NOR was ascertained by prostate-specific membrane antigen (PSMA) (38%), fluciclovine (50%), or MRI/CT (12%). Median follow-up was 50 months (1-262). The median pre-salvage PSA was 6.5 ng/mL (range, 0.1-335). The median number of involved nodes was 3 (range, 1-16). The local control at 1 and 2 years was 98% and 93%, respectively. The 1- and 2-year progression-free survival was 78% and 50%, respectively. Twenty percent of treatment courses were followed by acute Grade 2 gastrointestinal (GI) toxicity: diarrhea (9%) and/or nausea (14%). Two patients (3%) experienced late Grade 2 nausea. On univariate analysis, measures of disease volume such as hormone sensitivity (p = 0.03), increasing involved node number (p = 0.008), and abdominal treatment (p = 0.03) were significantly associated with GI toxicity. With the widespread adoption of PSMA agents, NORs are likely to increase. The optimal combination of local and systemic therapy in this population is unknown. With a favorable toxicity profile, IF-SBRT represents a safe and convenient local therapy treatment option for an elderly patient population. Patient- and treatment-related factors such as a large number of involved nodes and/or abdominal treatment may be associated with an increased risk of GI toxicity.

EFFICIENCY OF AUTONOMOUS HEATING SYSTEM IN INTERMITTENT MODE WITH HEAT ACCUMULATOR

Theeffectiveness of the autonomous heating system in intermittent mode with a heat accumulator of the building of the educational building of the Odessa National Polytechnic University was studied. The main requirements for solving the task of optimizing the room heating process are formulated. Ways to increase the efficiency of morning room heating are considered. On the basis of the developed mathematical model of the dynamics of thermal processes of the elements of the autonomous heating system, the regimes of the thermal load of the heating system when the temperature of the outside air changes are investigated. The main directions for improving the heat supply of buildings in the mode of intermittent-frequent heating are proposed and their practical application in modeling and research of the system is taken into account. The results of optimizing the daily load schedules of the main elements of the autonomous heating system under variable external conditions are presented. The optimal daily schedules of the dynamics of indoor air temperature and network water temperature of the heating system are given. The dependence of the filling factor of the load schedule of the heating system and the heat generator on the outside air temperature in the range from 5 to –15 °С was studied. The effect of daily heat accumulation on the reduction of the nominal thermal power of the heat generator was studied. Heat savings were evaluated based on the results of optimization of load modes of the proposed system in the intermittent heating mode compared to the 24-hour heating mode, which amounted to 25.2%, respectively. Based on the results of the study, it was concluded that daily heat accumulation for heating systems operating in intermittent mode is an effective measure for increasing the efficiency of morning room heating, achieving the maximum possible thermal power of the heating system during heating and reducing its duration to 1 hour. Keywords: intermittent heating mode, mathematical modeling, heat accumulation, morning heating of the room, load schedule filling factor, optimization of load modes

To flare or not to flare: patients' and rheumatologists' perceptions on the on-flare retreatment strategy of rituximab in rheumatoid arthritis.

Several retreatment strategies exist for rituximab in rheumatoid arthritis (RA). In some countries, reimbursement criteria require a loss of disease control for rituximab retreatment. Understanding the patients' and rheumatologists' perceptions regarding this retreatment strategy would be informative in identifying the optimal treatment administration schedule. This study aimed to uncover patients' and rheumatologists' perceptions regarding retreatment strategies of rituximab. Qualitative study - semi-structured interviews. Patients with RA, treated with rituximab, and rheumatologists were invited to participate in a qualitative study consisting of individual, in-depth, semi-structured interviews. Interviews were analysed according to the Qualitative Analysis Guide of Leuven. A total of 16 patients and 13 rheumatologists were interviewed. Benefits (e.g. decreased risk of overtreatment, cost savings and long-lasting effectiveness of rituximab) and barriers (e.g. fluctuating disease activity, slow mode of action and increased glucocorticoid use) of on-flare retreatment were identified. To effectively treat on-flare, flares must first be identified timely. Both stakeholder groups acknowledged that patients are capable of recognizing flares. However, the patient's ability to discriminate between inflammatory and other types of pain was perceived as difficult. Furthermore, patients and rheumatologists stressed that patients must timely seek professional help in case of a flare, followed by a swift response from the rheumatologists. Remarkably, retreatment was approached in various ways among rheumatologists, and not always adhering strictly to the on-flare reimbursement criteria. This study revealed that both stakeholder groups perceived the heterogeneity in recognition of and reaction to a flare as important in influencing the effectiveness of the on-flare retreatment strategy. Moreover, this study identified the benefits and barriers of treating on-flare, which could be informative for daily practice decisions.

