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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]

Most tourist destinations are facing regular and consistent seasonality with significant economic and social impacts. This phenomenon is more pronounced in the post-covid era, where demand for travel has increased but unevenly among different geographic areas. To counter these problems that both customers and hoteliers are facing, we have developed two auctioning systems that allow hoteliers of lower popularity tier areas or during low season periods to auction their rooms in what we call a forward auction model, and also allows customers to initiate a bidding process whereby hoteliers in an area may make offers to the customer for their rooms, in what constitutes a reverse auction model initiated by the customer, similar to the bidding concept of priceline.com. We develop mathematical programming models that define explicitly both types of auctions, and show that in each type, there are significant benefits to be gained both on the side of the hotelier as well as on the side of the customer. We discuss algorithmic techniques for the approximate solution of these optimization problems, and present results using exact optimization solvers to solve them to guaranteed optimality. These techniques could be beneficial to both customer and hotelier reducing seasonality during middle and low season and providing the customer with attractive offers. We have integrated these techniques in a fully functional working prototype web application (). [ABSTRACT FROM AUTHOR]

Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact sets. In particular, we discuss necessary conditions for local optimality, such as that a locally optimal configuration is always contained in the convex hull of the respective darkest points. Building on this, we propose two sequences of mixed-integer linear programs in order to compute lower and upper bounds on the maximal polarization, where the lower bound is constructive. Moreover, we prove the convergence of these sequences towards the maximal polarization. [ABSTRACT FROM AUTHOR]

This paper considers a single machine identical-jobs order scheduling problem with a position-dependent learning effect (SIOSLE) to minimize the total tardiness. A learning effect is common in the identical-jobs order manufacturing, such as clothing, bicycles, shoes, and so on, but its impact on the order scheduling problem has not been studied, especially for orders with different numbers of the same type of jobs. A mixed integer programming (MIP) model is first formulated for SIOSLE and serves as a benchmark. A new branch-and-bound algorithm was developed to handle computational complexity based on the Dominance, Split, Elimination, and Decomposition rules revised from the traditional job scheduling problem and new lower and upper bounds. Numerical experiments demonstrate that the proposed branch-and-bound algorithm is computationally better than the performance of using Gurobi, a popular commercial solver, to solve the MIP. The experiments for large-sized problems found that the proposed branch-and-bound algorithm can solve instances with up to 120 orders. The algorithm is more efficient for instances with a strong or weak learning effect, with tight or loose due dates, or with heterogeneous due dates. The effectiveness of the Dominance, Split, Elimination, and Decomposition rules varies with parameter settings. In addition, the proposed branch-and-bound algorithm can yield better solutions than traditional meta-heuristic algorithms but may require longer run time for large instances. [ABSTRACT FROM AUTHOR]

We describe a diving heuristic framework based on constraint propagation for mixed integer linear programs. The proposed approach is an extension of the common fix-and-propagate scheme, with the addition of solution repairing after each step. The repair logic is loosely based on the WalkSAT strategy for boolean satisfiability. Different strategies for variable ranking and value selection, as well as other options, yield different diving heuristics. The overall method is relatively inexpensive, as it is basically LP-free: the full linear programming relaxation is solved only at the beginning (and only for the ranking strategies that make use of it), while additional, typically much smaller, LPs are only used to compute values for the continuous variables (if any), once at the bottom of a dive. While individual strategies are not very robust in finding feasible solutions on a heterogeneous testbed, a portfolio approach proved quite effective. In particular, it could consistently find feasible solutions in 189 out of 240 instances from the public MIPLIB 2017 benchmark testbed, in a matter of a few seconds of runtime. The framework has also been implemented inside the commercial MIP solver Xpress and shown to give a small performance improvement in time to optimality on a large internal heterogeneous testbed. [ABSTRACT FROM AUTHOR]

This paper introduces a novel mixed integer programming (MIP) reformulation for the joint chance-constrained optimal power flow problem under uncertain load and renewable energy generation. Unlike traditional models, our approach incorporates a comprehensive evaluation of system-wide risk without decomposing joint chance constraints into individual constraints, thus preventing overly conservative solutions and ensuring robust system security. A significant innovation in our method is the use of historical data to form a sample average approximation that directly informs the MIP model, bypassing the need for distributional assumptions to enhance solution robustness. Additionally, we implement a model improvement strategy to reduce the computational burden, making our method more scalable for large-scale power systems. Our approach is validated against benchmark systems, i.e., IEEE 14-, 57- and 118-bus systems, demonstrating superior performance in terms of cost-efficiency and robustness, with lower computational demand compared to existing methods. [ABSTRACT FROM AUTHOR]

