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A bi-objective distributed flow-shop scheduling problem with multistep electricity pricing and carbon emissions is studied. One objective is to minimise the completion time of production, and the other is to minimise the total cost of multistep electricity pricing and carbon emissions. A mixed integer programming model and a two-stage knowledge based cooperative algorithm with a local reinforcement strategy are proposed for the problem. The extensive numerical experiments show that the two-stage algorithm was effective statistical significantly in generating non-dominated solution sets and Pareto frontiers. Simulations on Electricity Prices are applied to examine different multistep electricity pricing schemes, and management implications were drawn for both government and companies. [ABSTRACT FROM AUTHOR]

The solution to the assembly line balancing with the hierarchical worker assignment problem (ALBHWP) provides the optimal allocation of workers and tasks to the stations that minimise the total worker cost. In the ALBHWP, tasks differ in terms of the qualification requirements of workers, and the qualification levels of workers are hierarchical. In the hierarchical workforce structure, a lower qualified worker can be replaced by higher qualified ones with higher costs, while the vice versa is not applicable. This problem has only been studied for straight assembly lines so far. In this paper, we introduce the ALBHWP for U-shaped assembly lines. We developed integer and constraint programming models for solving the ALBHWP and compared their effectiveness using an extensive set of benchmark instances. We solved the ALBHWP for straight and U-shaped assembly lines comparatively. Constraint programming models have been statistically proven to provide better quality solutions faster than integer programming models. Besides, the CP model outperforms the only available metaheuristic in the literature for the S-ALBHWP in almost all problem sizes. Another observation is that a U-shaped line design is more cost-effective than a straight line design, but solving the ALBHWP for U-shaped lines is more difficult regarding computational complexity. [ABSTRACT FROM AUTHOR]

Modular integrated construction (MiC) is an innovative construction method that is widely used in practice, but high transportation cost is an obstacle to its wider implementation. This paper is motivated by the real-world need for a scientific approach for MiC transport scheduling, and addresses the practical problem of how to achieve on-time door-to-door MiC delivery in an economical manner. An innovative integer programming model is formulated with the objective of minimising the total transportation costs, including trailer rental, fuel costs, and worker salaries. A case study based on Hong Kong data validates that the developed model can be efficiently solved for problems of practical size. The results also demonstrate that the derived MiC schedule plan can reduce transportation costs by 58.7% compared with a just-in-time (JIT) strategy, thus bringing great economic benefits to off-site construction practitioners. Useful managerial implications related to on-site MiC storage areas are derived through sensitivity analysis. Overall, this paper sets the ground for the application of mathematical programming methodology to the off-site construction field. Future research may be devoted to MiC transport scheduling under uncertainty. [ABSTRACT FROM AUTHOR]

Human-robot collaborative disassembly lines are widely used by remanufacturing companies to disassemble end-of-life (EOL) products. When disassembling large-sized EOL products, each workstation on a disassembly line is generally divided into multiple operating positions, so that different operators can disassemble the same product at their respective positions at the same time, thereby greatly improving efficiency. This paper focuses on a position-constrained human-robot collaborative disassembly planning (PC-HRCDP) problem for the above-mentioned lines, including three subproblems of disassembly sequence planning, disassembly line balancing and robot path planning. A multi-objective mixed integer programming model for PC-HRCDP is developed to solve smallscale instances. Furthermore, a multi-objective multi-fidelity optimisation (MO-MFO) algorithm is proposed to solve large-scale instances. Comprehensive experiments are conducted based on 10 problem instances generated in this study. Experimental results show that the proposed MO-MFO is better than a high-fidelity optimisation algorithm in terms of running time. In addition, benefiting from the strategy of MO-MFO to allocate the limited high-fidelity computational budget to solutions in the two stages of multi-objective optimisation and optimal sampling, MO-MFO is significantly better than the existing representative multi-fidelity optimisation algorithms in terms of the hyper-volume and the inverted generational distance. [ABSTRACT FROM AUTHOR]

The train stowage planning problem (TSPP) of the steel industry aims to select steel coils and allocate them to trains cost-effectively. It is a key component in the transportation of steel products. This study focuses on a multiobjective train stowage planning problem (MoTSPP) that maximises both the loading efficiency of the crane and the loading rate of the train. The MoTSPP also considers operation constraints related to steel coils, train wagons, and stowage modes in real-life railway transportation. An integer programming model is established to mathematically describe this problem. To obtain an efficient solution, a multiobjective analytical evolutionary algorithm (MAEA) that combines evolutionary algorithm (EA) with machine learning (ML) is presented. The EA part is a multiobjective differential evolution that introduces guided evolution and parameter adaptation to produce promising individuals and parameters, respectively. ML part adopts clustering algorithm and surrogate model to accelerate the search. Extensive comparisons and insight analyses are conducted from various perspectives to demonstrate the effectiveness and efficiency of the MAEA for solving the MoTSPP. [ABSTRACT FROM AUTHOR]

In this paper, stochastic optimisation of CVaR is applied to maintain risk-averse viability and improve resilience of a supply chain under propagated disruptions. In order to establish the risk-averse boundaries on supply chain viability space, two stochastic optimisation models are developed with the two conflicting objectives: minimisation of Conditional Cost-at-Risk and maximisation of Conditional Service-at-Risk. Then, the risk-averse viable production trajectory between the two boundaries is selected using a stochastic mixed integer quadratic programming model. The proposed approach is applied to maintain the supply chain viability in the smartphone manufacturing and the results of computational experiments are provided. The findings indicate that when the decision-making is more risk-aversive, the size of the viability space between the two boundaries is greater. As a result, more room is available for selecting viable production trajectories under severe disruptions. Moreover, the larger is viability space, the higher is both worst-case and average resilience of the supply chain. Risk-neutral, single-objective decision-making may reduce the supply chain viability. A single-objective supply chain optimisation which moves production to the corresponding boundary of the viability space, should not be applied under severe disruption risks to avoid greater losses. [ABSTRACT FROM AUTHOR]