Revolutionizing Agriculture: Harnessing the Power of Artificial Intelligence for Sustainable Farming Practices

Artificial Intelligence (AI) has emerged as a groundbreaking technology with the potential to revolutionize various sectors, and agriculture stands as one of its prime beneficiaries. This paper delves into the transformative impact of AI in agriculture, exploring its multifaceted applications, benefits, and implications.AI-powered technologies, such as machine learning, robotics, and data analytics, are increasingly being integrated into agricultural practices, offering innovative solutions to age-old challenges. One of the pivotal areas where AI is making significant strides is in precision agriculture. Through the utilization of drones, sensors, and satellite imagery, AI enables farmers to collect real-time data on soil quality, crop health, and weather conditions. By leveraging this data, farmers can make informed decisions regarding irrigation, fertilization, and pest management, thereby optimizing resource usage and enhancing crop yields.Furthermore, AI-driven predictive analytics empower farmers to anticipate crop diseases, pests, and adverse weather events, allowing for proactive mitigation strategies. This predictive capability not only minimizes yield losses but also reduces reliance on chemical inputs, fostering sustainable agricultural practices. Moreover, AI facilitates autonomous farming machinery equipped with advanced sensors and actuators, enabling precise and efficient field operations. This not only enhances productivity but also alleviates the labor-intensive nature of traditional farming, addressing the challenge of labor scarcity in many agricultural regions.The impact of AI in agriculture extends beyond farm-level operations to supply chain management and market forecasting. AI algorithms analyze vast volumes of data encompassing market trends, consumer preferences, and climatic patterns to provide insights into optimal planting schedules, pricing strategies, and distribution logistics. By optimizing supply chain processes, AI enhances efficiency, minimizes wastage, and ensures food security.However, the widespread adoption of AI in agriculture raises pertinent concerns regarding data privacy, cybersecurity, and socioeconomic disparities. The collection and utilization of vast amounts of agricultural data necessitate robust data governance frameworks to safeguard farmer privacy and prevent unauthorized access. Additionally, the digital divide between large-scale commercial farms and smallholder farmers must be addressed to ensure equitable access to AI technologies. Governments, policymakers, and industry stakeholders need to collaborate to develop inclusive policies and infrastructure that foster the equitable deployment of AI in agriculture.In conclusion, the integration of AI in agriculture represents a paradigm shift towards more sustainable, efficient, and resilient food production systems. By harnessing the power of AI-driven technologies, farmers can mitigate risks, optimize resource utilization, and improve livelihoods. However, realizing the full potential of AI in agriculture requires concerted efforts to address regulatory, ethical, and socioeconomic challenges. Through strategic collaboration and innovation, AI has the potential to transform agriculture, ensuring food security and sustainability for future generations.

A Hybrid Bearing Prognostic Method With Fault Diagnosis and Model Fusion

Accurate bearing fault diagnosis and prognosis (FDP) is critical for optimal maintenance schedules, safety and reliability. The existing methods face some problems and challenges in detecting the starting time for prognosis and using a single model to describe fault dynamics. With these motivations, this paper presents a hybrid bearing FDP framework with fault detection and automatic fault model selection. In the proposed approach, convolutional neural network is used to detect fault and select the appropriate fault dynamic model. To improve the performance, power spectrum of vibration signals are fused with operating conditions to built information maps for fault detection and model selection. After a fault is detected, a Bayesian method is triggered to estimate the fault state and predict the remaining useful life. In the prognosis, Dempster-Shafer theory is employed to fuse prediction results from different models if necessary. The proposed approach is verified with bearings under different operating conditions. Experimental results and comparison studies verify the high accuracy and efficiency of the proposed method.