Adjusting the deployment of each server in a server cluster in real-time and online based on a changing load has important considerations. In response to the deficiencies in the existing research on server switch jitter and real-time optimization, this paper proposes a periodic energy consumption optimization strategy based on mixed integer programming (MIP) for server clusters. During an optimization period, the strategy allows the CPU of the server to switch between adjacent frequencies to optimize cluster energy consumption at a granular level. First, we describe cluster energy optimization as a basic MIP model, with a reasonable definition of the decision variables and the modeling of the server load and power. Then, we include the server switch overhead in the objective function of the model, considering the joint optimization of multiple periods. Finally, we design an efficient solution scheme based on Gurobi and create two solution adjustment schemes that can reduce CPU frequency switching. The test results reveal that the proposed strategy can effectively suppress server switch jitter and can be carried out in real-time. The extra power cost of reducing CPU frequency switching is also evaluated and analyzed in the testing section. [ABSTRACT FROM AUTHOR]

This paper investigates the vehicle routing problem faced by a third‐party logistics (3PL) provider that performs the last‐mile delivery service in omni‐channel retailing for a number of companies engaged in household appliances and furniture. In the problem, each company is associated with a set of warehouses, physical stores, and customers that provide or require various commodities. The request of a company is to transport commodities from the selected warehouses and stores to the customers. In addition, the pickup or delivery service at each location should be started in a predefined time window. Since the loading and unloading follow the last‐in‐first‐out fashion, the handling time incurred by additional operation is considered. The studied problem is formulated as a multicommodity pickup and delivery problem with time windows and handling time (MPDPTWH). MPDPTWH aims to satisfy the requests on the 3PL platform with the minimum total duration of the routes. We present a mixed integer programming formulation of the problem and propose a multirestart randomized tabu thresholding algorithm (MRTTA) as well as a memetic algorithm (MA) to solve this problem heuristically. Then, the performance of the mathematical model and the two heuristics is assessed over three sets of MPDPTWH instances. After this, we compare the proposed MRTTA and MA with algorithms from the literature on a related problem. Furthermore, we perform the sensitivity analysis in a case study by discussing the impact of picking cost and handling time on the solution, and give the managerial insights. [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]

Inland waterway transportation plays a crucial role in Europe's transportation network and economy. It is an efficient and sustainable mode of transportation, with lower emissions and energy consumption than other modes of transportation, such as road and air. However, the services provided by inland waterway transport can be significantly impacted by adverse weather conditions such as heavy rain, strong winds, and flooding. These disruptions can cause delays, cancellations, or even damage to vessels or infrastructure. To improve the system reliability, we propose a set of revenue management based (demand itinerary) rerouting mechanisms for intermodal barge transportation optimisation. Revenue Management policies including several customer categories and fare differentiation are applied. Sequential accept/reject decisions are made based on a probabilistic mixed integer programming model maximising the expected revenue of a carrier. A booking framework is defined over a rolling horizon and capacity allocation/reallocation decisions are made for a set of demands including the current and relevant past and potential future transportation requests. Several (demand) rerouting mechanisms are defined and implemented on different service network configurations. The service network status is regularly updated, in particular with respect to barge capacity variations due to changing water levels. An extensive set of experiments is performed and numerical results are analysed. The study results emphasise the added value but also the need for data availability and information sharing between the different stakeholders of Inland Waterway Transportation systems. [ABSTRACT FROM AUTHOR]