Reconfigurable manufacturing systems (RMS) intend to bridge the gap between dedicated and flexible manufacturing systems. If the literature is mainly focused on the design step and tactical planning of such systems, few research projects have addressed scheduling at the operational level. While setup times may occur in flexible manufacturing systems, reconfiguration times considered in RMS may affect several resources at once, and hence require specific modelling and solving approaches to be considered. This paper first formalises the problem at hand through integer linear programming. An iterative search method is then provided to obtain solutions to larger-scale instances. Results obtained on generated instances show that managing even few possible configurations can yield significant improvements in solutions' quality. Meanwhile, the extended search space implied by the increase in available configurations hinders the convergence to a good solution in a reasonable computation time, which suggests further investigations. [ABSTRACT FROM AUTHOR]

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and non-convex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction problems. Tree search algorithms come with a variety of tunable parameters that are notoriously challenging to tune by hand. A growing body of research has demonstrated the power of using a data-driven approach to automatically optimize the parameters of tree search algorithms. These techniques use a training set of integer programs sampled from an application-specific instance distribution to find a parameter setting that has strong average performance over the training set. However, with too few samples, a parameter setting may have strong average performance on the training set but poor expected performance on future integer programs from the same application. Our main contribution is to provide the first sample complexity guarantees for tree search parameter tuning. These guarantees bound the number of samples sufficient to ensure that the average performance of tree search over the samples nearly matches its future expected performance on the unknown instance distribution. In particular, the parameters we analyze weight scoring rules used for variable selection. Proving these guarantees is challenging because tree size is a volatile function of these parameters: we prove that, for any discretization (uniform or not) of the parameter space, there exists a distribution over integer programs such that every parameter setting in the discretization results in a tree with exponential expected size, yet there exist parameter settings between the discretized points that result in trees of constant size. In addition, we provide data-dependent guarantees that depend on the volatility of these tree-size functions: our guarantees improve if the tree-size functions can be well approximated by simpler functions. Finally, via experiments, we illustrate that learning an optimal weighting of scoring rules reduces tree size. [ABSTRACT FROM AUTHOR]

A class of strong lower bounds on the solution value of a Linearised Integer Programming reformulation is introduced for the binary quadratic optimisation model to assign origin and destination nodes to strip and stack doors, resp., in a cross-dock infrastructure. The goal is to minimise the transportation cost of the commodities to be handled at the cross-dock. Strip- and stack-related decomposition submodels are developed by taking benefit of the Integer Linearisation Property that appears in the new model. A linear search heuristic is also provided for obtaining feasible solutions by exploiting the special structure of the problem. We present an extensive computational study on a testbed of 55 instances to show that the proposed joint scheme for lower bounding and feasible solution providing is very efficient. The results obtained by our proposal are similar to those obtained by CPLEX in the 50 instances taken from the literature, but usually the time is much smaller for the large instances. The comparison with CPLEX is particularly good for the new five largest instances, which make it very promising for its application in real-life cases. [ABSTRACT FROM AUTHOR]

Dynamic facility layout planning (DFLP) involves determining an appropriate arrangement scheme of the elements making up the production system for each time period into which the planning horizon is divided. When formulating the problem as an optimisation model, using the traditional top-down approach is usual, which firstly determines the block layout (BL) and then the detailed layout (DL) of each work cell. However by this approach, the BL generates area constraints in the detailed phase, which sometimes limit its implementation. In this context, the present paper presents a multi-objective mixed integer non-linear programming (MOMINLP) model that allows the problem to be addressed by considering an alternative approach, known in the literature as the bottom-up approach. The proposed model, called bottom-up mDFLP, considers three objective functions: (1) minimise the total material handling cost (TMHC) and the total rearrangement cost (TRAC); (2) maximise the total closeness rating (TCR) between departments; (3) maximise the area utilisation ratio (AUR). The original MOMINLP is transformed into a more computationally efficient multi-objective mixed integer linear programming (MOMILP) model. The proposed model is applied and validated in a case study of a company in the metal-mechanic sector with 12 departments for three 4-month periods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the non-unit demand capacitated minimum spanning tree problem with arc time windows and flow costs. The problem is a variant of the capacitated minimum spanning tree problem with arc time windows (CMSTP_ATW). We devise a mixed integer programming (MIP) formulation to model the problem and solve it using CPLEX. Furthermore, we propose three sets of inequalities, and we prove that they are valid. These valid inequalities tighten the model and lead to better lower bounds. To examine the quality of the solutions obtained, we convert the original data sets of Solomon (1987, "Algorithms for the Vehicle Routing and Scheduling Problem with Time Window Constraints." Operations Research 35 (2): 254–265. ) to approximate the non-unit demand CMSTP_ATW instances and provide results for the problems with 100 nodes. We execute extensive computational experiments, and the results show the positive effect of the inclusion of valid inequalities in the MIP. [ABSTRACT FROM AUTHOR]

Urged by the necessity to establish sustainable supply chains (SCs), this study focuses on exploring the closed-loop inventory routing problem (CIRP) for perishable food packed by multi-type returnable transport items (RTIs). The selling revenue of perishable food is dependent on food's remaining shelf life and the specific type of RTIs used for packaging. RTI selection decisions need to be jointly considered in the CIRP to weigh the potential benefits against associated costs. For this problem, we first develop an integer linear programme (ILP) to maximise the total profit of the holistic SC. Subsequently, we design a tailored kernel search (KS) matheuristic as an efficient solution. A real CIRP with multi-type RTIs for fresh strawberries is used to demonstrate the practicality of the ILP. For this case study, we perform extensive sensitivity analysis of the relevant parameters, extracting valuable managerial insights. Finally, experiments are conducted on 170 randomly generated instances. Computational results show that the proposed KS manages to achieve competitive solutions for instances with up to 10 retailers much more efficiently than CLPEX. For instances with up to 40 retailers, the KS algorithm significantly outperforms CPLEX in terms of solution quality, improving the obtained profit by 80.03% on average under the same computational time. [ABSTRACT FROM AUTHOR]