Optimal non-linear tax schedule with investment in education

Optimal non-linear tax schedule with investment in education

Promotion of tumor angiogenesis and growth induced by low-dose antineoplastic agents via bone-marrow-derived cells in tumor tissues.

More research is needed to solidify the basis for reasonable metronomic chemotherapy regimens due to the inconsistent clinical outcomes from studies on metronomic chemotherapy with antineoplastic agents, along with signs of a nonlinear dose-response relationship at low doses. The present study therefore explored the dose-response relationships of representative antineoplastic agents in low dose ranges and their underlying mechanisms. Cyclophosphamide (CPA) and 5-fluorouracil (5-Fu) were employed to observe the effects of the frequent administration of low-dose antineoplastic agents on tumor growth, tumor angiogenesis, and bone-marrow-derived cell (BMDC) mobilization in mouse models. The effects of antineoplastic agents on tumor and endothelial cell functions with or without BMDCs were analyzed in vitro. Tumor growth and metastasis were significantly promoted after the administration of CPA or 5-Fu at certain low dose ranges, and were accompanied by enhanced tumor angiogenesis and proangiogenic factor expression in tumor tissues, increased proangiogenic BMDC release in the circulating blood, and augmented proangiogenic BMDC retention in tumor tissues. Low concentrations of CPA or 5-Fu were found to significantly promote tumor cell migration and invasion, and enhance BMDC adhesion to endothelial cells in vitro. These results suggest that there are risks in empirical metronomic chemotherapy using low-dose antineoplastic agents and the optimal dosage and administration schedule of antineoplastic agents need to be determined through further research.

Multi-objective Feed Reservoir Control via Optimal Pump Scheduling

Pumping acid mine drainage water from source to the feed reservoir that feeds the eMalahleni Water Reclamation Plant, using fixed-speed pumps, in an optimal manner takes the form of a mixed-integer quadratic programming problem. A simulation study is presented where the most optimal pumping schedule is determined using a differential evolution algorithm. The pumping schedule has to adhere to feed reservoir level constraints while minimizing composition fluctuations. The optimized pumping schedule leads to overall stabilization of the feed reservoir composition and level, which has a direct benefit to the operation of the processing plant.

JAK Inhibitors in Cytokine Storm Syndromes.

Cytokine storm syndromes (CSSs) comprise a group of severe and often fatal hyperinflammatory conditions driven by the overproduction of pro-inflammatory cytokines by activated cells of the immune system. Many of the CSS-associated cytokines mediate their downstream effects by signaling through the Janus kinases (JAKs) and signal transducers and activators of transcription (STATs). In addition, several of these cytokines are produced downstream of JAK/STAT pathway activation. Therefore, targeting JAK/STAT signaling using small molecule JAK inhibitors has become an increasingly appealing therapeutic option to dampen hyperinflammation in patients with CSSs. Application of JAK inhibitors in preclinical CSS models has shown improvements in multiple sequelae of hyperinflammation, and there is growing clinical evidence supporting the efficacy of JAK inhibition in patients with these conditions. Although generally well tolerated, JAK inhibitor use is not without potential for toxicity, especially in settings like CSSs where end-organ dysfunction is common. More prospective clinical trials incorporating JAK inhibitors, alone or in combination with other immunomodulatory therapies, are necessary to determine the optimal dosing, schedule, efficacy, and tolerability of these agents for patients experiencing CSSs.

Online Rectangle Packing Algorithm for Swapped Battery Charging Dispatch Model Considering Continuous Charging Power