Copyright of Operations Research Transactions / Yunchouxue Xuebao is the property of Editorial office of Operations Research Transactions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Purpose: In this research, a modular hub location problem has been investigated where the objective is to reduce the transportation costs in the hub network. The proposed model determines the location of hubs, allocation of the non-hub nodes to the hubs, and the optimal vehicle traffic, i.e., the number of flights or the number of trucks traveling in the network, considering the appropriate capacity for each vehicle. Also, decisions regarding the percentage of the traffic volume sent via multiple network routes are made by the presented model. Methodology: The mathematical model, including the objective function and constraints, is constructed and solved by GAMS software. The effect of different parameters on the results is investigated. Due to long solution times for the MIP model, a heuristic solution method based on LP relaxation of the integer variables is developed for the proposed problem, which is able to obtain near-optimal solutions in less time. Findings: The developed mathematical model is implemented on the air passenger transportation data for the airports of the United States of America, which is known as the CAB data set. The results give the optimal number of hubs, as well as the optimal number of transportation units on each arc of the network, which depend on the capacity of the means of transportation. Originality/Value: In this research, a mixed integer programming model is developed for the multiple allocation modular hub location problem. Numerical experiments are conducted with the use of GAMS software and the results are discussed. [ABSTRACT FROM AUTHOR]

The fragmentation of natural environments, generally a consequence of human activity, is one of the main threats to biodiversity. The conservation or creation of ecological corridors is essential in an attempt to remedy this fragmentation. We propose a multi-species model to help decision-makers select an optimal network of corridors from a very general potential network, within a budgetary constraint. The selected network must link a given set of biodiversity reservoirs both spatially and biologically. It must therefore be adapted to a given set of species, i.e. it must take account of the fact that certain corridors and reservoirs are more or less suitable for certain species. The quality of the selected network is measured against the quality of the potential network. This network must also take into account the distance certain species have to travel to connect reservoirs, as well as the possibility for certain species to connect reservoirs even when certain corridors have become impassable, thanks to redundant paths. The proposed model is formulated by a mixed-integer mathematical program. A small example illustrates the model and its resolution in detail. Experiments on larger examples using one of the efficient commercial solvers currently available demonstrate the model's practicability. [ABSTRACT FROM AUTHOR]

HIGHLIGHTS Some forest harvest scheduling processes that have been used for many years in practice and research employ rules that emulate human behaviour. Linear programming and mixed integer programming represent sophisticated mathematical procedures, yet there is arguably nothing intelligent inherent in the search process to allow them to emulate human behaviour. With basic random search, no intelligence is employed, and the search process lacks functions that would allow adaptation of search behaviour based on knowledge gained. With hill-climbing search, very little intelligence is employed, and the search process lacks functions that would allow adaptation of search behaviour based on knowledge gained. With other heuristic search processes and evolutionary computation methods, some intelligence is employed, and the search processes may contain functions that would allow adaptation of search behaviour based on knowledge gained. While some forest harvest scheduling processes are similar in how they solve a complex problem, the degree to which they emulate artificial intelligence (learning from search history, adapting the search behaviour) varies. SUMMARY Contemporary tactical forest harvest scheduling efforts address planning problems that generally have an economic or commodity production objective, accounting routines to accumulate outcomes or to assess the extent of forest conditions, and constraints (policy or resource) that limit the assignment of management actions to subdivisions of a forest (stands or strata). Operations research methods have proven useful for addressing these problems and providing guidance, in the form of a harvest schedule, to people managing forests. Heuristic search and simulation methods have also shown promise for addressing these types of problems. Artificial intelligence includes some of these forms of search processes. When concepts of learning, adaptation, and emulation of human thought describe certain search processes, they can be considered under the broad umbrella of artificial intelligence. In this work, many of the operations research, heuristic search, and simulation methods that have been demonstrated as useful for forest harvest scheduling efforts are assessed for their association with artificial intelligence. In some cases, it is argued that the forestry profession has been using artificial intelligence for quite some time to develop tactical forest harvest schedules. Les efforts contemporains de planification pour une récolte forestière tactique font face à des problèmes de planification ayant en général un objectif économique ou de production de commodité, des routines comptables pour accumuler les résultats ou pour évaluer l'étendue des conditions forestières, et des contraintes (de politique ou de ressources) qui limitent l'octroi d'actions de gestion à des subdivisions de forêt (parcelles ou données). Les méthodes de recherche d'observation se sont montrées être utiles pour faire face à ces problèmes et pour offrir de l'aide, sous forme d'une planification de la récolte aux personnes gérant la forêt. Une recherche heuristique et des méthodes de simulation ont également été prometteuses pour faire face à ces types de problèmes. L'intelligence artificielle inclut certaine de ces formes de processus de recherche. Quand les concepts d'apprentissage, d'adaptation et d'émulation de la pensée humaine décrivent certain processus de recherche, ils peuvent être considérés comme étant sous la large égide de l'intelligence artificielle. Dans ce travail, plusieurs des recherches d'opérations, la recherche heuristique et les méthodes de simulation qui ont prouvé être utiles aux efforts de planification de la récolte forestière sont évaluées du point de vue de leur association avec l'intelligence artificielle. Dans certains cas, il est avancé que la profession de foresterie a utilisé l'intelligence artificielle depuis longtemps pour développer des planifications tactiques de récolte forestière. Los esfuerzos contemporáneos de programación táctica de aprovechamientos forestales abordan problemas de planificación que generalmente tienen un objetivo económico o de producción de materias primas, rutinas contables para acumular resultados o evaluar el alcance de las condiciones forestales, y restricciones (políticas o de recursos) que limitan la asignación de acciones de gestión a subdivisiones de un bosque (rodales o estratos). Los métodos de investigación operativa han demostrado su utilidad para abordar estos problemas y ofrecer orientación, en forma de calendario de aprovechamientos, a quienes gestionan los bosques. La búsqueda heurística y los métodos de simulación también han demostrado ser prometedores para abordar este tipo de problemas. La inteligencia artificial incluye algunas de estas formas de procesos de búsqueda. Cuando los conceptos de aprendizaje, adaptación y emulación del pensamiento humano describen ciertos procesos de búsqueda, pueden considerarse parte del amplio abanico de la inteligencia artificial. En este trabajo se evalúan muchos de los métodos de investigación operativa, búsqueda heurística y simulación que se han demostrado útiles para la programación de los aprovechamientos forestales por su asociación con la inteligencia artificial. En algunos casos, se sostiene que la silvicultura lleva bastante tiempo utilizando la inteligencia artificial para elaborar programas tácticos de aprovechamientos forestales. [ABSTRACT FROM AUTHOR]