In this paper, a new mixed integer programming (MIP) formulation is developed for balancing and scheduling of mixed model assembly lines with disjunctive precedence constraints among assembly tasks. To represent alternative precedence relations, AND/OR assembly graph was adopted. In case of alternative precedence relations, for each product multiple assembly plans exist, which can be represented by a set of alternative precedence subgraphs and only one of such subgraphs should be selected for each product. As the number of subgraphs exponentially increases with the number of disjunctive relations among the tasks, the computational complexity of simultaneous balancing and scheduling along with the assembly subgraph selection increases with the number of alternative precedence relations. Unlike the other MIP approaches known from the literature, the new model does not need the alternative assembly subgraphs to be to explicitly enumerated as input data and then used for indexing the variables. Instead, a new disjunctive precedence selection and task assignment variable and new constraints are introduced to optimally choose one relation for each subset of alternative precedence relations. The optimal solutions for computational examples of balancing and scheduling problems illustrate a superior performance of the new modelling approach. [ABSTRACT FROM AUTHOR]

In the era of Industry 4.0, the demand fluctuation has become fiercer due to the characteristics of diversification, customisation, and uncertainty. Reconfigurability of manufacturing systems has been proven to be a useful and necessary feature when it comes to handling demand uncertainty. This feature can be achieved through the implementation of reconfigurable manufacturing system (RMS) and delayed reconfigurable manufacturing system (D-RMS). D-RMS is a subclass of RMS that focuses primarily on improving the convertibility of the manufacturing system. The two main phases involved in implementing D-RMS are part family formation and configuration design. Therefore, we proposed a multi-objective joint optimisation method of part family formation and configuration design according to the philosophy of D-RMS. Firstly, we develop a multi-objective joint optimisation model that takes into account investment cost, reconfiguration cost, similarity coefficient, and delayed reconfiguration to optimise the part family and configuration of D-RMS simultaneously. Three types of machine tools namely dedicated machine tools, flexible machine tools, and reconfigurable machine tools are considered in the optimisation model. Secondly, the non-dominated sorting genetic algorithm-III (NSGA-III) is adopted to solve the proposed multi-objective integer programming problem. Finally, numerical experiments are presented to demonstrate the effectiveness of the proposed multi-objective joint optimisation method. [ABSTRACT FROM AUTHOR]

In this paper, a variant of the open shop scheduling problem is considered in which the intermediate storage is forbidden among two adjacent production stages (zero buffer or machine blocking constraint). The performance measure is to minimise the maximal completion time of the jobs (makespan). Since this is an NP-hard problem, a two-stage constraint programming approach is proposed as a new exact method. Computational experiments were carried out on 222 literature problem instances in order to test the performance of the proposed algorithm. The relative deviation is adopted as the performance criteria. Computational results point to the ability of the proposed method to solve large-sized instances in comparison with the developed mixed-integer linear programming model and a simple constraint programming model, both with user cuts. In all set of instances, the proposed two-stage method performed better than benchmarking methods and integer programming models, with average relative deviation regarding objective values as lower as 12%. In addition, the results point to a competitive efficiency in computational times of the proposed method with less than 200 s in the most instances to obtain the optimal solution, in comparison to competitive metaheuristics from literature of the problem, for the tested test instances. [ABSTRACT FROM AUTHOR]

This paper proposes a prediction-based product change recovery strategy for the SC (supply chain) under long-term disruptions. A real-world case composed of multi-period planning and dynamic customer demand is considered. First, to forecast dynamic customer demand, a data-based demand predictive method with feedback errors is designed. Second, to schedule procurement and production in advance, based on the predicted demand, the selection of the supply portfolio is transformed into a bi-objective mixed integer programming problem incorporating product change. Furthermore, goods allocation and customer order fulfillment strategy is also designed to finish the transportation of goods and delivery of customer orders. To systematically synthesise and address the problems aforementioned, a three-stage heuristic method is further developed. Finally, a case study is presented to substantiate the reliability of the proposed strategy via an actual SC model of Dongsheng Electronics Co., Ltd. Based on the results obtained after one month, the proposed disruption recovery strategy can reduce the unit product cost and improve the service level, which outperforms the original method adopted by Dongsheng. Additionally, sensitivity analysis of unit product change cost is conducted to reveal the effect of different unit product change costs on SC performance. [ABSTRACT FROM AUTHOR]

Order picking is the process of retrieving ordered products from storage locations in warehouses. In picker-to-parts order picking systems, two or more customer orders may be grouped and assigned to a single picker. Then routing decisions regarding the visiting sequence of items during a picking tour must be made. Won and Olafsson (2005) found that solving the integrated problem of batching and routing enables warehouse managers to organize order picking operations more efficiently compared with solving the two problems separately and sequentially. We therefore investigate the mathematical programming formulation of this integrated problem. We present several improved formulations of the problem based on the findings of Valle, Beasley, and Salles da Cunha (2017), that can significantly improve computational results. More specifically, we reconstruct the connectivity constraints and generate new cutting planes in our branch-and-cut framework. We also discuss some problem properties by studying the structure of a graphical representation of the warehouse, and we present two types of additional constraints. We also consider the no-reversal case of this problem. We present efficient formulations by building different auxiliary graphs. Finally, we present computational results for publicly available test problems for single-block and multiple-block warehouse configurations. [ABSTRACT FROM AUTHOR]

This study addresses a multi-stage flow shop scheduling problem in which a job is reworked when its queue time between two arbitrary stages exceeds an upper limit. The problem is to determine the start times of jobs and rework setups/operations if incurred for the objective of minimising makespan. As an extension of the previous studies, multiple overlapped queue time limits are considered, i.e. some in-between stages of queue time limits for a job are overlapped. A mixed integer programming model is developed and its performance is reported for small-sized test instances. Then, due to the limited applications of optimal solution approaches, a variable neighbourhood search (VNS) algorithm is proposed that generates an initial solution and improves it using a shaking and a local search improvement methods. In addition, it is extended to the general variable neighbourhood search (GVNS) algorithms with variable neighbourhood descent (VND) methods. Computational results show that the GVNS algorithms outperform the VNS algorithm significantly and also give near optimal solutions for small-sized test instances within a reasonable amount of computation times. [ABSTRACT FROM AUTHOR]

We study a two-stage hybrid flow shop problem arising from a fine chemicals production facility, where the first stage is a continuous chemical reaction process and the second stage is a discrete filling-packaging process. The objective is to minimise the total weighted completion time through batching of the jobs and scheduling of the batches at first stage and scheduling of the jobs at second stage. We formulate the problem as a mixed integer programming model and develop a Lagrangian relaxation-based framework for solving it, where the original problem is decomposed into family-level subproblems, and each subproblem is transformed into a set-partitioning problem. The subproblems are solved to optimality via branch and price algorithm. We also propose two heuristic algorithms for reducing computational efforts without much loss of solution quality. Finally, we conduct computational experiments with both randomly generated and real data sets to test the performance of the three proposed algorithms and demonstrate that the algorithms perform efficiently. [ABSTRACT FROM AUTHOR]