The vigorous development of electric vehicles (EVs) is an important means of reducing carbon emissions and mitigating environmental problems such as the greenhouse effect. Battery swapping stations (BSSs) can both provide battery swapping services for large-scale EVs and charge batteries centrally. As the supply of fully charged batteries in the BSS shrinks, it becomes necessary to schedule the charging of the depleted batteries rapidly that users have swapped for fully-charged ones. The charging schedule for depleted batteries must be made without knowledge of future battery arrivals. In this context, this paper develops a mathematical model for online charging scheduling of BSSs, formulates the charging strategy as a two-dimensional rectangle packing problem, and quickly calculates the scheduling arrangement of batteries by partitioning the remaining available capacity of a BSS. Since there are limited battery types within the BSS which can provide battery replacement services, this paper supplements the proposed model with known battery types, which improves the utilization of the available capacity of BSSs. Finally, numerical results verify the effectiveness of the proposed model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Electric vehicles (EVs) are becoming an alternative way to reduce carbon emissions in transportation systems. Herein, the optimal battery charging problem is the core problem when it comes to dispatching a huge number of EVs. Up to now, battery-swapping is widely used for EVs due to its simple, convenient way. Furthermore, a business model for the battery swapping stations (BSSs) is brought up, where EV users send their depleted batteries to the BSS and the BSS provides the users with a fully charged replacement battery from its warehouse, which only takes a few minutes. Since the maximum charging power of the BSS is limited by the capacity of the transformer connecting the BSS to the power grid, the BSS will adopt an optimal charging schedule that maximizes the charging benefit for large quantities of depleted batteries in the warehouse. However, the challenge is that the charging schedule for depleted batteries must be made without knowledge of future battery arrivals because the EV behaviors are difficult to predict. To address this problem, this paper developed an online charging scheduling algorithm, which formulates the charging strategy as a two-dimensional rectangle packing problem. The proposed method can provide battery replacement services in real-time and solve quickly without any information about incoming depleted EV batteries. The proposed model and method have been tested on the system with different numbers of batteries to show the effectiveness. Besides, the online two-dimensional rectangle packing problem can provide an online decision for BSSs.

Developing an Efficient Support Vector Machine Learning Model for Mobile Charging Stations.

In the context of increasing global energy scarcity, optimizing electric vehicle (EV) mobile charging stations is critical for promoting sustainable transportation. This study introduces the use Artificial Neural Network (ANN) models, and Support Vector Machine (SVM) enhanced with the Adams optimizer, to address the challenge of efficient EV charging in energy-constrained environments. The models are designed to predict optimal charging station locations and schedules, with the ANN-Adams optimization fine-tuning the model parameters to improve accuracy and performance, while ensuring dynamic adaptation to fluctuating energy availability and demand patterns. This research contributes to the development of intelligent, adaptive systems for EV infrastructure, paving the way for more resilient and energy-efficient urban mobility solutions. The system employs supervised learning, where models were trained and tested on labeled datasets. The performance of the SVM models was compared to that of a Multilayer Perceptron Network (MLPN) with Adams optimization. The results showed that the MLPN with Adams optimization achieved an accuracy of 97.85%, while the SVM model had a prediction accuracy of 81%. The ANN recorded 91.29% accuracy. Both approaches significantly improved classification accuracy, model generalization on testing datasets, and reduced misclassification errors.

An Integer Linear Programming Model for the Examination Timetabling Problem: A Case Study of a University in Thailand

This paper considers the examination timetabling problem (ETTP) at the College of Industrial Technology (CIT) of the King Mongkut’s University of Technology North Bangkok in Thailand. A new integer linear programming (ILP) formulation for the ETTP at the CIT is presented. The objectives were to minimize both the number of examination days (the main objective) and the number of rooms used throughout the entire examination period (the secondary objective). In this paper, a course can have multiple sections, and an examination room can accommodate exams for more than one course section. To illustrate the proposed ILP model, real data on courses acquired from the CIT were used to generate two test problems: a small problem and a large problem. The small problem included 32 courses with 69 sections. The large problem included 73 courses with 341 sections, which was the real data required for generating the midterm examination timetable for all first‐year courses in the first semester of 2021. Both problems were solved using the CPLEX solver software. The results show that the proposed model could find an optimal examination timetable for the small problem with a computational time of 2 min and 46 s. It also could find a good feasible midterm examination timetable that satisfied the requirements of the CIT for the large problem within the 2‐h time limit, much less time than that compared to manual scheduling by the CIT’s administrative staff. The obtained midterm examination timetable required five examination days and could reduce 104 examination rooms compared to assigning each course section to a separate examination room. The proposed ILP model can be used in a real‐life situation and can be a good option to generate an optimal schedule or a good feasible schedule for examinations at the CIT or other institutions that have similar requirements.