Mixed integer programming is inherently involved in solving a significant number of practical problems. This paper focuses on mixed integer programming, where the objective function is the summation of N functions, and the constraints include both scalar coupling and set constraints. Given the potentially large scale of these problems, the goal of this work is to propose a distributed method to solve large-scale problems more efficiently. The right-hand side allocation decomposition approach is employed to address the large-scale mixed integer programming problem. Algorithms are then proposed for solving these problems, based on the analysis of the continuity, differentiability, and local convexity properties of the decomposed subproblems. Simulation experiments with randomly generated coefficients demonstrate the superior performance of the proposed algorithms compared to the Gurobi solver, offering higher solution accuracy and faster processing time for large-scale mixed integer programming problems with nonlinear objective and constraint functions. [ABSTRACT FROM AUTHOR]

To guarantee the safety of flight operations, decision-support systems for air traffic control must be able to improve the usage of airspace capacity and handle increasing demand. This study addresses the aircraft conflict avoidance and trajectory recovery problem. The problem of finding the least deviation conflict-free aircraft trajectories that guarantee the return to a target waypoint is highly complex due to the nature of the nonlinear trajectories that are sought. We present a two-stage iterative algorithm that first solves initial conflicts by manipulating their speed and heading control and then identifying each aircraft's optimal time to recover its trajectory towards their nominal one. We extend existing mixed-integer programming formulations by modelling speed and heading control as continuous variables while recovery time is treated as a discrete variable. We develop a novel iterative approach which shows that the trajectory recovery costs can be anticipated by inducing avoidance trajectories with higher deviation, therefore obtaining earlier recovery time within a few iterations. Numerical results on benchmark conflict resolution problems show that this approach can solve instances with up to 30 aircraft within 10 min. [ABSTRACT FROM AUTHOR]