We seek to optimize the production planning of a three-echelon remanufacturing system under uncertain input data. We consider a multi-stage stochastic integer programming approach and use scenario trees to represent the uncertain information structure. We introduce a new dynamic programming formulation that relies on a partial nested decomposition of the scenario tree. We then propose a new approximate stochastic dual dynamic integer programming algorithm based on this partial decomposition. Our numerical results show that the proposed solution approach is able to provide near-optimal solutions for large-size instances with a reasonable computational effort. [ABSTRACT FROM AUTHOR]

We study the problem of category space location-allocation in the retail industry. We introduce a new attractiveness factor to reflect the product-based visibility level in designing the optimal allocation policy. This factor will be determined for each aisle by the lineup of product categories allocated to that aisle and all other aisles sharing a shopping path with it. We explore how considering the classical location-based attractiveness and the proposed product-based attractiveness can improve a retailer's overall space profitability. We develop a modelling framework that integrates both location-based and product-based attractiveness factors in a mixed-integer nonlinear program. Due to the non-linearity and non-convexity of the proposed model, large-scale instances are computationally challenging to solve using the state-of-the-art commercial solvers. We thus introduce a two-stage heuristic solution method that generates a near-optimal solution in a reasonable amount of time. Using the two-stage model, we explore the optimal store design for an illustrative case study. The results couple the optimal category space allocation to customers' shopping paths and create a profitability-maximising balance between the placement of high-demand and high-impulse product categories. We show that focussing on product-based attractiveness exposes the store to congestion risks, which can be prevented by adding constraints limiting congestion in different aisles of the store. [ABSTRACT FROM AUTHOR]

The application of new information technologies such as the Internet of Things (IoT) has caused a deep impact on production and operations management in various fields. In this paper, a mixed-integer programming model is proposed to generate integrative decision-making in the IoT-enabled fresh agri-products supply chains. The designed model integrates three key stages, that is, planting, storage, and distribution, to help growers make the optimal decisions for maximising revenue. Decisions are made after comprehensive consideration of market factors such as price and demand as well as agricultural characteristics such as crop yield and shelf life. Results of numerical experiments show that significant improvement of benefits can be obtained through the overall decision-making of planting, storage, and distribution. Additionally, it may be most beneficial for growers to keep the warehouse's storage time and storage capacity at a medium level. The IoT-based integrative decision-making method explored in this study can be applied to other fields including manufacturing to achieve more efficient production and operations management. [ABSTRACT FROM AUTHOR]

AbstractThis study addresses a scheduling problem arising from the “Rent Instead of Buy” business model where rental service platforms rent equipment from suppliers to satisfy customer requests in exchange for a lump-sum payment. Suppliers often implement piecewise linear concave charging policies to encourage longer rental duration. This policy prompts the platform to consolidate service periods into longer rental agreements for lower rental rates, potentially necessitating the splitting of a customer request among multiple facilities. We establish an integer programming model to maximize the platform’s profit, which is equal to the total revenue from serving customers minus the total rental and scheduling costs. To solve the problem, we propose two Dantzig-Wolfe decomposition reformulations and design branch-and-price algorithms accordingly. Furthermore, by exploiting the property of the concave rental cost functions, we derive the optimal structure regarding the start and end times of services, significantly reducing the subproblem’s search space. Numerical experiments based on real-life data validate the efficiency of the designed algorithms compared to commercial solvers and highlight the benefits of split services. Sensitivity analysis reveals that as the rental cost function becomes more segmented, more requests are split-serviced, but the times for splitting a request are seldom more than once. [ABSTRACT FROM AUTHOR]

Hydrogen production is a vital development trend to improve the economics and penetration rate of offshore wind farms (OWFs), and distributed hydrogen production (DHP) is a preferred solution for deep and far sea OWFs without expensive submarine cables and offshore substations. The export pathway of OWF-DHP consists of collection pipelines, transmission pipelines, and offshore compressor stations. In this paper, mathematical programming is introduced to explore the export pathway planning problem of OWF-DHP. Firstly, the area of OWF is discretized into multiple grids with the center of the grids being the candidate locations of the offshore compressor station. Then, a binary integer quadratic programming problem is established to optimize both the offshore compressor station location and pipeline construction with different topologies. Further, the mathematical model is solved by the branch and cut algorithm integrated with the proposed dimension reduction methods. Finally, the effectiveness of the proposed export pathway planning approach is verified by the actual data of Baltic Eagle OWF in Germany, which would support the construction of the OWF-DHP project. [Display omitted] • Studying export pathway planning (EPP) for OWF-distributed hydrogen production. • Introducing mathematical programming to model EPP as a BIQP problem. • Proposing dimension reduction methods to accelerate BIQP problem solving. • Verifying the effectiveness of the EPP approach with the Baltic Eagle OWF case. • Conducting sensitivity analysis on transportation carrier and pipeline topology. [ABSTRACT FROM AUTHOR]

Using scenarios to model a stochastic system's behavior poses a dilemma. While a large(r) set of scenarios usually improves the model's accuracy, it also causes drastic increases in the model's size and the computational effort required. Multi-period descriptive sampling (MPDS) is a new way to generate a small(er) set of scenarios that yield a good fit both to the periods' probability distributions and to the convoluted probability distributions of stochastic variables (e.g., period demands) over time. MPDS uses descriptive sampling to draw a sample of S representative random numbers from a period's known (demand) distribution. Now, to create a set of S representative scenarios, MPDS heuristically combines these random numbers (period demands) period by period so that a good fit is achieved to the convoluted (demand) distributions up to any period in the planning interval. A further contribution of this paper is an (accuracy) improvement heuristic, called fine-tuning, executed once the fix-and-optimize (FO) heuristic to solve a scenario-based mixed integer programming model has been completed. Fine-tuning uses linear programming (LP) with fixed binary variables (e.g., setup decisions) generated by FO and iteratively adapts production quantities so that compliance with given expected service level constraints is reached. The LP is solved with relatively little computational effort, even for large(r) sets of scenarios. We show the advancements possible with MPDS and fine-tuning by solving numerous test instances of the stochastic capacitated lot-sizing problem under a static uncertainty approach. [ABSTRACT FROM AUTHOR]