Resource constraint scheduling on two dedicated machines: Application to avionics

In civil aircraft, two partially redundant hydraulic circuits typically power various systems. During assembly, a critical phase involves simultaneously rinsing and purging these hydraulic circuits using loops. Precedence constraints are necessary to prevent the recontamination of already rinsed loops, leading to increased rinsing time. This paper presents this problem as a unique instance of the Resource Constrained Parallel Machine Scheduling Problem, where each circuit represents a machine, pipe loops to be rinsed represent jobs, and machines share a hydraulic power source. For two dedicated processors and a single resource, an optimal schedule minimizing the makespan can be generated in polynomial time. However, due to the requirement of rinsing certain pipe loops on a circuit before others, there are precedence constraints between some jobs within the same circuit. By employing a reduction of the 3-partition problem, we demonstrate that this situation results in a problem that is NP-hard in the strong sense. We evaluate several Mixed-Integer Linear Programming and Constraint Programming formulations of the problem, using Cplex, CPO, Gurobi, and Z3, against several proposed heuristics. Given that the size of the instances we need to solve exceeds what can be solved in acceptable time by solvers, we propose a heuristic and compare its performance with the optimum.

A multi-objective grey wolf optimizer for energy planning problem in smart home using renewable energy systems

This paper presents the energy planning problem (EPP) as an optimization problem to find the optimal schedules to minimize energy consumption costs and demand and enhance users’ comfort levels. The grey wolf optimizer (GWO), One of the most powerful optimization methods, is adjusted and adapted to address EPP optimally and achieve its objectives efficiently. The GWO is adapted due to its high performance in addressing NP-complex hard problems like the EPP, where it contains efficient and dynamic parameters that enhance its exploration and exploitation capabilities, particularly for large search spaces. In addition, new energy and real-world resources based on solar renewable energy systems (RESs) are combined with the proposed GWO to enhance its performance and ensure the optimisation of EPP objectives. Furthermore, EPP is presented as a multi-objective planning problem to optimize all objectives simultaneously. To efficiently investigate the proposed method performance, the results obtained by the GWO with the RESs are compared in three stages: comparison with original methods without RESs, comparison with methods using RESs, and comparison with state-of-the-art. The obtained results proved the robust performance of the proposed method in handling EPP and optimizing its objectives.

Improving the Performance of the General Course Scheduling System at UPN Veteran Jawa Timur through the Application of the IWCFPSO Algorithm

Algorithm selection is the main key in producing a system, especially an artificial intelligence-based system, for example, a course scheduling system that involves many constraints in producing an optimal schedule. This research develops a scheduling system using the ICWFPSO algorithm which is a development from previous research, namely the development of a scheduling system using the MIPSO algorithm. The use of inertia weight in the MIPSO algorithm which is used as a scheduling algorithm in previous research can be optimized by using a combination of inertia weight and constriction factor. Scheduling system development is carried out using the waterfall method with research steps namely problem and needs analysis, data collection and literature study, system design, system implementation, and ends with testing the performance of the algorithms that are applied to the scheduling system that is built. Based on the tests carried out, it can be concluded that the ICWFPSO algorithm provides 2 times better performance compared to the MIPSO algorithm in terms of optimal schedule generation time. Meanwhile, tests carried out on CPU and RAM usage showed that there was no significant impact on these two parameters through the implementation of MIPSO and ICWFPSO in the course scheduling system created.&#x0D; &#x0D; Keywords: best scheduling, ICWFPSO, number of iterations

Risk assessment and optimal scheduling of serial projects

The valuation and planning of complex projects are becoming increasingly challenging with rising market uncertainty and the deregulation of many industries, which have also raised the need for efficient risk management. We take the perspective of a private firm interested in sequential capacity expansion of a project and develop a framework for measuring the downside risk of the serial project and optimising the sequence of the stages. Under general distributional assumptions for the duration of each stage, we present an accurate representation of the project’s net present value (NPV) distribution based on a Pearson curve fit, leading to closed-form expressions for the associated risk measures. We then assess the impact of duration variability on the value at risk and demonstrate its role in stochastic project scheduling. We also account for the trade-off between maximising the expected NPV and minimising the risk exposure, and obtain the optimal schedule for risk-averse decision-makers. It becomes obvious that both the duration variability of each stage and the decision-makers’ risk preferences can significantly affect the optimal sequence of the stages and that high duration variability is not always undesirable, even for risk-averse decision-makers.