Copyright of GeSec: Revista de Gestao e Secretariado is the property of Sindicato das Secretarias e Secretarios do Estado de Sao Paulo (SINSESP) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a framework for classifying and comparing instances of integer linear programs (ILPs) based on their mathematical structure. It has long been observed that the structure of ILPs can play an important role in determining the effectiveness of certain solution techniques; those that work well for one class of ILPs are often found to be effective in solving similarly structured problems. In this work, the structure of a given ILP instance is captured via a graph-based representation, where decision variables and constraints are described by nodes, and edges denote the presence of decision variables in certain constraints. Using machine learning techniques for graph-structured data, we introduce two approaches for leveraging the graph representations for relating ILPs. In the first approach, a graph convolutional network (GCN) is used to classify ILP graphs as having come from one of a known number of problem classes. The second approach makes use of latent features learned by the GCN to compare ILP graphs to one another directly. As part of the latter approach, we introduce a formal measure of graph-based structural similarity. A series of empirical studies indicate strong performance for both the classification and comparison procedures. Additional properties of ILP graphs, namely, losslessness and permutation invariance, are also explored via computational experiments. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0255) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2023.0255). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The subject of this paper is to develop a method for synthesizing stable neural network controllers with optimization of transient process parameters. The goal is to develop a method for synthesizing a neural network controller for control systems that guarantees the closed-loop system stability through automated selection of Lyapunov function with the involvement of an additional neural network trained on the d ata obtained in the solving process the integer linear programming problem. The tasks to be solved are: study the stability of a closed-loop control system with a neural network controller, train the neurocontroller and Lyapunov neural network function, create an optimization model for the loss function minimization, and conduct a computational experiment as an example of the neural network stabilizing controller synthesis. The methods used are: a neural network - based control object simulator training method described by an equations system taking into account the Smooth-ReLU activation function, a direct Lyapunov method to the closed-loop system stability guarantee, and a mixed integer programming method that allows minimizing losses and ensuring stability a nd minimum time regulation for solving the optimization problem. The following results were obtained: the neural network used made it possible to obtain results related to the transient process time reduction to 3.0 s and a 2.33 -fold reduction in overregulation compared to the traditional controller (on the example of the TV3 -117 turboshaft engine fuel consumption model). The results demonstrate the proposed approach's advantages, remarkably increasing the dynamic stability and parameter maintenance accuracy, and reducing fuel consumption fluctuations. Conclusions. This study is the first to develop a method for synthesizing a stabilizing neural network controller for helicopter turboshaft engines with guaranteed system stability based on Lyapunov theory. The proposed method's novelty lies in its linear approximation of the SmoothReLU activation function using binary variables, which allowed us to reduce the stability problem to an optimization problem using the mixed integer programming method. A system of constraints was developed that considers the control signal and stability conditions to minimize the system stabilization time. The results confirmed the proposed approach's effectiveness in increasing engine adaptability and energy efficiency in various operating modes. [ABSTRACT FROM AUTHOR]

We consider a staff allocation problem at a sequential sorting facility. In this facility, staff need to be assigned to work areas, through which commodities flow sequentially to be processed. Assigning staff optimally involves a trade-off between several different objectives, such as minimising the overall number of workers, as well as having fewer changes in the staff levels over time. While optimising for these, many operational requirements need to be met, including minimum processing volumes, correct ordering/processing of the commodities, and not exceeding staff resource constraints. We develop a deterministic time-expanded network flow model to solve the staff allocation problem. The model addresses the problem at a more granular timescale and with more operational constraints than previously used models. We use a lexicographical approach to deal with the multiple objectives. To demonstrate the model's value, we apply it to a staff problem of a UK mail centre, showing that in the majority of cases, our model improves on current staffing practises on both objectives. We also show how the model performs in several different scenarios, including increasing total mail volumes and changing the proportion of letters and parcels to be sorted. [ABSTRACT FROM AUTHOR]

Motivated by the operational scenarios of lock scheduling, we propose a serial-lock chain navigation problem (SLCNP) modeled on the Three Gorges-Gezhouba Dam (TGGD) for the first time. Ship grouping, synchronized moving, and grouped waiting operations are integrated into the ship navigation process. A mixed integer programming (MIP) model that incorporates real-world constraints such as ship priority, service fairness, traffic flow equilibrium, and phased ship placement is presented to optimize ship throughput and ship stay time. To solve the SLCNP, a sort-pick strategy-based swarm intelligence algorithm (SPSSIA) framework is developed that integrates the characteristics of SLCNP through a hybrid multi-section encoding method and a two-stage heuristic decoding approach. A swarm intelligence evolution mechanism is used to improve the search ability and robustness of the framework. Several instances are generated based on real data to verify the correctness and effectiveness of the model and algorithm. Computational results demonstrate the applicability and effectiveness of the proposed SPSSIA. Further analysis of the experimental results indicates that the key impact factors significantly influence the navigational performance of the TGGD system. The results of this study will provide practical guidance for the operational processes of inland river hubs with comparable characteristics. [ABSTRACT FROM AUTHOR]