Physical therapy in acute care hospitals plays an important role in the rehabilitation of patients. Nevertheless, the profession must deal with staff shortages caused by a lack of potential employees and absenteeism which are results of high physical and mental workloads. The therapist shortage negatively affects the total number of daily appointments the department can fulfill. For appointments that can be successfully scheduled, continuity of care with the same therapist cannot be guaranteed for individual patients. Lack of continuity of care negatively influences the therapist's satisfaction. Therapist preferences for individual appointments in general cannot always be guaranteed when designing schedules, which also hurts satisfaction. This paper develops a multi-criteria model for the daily therapy appointment-scheduling problem. The primary objective is to minimize the total sum of priority violations for unscheduled appointments. To improve therapist satisfaction, we consider therapist preferences including continuity of care as a secondary objective. Here, our integer programming formulation aims to minimize the total sum of preference violations for scheduled appointments. We are dealing with an operational planning problem with a daily planning horizon. The operational objective is to achieve therapist schedules in at most two hours. The therapists' schedules together need to include several hundred appointments for a planning day. Due to intractability, the developed integer program cannot provide schedules for such problem sizes. Therefore, we develop a customized Greedy Randomized Adaptive Search Procedure (GRASP) with six innovative local search operations to improve an initially constructed solution. We test the heuristic algorithm on realistic data instances. The metaheuristic provides high-quality schedules for various problem sizes in short runtimes, i.e., within minutes. Comparisons with the optimal solutions for small problem instances show very good results of the GRASP with a similar number of scheduled appointments and good adherence to continuity of care and therapist preference requirements. [ABSTRACT FROM AUTHOR]

Fixture layout is an essential factor in intelligent manufacturing in the shipbuilding industry, affecting assembly quality and efficiency. Its optimization has become an urgent problem in the assembly process of compliant parts. Traditional fixture layout depends on workers' experience, which leads to butt clearance along the assembly interface. Thus, this article proposes a butt clearance control-oriented fixture layout optimization (BCCFLO) methodology. First, a method for calculating the part dimensional variation under the influence of fixture layout and fixture locating error is developed. Then, a constrained multi-objective integer nonlinear programming (CMINP) model is innovatively formulated to optimize the fixture layout. Furthermore, the non-dominated sorting genetic algorithm-II based on Latin hypercube sampling is designed to address the CMINP model. The case study illustrates and validates that the fixture layout achieved by the proposed method could significantly control the butt clearance for large compliant part assembly in the shipbuilding industry. [ABSTRACT FROM AUTHOR]

Estimating railway capacity is both valuable and challenging. This paper introduces a novel approach to high-railway capacity calculation by incorporating cross-line trains. Leveraging the concept of compressing timetable diagrams, we generate diverse structured diagrams randomly and subsequently create a train timetable without buffer time using a genetic algorithm framework. We establish ideal arrival times for cross-line trains and comprehensively analyze the impact of these trains by comparing ideal and actual arrival times. Unlike traditional models that only consider single-line train operations, our model provides a more comprehensive evaluation of railway capacity. The NSGA-II algorithm developed for this model is innovative and efficient, generating a high-quality Pareto front solution set that offers multiple decision-making schemes for stakeholders. The results show that a heuristic algorithm can obtain a feasible solution more quickly when the objective is nonlinear. Compared with the ideal time deviation of cross-line trains without considering the ideal time deviation, the ideal time deviation derived by the heuristic algorithm is reduced by 93.2%; the GAP of train occupancy time obtained with the heuristic algorithm is 3.58%. [ABSTRACT FROM AUTHOR]

Power distribution networks should strive for reliable delivery of energy. In this paper, we support this endeavor by addressing the Maintenance Resources Allocation Problem (MRAP). This problem consists of scheduling preventive maintenance plans on the equipment of distribution networks for a planning horizon, seeking the best trade-offs between system reliability and maintenance budgets. We propose a novel integer linear programming (ILP) formulation to effectively model and solve the MRAP for a single distribution network. The formulation also enables flexibility to suit new developments, such as different reliability metrics and smart-grid innovations. Then we develop a straightforward ILP formulation to address the MRAP for several distribution networks which takes the advantages of exchanging maintenance information between local agents and upper management. Using a general-purpose ILP solver, we performed computational experiments to assess the performance of the proposed approaches. Optimal maintenance trade-offs were achieved with the new formulations for real-scale distribution networks within short running times. To the best of our knowledge, this is the first time that the MRAP is optimally solved using ILP, for single or multiple distribution networks. [ABSTRACT FROM AUTHOR]

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum scalarization of the MOIP. At unsupported solutions, the convex hull relaxation is not tight and a Lagrangian relaxation may provide a tighter bound. Using the Lagrangian relaxation, we define a Lagrangian dual of an MOIP that satisfies weak duality and is strong at supported solutions under certain conditions on the primal feasible region. We include a numerical experiment to illustrate that bound sets obtained via Lagrangian duality may yield tighter bounds than those from a convex hull relaxation. Subsequently, we generalize the integer programming value function to MOIPs and use its properties to motivate a set-valued superadditive dual that is strong at supported solutions. We also define a simpler vector-valued superadditive dual that exhibits weak duality but is strongly dual if and only if the primal has a unique nondominated point. [ABSTRACT FROM AUTHOR]

Transforming hand-drawn sketches into digital wireframes is a pivotal yet time-intensive step in the early stages of User Interface (UI) design. Despite advancements in technology aiming to streamline this task, challenges arise from the multi-scale variations of UI elements and inherent imperfections in the geometric information of sketches. We introduce Sketch2Wireframe, a tool designed to swiftly transform these sketches into refined digital wireframes. The process unfolds in two primary phases: UI element detection and UI layout optimization. First, we propose an object detection model named Attention-based Multi-Scale Region-based Convolutional Neural Network (AMS-RCNN). This model efficiently detects multi-scale elements in sketches by leveraging multi-scale convolution and an attention mechanism, ensuring rich feature extraction for prediction. We then implement a hybrid layout optimization method, which initially utilizes heuristic rules to recognize hierarchy and element organization from sketches, followed by an Integer Programming (IP) approach to globally optimize the layout in compliance with design guidelines. Experimental findings suggest that the AMS-RCNN outperforms baseline models, evidencing a 2.2% mAP increase in element detection. Moreover, our hybrid layout optimization method considerably outperforms the heuristic methods in terms of the perceived quality of the layouts. [ABSTRACT FROM AUTHOR]