Copyright of Palestine Journal of Mathematics is the property of Palestine Polytechnic University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We consider an integrated batching problem for steel-making and continuous casting process of steel plate manufacturing. For steel-making, slab batching problem is defined to make charges from slabs, and for continuous casting, charge batching problem is defined to make casts from charges. Our batching problem is regarded as a combination of slab batching and charge batching problems. Since steel-making and continuous casting are processes that must be synchronised, two batching problems must be integratedly handled. However, because of their difficulties, most papers solved each batching problem sequentially. We deal with a batching problem under bi-strand casting environment where slabs are cast with two strands. We also consider practical aspects that were barely considered before such as slab length difference constraints between strands and casts having few charges. We propose two mixed integer programming models. The first one is to create frames to define the overall structure of the solution and the second one is to fill the created frames with slabs to concretise the solution. The proposed matheuristic algorithm solves the problem in an integrated manner and finds a near-optimal solution in a reasonable time. It outperforms the company's current practice, as shown in experiments with real and randomly generated data. [ABSTRACT FROM AUTHOR]

In deterministic optimization, it is typically assumed that all problem parameters are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from contextual information. A typical predict-then-optimize approach separates predictions and optimization into two distinct stages. Recently, end-to-end predict-then-optimize has emerged as an attractive alternative. This work introduces the PyEPO package, a PyTorch-based end-to-end predict-then-optimize library in Python. To the best of our knowledge, PyEPO (pronounced like pineapple with a silent "n") is the first such generic tool for linear and integer programming with predicted objective function coefficients. It includes various algorithms such as surrogate decision losses, black-box solvers, and perturbated methods. PyEPO offers a user-friendly interface for defining new optimization problems, applying state-of-the-art algorithms, and using custom neural network architectures. We conducted experiments comparing various methods on problems such as the Shortest Path, the Multiple Knapsack, and the Traveling Salesperson Problem, discussing empirical insights that may guide future research. PyEPO and its documentation are available at https://github.com/khalil-research/PyEPO. [ABSTRACT FROM AUTHOR]

Introduction and objectives: Sustainable development is defined as development that meets the needs of the present generation without compromising the ability of future generations to meet their own needs. It encompasses economic, social, and environmental dimensions that must be considered simultaneously. With the increasing importance of sustainable development, many companies worldwide are motivated, either proactively or reactively, to collect their used products. In such circumstances, establishing a reverse logistics network based on sustainable development is essential. The decision to outsource logistics has gained significance due to the need to avoid fixed costs, heavy investment, and achieve economic advantages, with many companies recognizing the potential benefits of high-quality logistics services. Method: This research presents a mixed integer programming model for planning reverse logistics outsourcing in the assembly cycle of the automotive industry, focusing on a cost-oriented objective function. The research scope includes the assembly cycle of production lines, specifically prioritizing high-volume car manufacturers (light vehicles), and focuses on the Saipa Automotive Industrial Group, including the Ryan Saipa Leasing Group. The research period spans from 1389 to 1398 in the Iranian calendar. Variables such as non-commercial receivables, total assets, operating profit, net profit, and market value were evaluated using MATLAB software based on published statistics from Saipa. Findings: The research findings indicate that among the variables of non-commercial receivables, total assets, operating profit, net profit, and market value, net profit to operating profit and sales (operating income) are of significant importance. The highest amount of non-commercial receivables for Saipa occurred in 1398 during the summer, while the highest total assets were recorded in 1392 during the summer. The highest operating profit was observed in 1398 during the winter, and the highest net profit was in 1390 during the spring. The degree of data convergence was calculated in the regression charts of sales (operating income) to operating profit and net profit to operating profit for the years 1389-1398. The degree of data convergence in the regression chart of sales to operating profit based on the conceptual model in 1398 was 0.9895, and for net profit to operating profit in 1398, it was 0.9961. The regression rate for the conceptual model in the test phase was 0.79, and in the overall processing stage, it was also 0.79. The histogram error rate was calculated for all three stages of learning, validation, and testing, with an error rate of 0.002375, which is acceptable due to its proximity to zero. Comparing these results with other studies shows an improvement in the regression and error rate in the analysis of the objective function. Conclusion: Based on the calculated weight of the criteria in two-way assembly line balancing issues, it can be concluded that the decision team pays special attention to strategic issues in addition to production issues. The production rate of the line, which is the inverse of the production cycle time, affects the company's market share in the long term and increases its market share. [ABSTRACT FROM AUTHOR]