The network design problem with vulnerability constraints and probabilistic edge reliability (NDPVC‐PER) is an extension of the NDPVC obtained by additionally considering edge reliability. We consider the design of a telecommunication network in which every origin‐destination pair is connected by a hop‐constrained primal path, and by a hop‐constrained backup path when certain edges in the network fail. The edge failures occur with respect to their reliability, and the network is designed by considering a minimum reliability level. Therefore, a hop‐constrained backup path must be built by considering all simultaneous edge failures that have a certain probability of realization. While there exist models to solve the NDPVC without enumerating all edge subsets, edge reliability cannot be dealt with by applying the techniques applied to the NDPVC. Therefore, we develop models based on a new concept of resilient length‐bounded cuts, and solve the NDPVC‐PER without edge set enumerations. We perform extensive testing of the model to determine the best performing settings, and demonstrate the computational efficiency of the developed model. Our findings on these instances show that, in the dataset considered in this study, increasing the reliability level from 90% to 95% increases the average cost only by 12.4%, while increasing it from 95% to 99% level yields a cost increase of 93.9%. [ABSTRACT FROM AUTHOR]

The optimization of process systems within the field of Chemical Engineering often confronts uncertainties that can exert significant influences on the performance and dependability of the obtained solutions. This research endeavors to investigate the application of Bayesian optimization in the realm of constrained mixed integer nonlinear problems. A comparative analysis was conducted, exploring different surrogate models, and evaluating diverse kernel functions and acquisition functions. Furthermore, a sampling strategy was devised to assess the enhancement achieved by the acquisition function. The findings of this article reveal the superior performance of sparse Gaussian processes in conjunction with computationally inexpensive acquisition functions, thereby highlighting their suitability for addressing mixed integer nonlinear programming problems characterized by noisy functions and stochastic behavior. Consequently, this article presents a computationally efficient approach to effectively tackle the challenges associated with data‐driven mixed integer nonlinear programming problems within the domain of Process System Engineering. [ABSTRACT FROM AUTHOR]

Let G be a connected graph. The distance between two vertices u and v in G, denoted by d G (u , v) , is the number of edges in a shortest path from u to v, while the distance between an edge e = x y and a vertex v in G is d G (e , v) = min { d G (x , v) , d G (y , v) } . For an edge e ∈ E (G) and a subset S of V(G), the representation of e with respect to S = { x 1 , ... , x k } is the vector r G (e | S) = (d 1 , ... , d k) , where d i = d G (e , x i) for i ∈ [ k ] . If r G (e | S) ≠ r G (f | S) for every two adjacent edges e and f of G, then S is called a local edge metric generator for G. The local edge metric dimension of G, denoted by edim ℓ (G) , is the minimum cardinality among all local edge metric generators in G. For two non-trivial graphs G and H, we determine edim ℓ (G ⋄ H) in the edge corona product G ⋄ H and we determine edim ℓ (G ∘ H) in the corona product G ⋄ H . We also formulate the problem of computing edim ℓ (G) as an integer linear programming model. [ABSTRACT FROM AUTHOR]

In this paper, we present a heuristic for the non‐unicost set covering problem using local branching. Local branching eliminates the need to define a problem specific search neighbourhood for any particular (zero‐one) optimisation problem. It does this by incorporating a generalised Hamming distance neighbourhood into the problem, and this leads naturally to an appropriate neighbourhood search procedure. We apply our approach to the non‐unicost set covering problem. Computational results are presented for 65 test problems that have been widely considered in the literature. Our results indicate that our heuristic is better than six of the eight other heuristics we examined, slightly worse than that of one heuristic, but that there is a single heuristic that outperforms all others. We believe that the work described here illustrates that the potential for using local branching, operating as a stand‐alone matheuristic, has not been fully exploited in the literature. [ABSTRACT FROM AUTHOR]

The paper deals with assortment optimization when customers purchase products using a nonparametric choice model. Each customer is presented with a preference list and will buy an available highest‐ranked offered product on the preference list. The paper presents a novel bi‐objective integer programming model for assortment optimization following a ranking‐based consumer choice model. The objectives are maximizing the expected revenue and maximizing customer satisfaction. This problem is recognized as an NP‐hard problem. After developing the bi‐objective model, an improved version of the augmented ε$\varepsilon $‐constraint method is proposed to solve the problem and retrieve the Pareto‐optimal solutions. In each iteration, this algorithm solves a single‐objective linear integer programming sub‐problem. Our approach aims to obtain a complete set of Pareto‐optimal solutions. Finally, we present computational experiments on synthetic data. Several numerical illustrations are provided at the end to demonstrate the application of the proposed methodology. The computational results provide the decision‐makers with valuable information regarding the factors that mainly affect the solutions. [ABSTRACT FROM AUTHOR]

This paper introduces a new flow‐based mathematical formulation for the multivehicle covering tour problem. This problem determines a set of vehicle routes for the available fleet; therefore, the total distance traveled is minimal. In the proposed mathematical formulation, each vertex represents a location of interest, and these vertices belong to three sets: vertices that can be visited; vertices that must be visited; and vertices that must be covered, in the sense that each vertex must be close to a visited vertex in a route. The proposed formulation aims to find solutions with balanced routes (all the routes with an equal or similar number of visited nodes) and extends the previous formulations proposed in the literature by considering a two‐index vehicle flow formulation with a decision variable to find the balanced routes. It constitutes an NP‐hard integer programming problem based on a two‐commodity flow model, which is solved by applying the branch‐and‐cut and biased random‐key genetic algorithms. This paper reports computational results for some adapted instances from TSPLIB to evaluate the efficiency of the proposed model. The computational results validate the branch‐and‐cut and genetic algorithms, whereby the latter performs better in large‐size instances with reduced computational runtime. Finally, the used approaches obtained competitive solutions compared to the literature. [ABSTRACT FROM AUTHOR]

Chudnovsky and Seymour proposed the Three‐in‐a‐tree algorithm which solves the following problem in polynomial time: given three fixed vertices in a simple finite graph, check whether an induced tree containing these vertices exists. In this paper, we deal with a generalization of this problem, referred to henceforth as k$k$‐in‐a‐tree. The k$k$‐in‐a‐tree checks whether a graph contains an induced tree spanning k$k$ given vertices. When k$k$ is part of the input, the problem is known to be NP‐complete. If k≥4$k \ge 4$ is a fixed given number, its complexity is an open question, although there are efficient algorithms for restricted cases such as claw‐free graphs, graphs with a girth of at least k$k$ and chordal graphs. We present mixed‐integer programming formulations for this problem, and we show that instances with up to 25,000 vertices can be solved in reasonable computational time. [ABSTRACT FROM AUTHOR]

About 15 years ago, a paper proposed the first integer linear programming formulation for the constrained two‐dimensional guillotine cutting problem (with unlimited cutting stages). Since then, eight other formulations followed, seven of them in the last four years. This spike of interest gave no opportunity for a comprehensive comparison between the formulations. We review each formulation and compare their empirical results over instance datasets of the literature. We adapt most formulations to allow for piece rotation. The possibility of adaptation was already predicted but not realized by the prior work. The results show the dominance of pseudo‐polynomial formulations until the point instances become intractable by them, while more compact formulations keep achieving good primal solutions. Our study also reveals a mistake in the generation of the T instances, which should have the same optima with or without guillotine cuts. We also propose hybridising a recent formulation with a prior formulation for a restricted version of the problem. The hybridisations show a reduction of about 20% of the branch‐and‐bound time thanks to the symmetries broken by the hybridisation. [ABSTRACT FROM AUTHOR]

Operations Research (OR) plays a crucial role in strategic decision-making in today's business world; it uses complex algorithms and data analytic to provide decision-makers with the necessary information. The proposed study presents a novel ensemble clustering for decision making in various disciplines including OR problems which introduce a second-order conic optimization model. This method provides a significant advantage over the traditional difference of convex programming by continuously and convexly solving integer programming. The model optimizes the balance between accuracy and diversity, resulting in the selection of the best candidates for prediction. The study's remarkable contribution lies in the automatic sub-ensemble selection while optimizing for accuracy and diversity. The model has been verified using real data and achieves competitive prediction performance. Furthermore, this approach illustrates how OR can be utilized to enhance ensemble clustering and decision-making. [ABSTRACT FROM AUTHOR]

Summary Deterministic communication plays a crucial role for real‐time distributed embedded systems by guaranteeing a low end‐to‐end delay and minimal jitter. Conflict‐aware iterated ILP‐based scheduling (IIS) is an incremental approach to enhance the scalability of single‐shot ILP computation to solve the computationally hard Qbv‐compliant offline scheduling problem for IEEE 802.1 Time‐Sensitive Networking (TSN). Taking into account the conflicting demands of the streams, IIS computes no‐wait schedules by dividing the set of streams into disjoint partitions, each of which is incrementally scheduled by an ILP solver. In this work, defining the no‐wait communication constraints for TSN scheduling, we propose a novel iterated scheduling approach, namely, O‐IIS, with a backtracking mechanism and partial solution support extending the conventional IIS procedure. O‐IIS relies on an ordering strategy to determine the order in which the constructed partitions will be processed by an ILP solver. We evaluate the performance of our approach in terms of schedulability success rate and schedule synthesis time using various network topologies and different partitioning schemes to construct the partitions. The evaluation results show that our approach provides significantly better scheduling performance compared to the existing work in the literature. [ABSTRACT FROM AUTHOR]

Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints. [ABSTRACT FROM AUTHOR]

With the rapid advancement of intelligent transportation systems, cooperative vehicle infrastructure systems emerge as a vital frontier for development. Real-time mutual fusion of perception data is a crucial technology for ensuring the security of ITS systems. However, the computation-intensive nature of perception data fusion poses a significant challenge in terms of computing resource allocation and scheduling. In this paper, we propose a vehicle-road cooperative network that facilitates computation offloading during the real-time perception data fusion process. We present an architecture that enables users to generate tasks and offload computations, and we formulate an integer nonlinear programming problem within this framework. Considering the dynamic, random, and time-varying characteristics of cooperative vehicle infrastructure systems, we introduced the Deep Deterministic Policy Gradient (DDPG) algorithm for perception fusion computing offloading (DDPG-PFCO). Through extensive experiments conducted on a real map, experimental results show that the proposed algorithm outperforms other comparison algorithms, exhibiting significant improvements in performance. [ABSTRACT FROM AUTHOR]

The current arterial signal coordination models only target through traffic or critical traffic, resulting in fairness issues for traffic in other directions. Moreover, these models fail to achieve system optimality between intersections along the arterial. To address these problems, this paper establishes an arterial signal coordination optimization model based on all-direction pairs of adjacent intersections. The model takes the minimum weighted green wave band center offset of all-direction pairs at the intersections as the objective function. The optimization variables are the cycle length, offset, and phase sequence. The phase sequence structure adopts the ring-and-barrier structure, and the phase sequence optimization includes not only the main road but also the minor road intersecting with it. The model is an integer linear programming model, and it optimizes all-direction pairs of the upstream and downstream intersections. By analyzing the spatiotemporal diagram of the intersections, constraints are established for the phase sequence of the main road and intersecting roads. Through optimization of the offset and phase sequence, the coordination of flow direction pairs between upstream and downstream intersections can be optimized to improve the overall traffic fairness of the arterial. [ABSTRACT FROM AUTHOR]

Modular integrated construction (MiC) has witnessed increasing adoption in worldwide building projects, driven by various benefits, including improved construction efficiency, reduced on-site labor hours, and minimized waste and pollution. The construction industry has recognized the transportation of prefabricated modules as a huge obstacle to the wide implementation of MiC. In practice, transport planning of prefabricated modules is usually intuitively decided by general contractors based on experience. Intuitive decisions cannot ensure the just-in-time (JIT) module delivery, thereby incurring additional costs of early and late delivery. Motivated by this challenge, this study endeavors to design cost-minimized transportation plans for prefabricated modules using mathematical programming methodology. An integer programming model and a tailored solution method are proposed. Then, we use data from two real building projects in Hong Kong as model inputs to demonstrate the computation of optimal module transport plans using the proposed methodology. Numerical results show that, if the JIT strategy is not considered in module transport planning, the actual total transportation costs will be 21.74% higher than the expected ones. Comparative costs of JIT implementation and nonimplementation indicate the significance of the JIT strategy. Additionally, our proposed method can achieve punctual module delivery and reduce the overall transportation expenses by 10.13%, implying considerable cost savings. [ABSTRACT FROM AUTHOR]

This paper studies the problem of joint deployment, user association, channel, and resource allocation in unmanned aerial vehicle‐enabled access network. Since different user equipments performing different tasks and have different data rate requirements, the priority‐based traffic fairness problem is investigated. This problem, however, is a mixed integer nonlinear programming problem with NP‐hard complexity, making it challenging to be solved. To address this issue, a self‐organized and distributed framework "sense‐as‐you‐fly" based on the decomposition process, which divides the original problem into several subproblems, is proposed. Assuming without central controller, we derive the closed‐form resource allocation scheme and propose distributed many‐to‐one matching to optimize user association subproblem. Considering the coupled characteristics, the multi‐unmanned aerial vehicle deployment and channel allocation subproblems are modelled as a local altruistic game. The existence of Nash equilibrium is proved with the aid of exact potential game and efficient best response learning‐based algorithm is proposed. The original problem is finally addressed by solving the sub‐problems alternately and iteratively. Simulation results verify its effectiveness. By jointly optimizing multidimensional variables, the proposed algorithm unlocks network performance gains, especially in resource‐limited regimes. [ABSTRACT FROM AUTHOR]

Inland waterway transport is considered a critical component of sustainable maritime transportation and is subject to strict legal regulations on fuel quality. However, crew members often prefer cheaper, inferior fuels for economic reasons, making government inspections crucial. To address this issue, we formulate the ship selection and inspection scheduling problem into an integer programming model under a multi-inspector and multi-location scenario, alongside a more compact symmetry-eliminated model. The two models are developed based on ship itinerary information and inspection resources, aiming to maximize the total weight of the inspected ships. Driven by the unique property of the problem, a customized heuristic algorithm is also designed to solve the problem. Numerical experiments are conducted using the ships sailing on the Yangtze River as a case study. The results show that, from the perspective of the computation time, the compact model is 102.07 times faster than the original model. Compared with the optimal objectives value, the gap of the solution provided by our heuristic algorithm is 0.37% on average. Meanwhile, our algorithm is 877.19 times faster than the original model, demonstrating the outstanding performance of the proposed algorithm in solving efficiency. [ABSTRACT FROM AUTHOR]

This article introduces the concept of joint distribution context into the location-routing problem (LRP) to tackle the issue of resource waste and high costs in distribution centers (DCs) for multiple companies. Fixed costs of constructing DCs, fixed costs of hiring vehicles, and routing costs are taken into account when constructing the mixed integer programming (MIP) model. A two-stage algorithm is designed to solve this problem. In the first stage, K-means clustering is used to group demand nodes with vehicle capacity constraints. In the second stage, the simplified LRP model is solved by Lingo, and locations of DCs and routing schemes are obtained. Additionally, a cost-sharing model based on the desirability function is developed to address the cost allocation problem among companies. The results and sensitivity analysis demonstrate that the joint distribution can effectively reduce costs. [ABSTRACT FROM AUTHOR]

A large number of real-world optimization problems can be formulated as Mixed Integer Linear Programs (MILP). MILP solvers expose numerous configuration parameters to control their internal algorithms. Solutions, and their associated costs or runtimes, are significantly affected by the choice of the configuration parameters, even when problem instances have the same number of decision variables and constraints. On one hand, using the default solver configuration leads to suboptimal solutions. On the other hand, searching and evaluating a large number of configurations for every problem instance is time-consuming and, in some cases, infeasible. In this study, we aim to predict configuration parameters for unseen problem instances that yield lower-cost solutions without the time overhead of searching-and-evaluating configurations at the solving time. Toward that goal, we first investigate the cost correlation of MILP problem instances that come from the same distribution when solved using different configurations. We show that instances that have similar costs using one solver configuration also have similar costs using another solver configuration in the same runtime environment. After that, we present a methodology based on Deep Metric Learning to learn MILP similarities that correlate with their final solutions' costs. At inference time, given a new problem instance, it is first projected into the learned metric space using the trained model, and configuration parameters are instantly predicted using previously-explored configurations from the nearest neighbor instance in the learned embedding space. Empirical results on real-world problem benchmarks show that our method predicts configuration parameters that improve solutions' costs by up to 38% compared to existing approaches. [ABSTRACT FROM AUTHOR]

The combination processing of molds and electronic product joint inspection introduce the mandatory concurrent operations on the same machine (MCDSM), which breaks the constraint that the same machine cannot process different jobs at the same time in the job shop scheduling (JSP) To solve this type of job shop scheduling problem, this paper proposed an adaptive hybrid initialization genetic algorithm (AHIGA). Firstly, this paper defined the problem as a generalized JSP considering mandatory concurrent operations on the same machine (GJSPMCO) problem, and established an optimization model using mixed integer programming with the objective of minimizing the maximum completion time. Next, it designed corresponding encoding and decoding techniques to support the representation and resolution of feasible scheduling plans within the constraints of MCOSM. Meanwhile, it established a population hybrid initialization method to generate high-quality feasible solutions. This paper also designed novel crossover and mutation operation methods to ensure the feasibility of newly generated solutions under the constraint of MCOSM. Additionally, it constructed an adaptive crossover and mutation operators to enable the adaptive updating of offspring, thereby enhancing the algorithms global search capability. Finally, it constructed 40 test cases based on JSP benchmark, and used these test cases and an example of joint inspection of electronic products for experiments. The results show that the proposed model and algorithm can effectively solve GJSPMCO problem, and the improvement strategies can enhance the quality of solutions, demonstrating the feasibility of the model and the superiority of AHIGA. [ABSTRACT FROM AUTHOR]