In this paper, we address the difficulty of solving large-scale multi-dimensional knapsack instances (MKP), presenting a novel deep reinforcement learning (DRL) framework. In this DRL framework, we train different agents compatible with a discrete action space for sequential decision-making while still satisfying any resource constraint of the MKP. This novel framework incorporates the decision variable values in the 2D DRL where the agent is responsible for assigning a value of 1 or 0 to each of the variables. To the best of our knowledge, this is the first DRL model of its kind in which a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our framework is configured to solve MKP instances of different dimensions and distributions. We propose a K-means approach to obtain an initial feasible solution that is used to train the DRL agent. We train four different agents in our framework and present the results comparing each of them with the CPLEX commercial solver. The results show that our agents can learn and generalize over instances with different sizes and distributions. Our DRL framework shows that it can solve medium-sized instances at least 45 times faster in CPU solution time and at least 10 times faster for large instances, with a maximum solution gap of 0.28% compared to the performance of CPLEX. Furthermore, at least 95% of the items are predicted in line with the CPLEX solution. Computations with DRL also provide a better optimality gap with respect to state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

This paper mainly studies a task allocation and scheduling problem in the multi-thread fulfilment process of electronic order, which seeks to minimise the makespan under thread constraints and order precedence constraints. The problem is formulated as a Mixed Integer Programming (MIP) model and a novel depth-first heuristic is proposed to solve it. The depth-first heuristic shows high effectiveness and efficiency, compared with the current policy and the genetic algorithm in both small/medium-scale and large-scale cases from the real transaction data. In addition, two extensions on precedence constraint reduction and resource allocation are discussed to further improve and manage the e-order fulfilment process. [ABSTRACT FROM AUTHOR]

This paper studies the multi-trip vehicle routing problem with multiple time windows, which extends the multi-trip vehicle routing problem by deciding not only the sequence of customers that each vehicle serves but also the service time window of each customer. It also requires that the delivery service time is within the selected time windows and that the total demand of the customers served by the vehicle on each trip does not exceed the maximum carrying capacity. For solving the studied problem, we develop a mixed integer linear programming model with the objective of minimizing the total travel distance of vehicles and design a tailored iterative local search heuristic. Within the framework of the iterative local search, an improved Solomon greedy insertion algorithm suitable for multiple time windows and multi-trip scenarios is designed to generate the initial solution, and local search operators such as Or-opt and Relocate, as well as Random Exchange perturbation operations, are also developed. The experiment results demonstrate the effectiveness of the proposed model and algorithm and confirm that by providing customers with multiple time windows option, carriers can flexibly plan vehicle routes and select appropriate service time windows, thereby reducing the number of vehicles used and the total distance travelled and improve delivery success. [ABSTRACT FROM AUTHOR]

Log transportation accounts for a significant portion of the total delivered cost of logs due to the considerable number of truckloads between origins and destinations. Hence, an efficient transportation plan at the operational level can generate cost savings for forest companies. In this paper, a mixed integer linear programming model is developed for daily routing and scheduling of heterogeneous trucks considering synchronization constraints. Continuous time representation is used for modeling the problem to generate accurate schedules and to synchronize the trucks and loaders at cut blocks and sort yards. Compatibility requirements, overtime, and decisions related to the trucking contractors are incorporated in the model. The outputs of the model include the number of trucks utilized by each contractor, the arrival times and waiting times of trucks at each location, the detailed schedule of loaders, and the amount of overtime assigned to the drivers. To validate the model, it is applied to test problems from a case of a Canadian forest company, where transportation activities are contracted out. Results show it is more economical to pay overtime than dispatching additional trucks to carry logs. Additionally, variable costs and maximum driving time have the most impact on the total transportation cost. [ABSTRACT FROM AUTHOR]

We review existing approaches to optimizing the deployment of genetic biocontrol technologies--tools used to prevent vector-borne diseases such as malaria and dengue--and formulate a mathematical program that enables the incorporation of crucial ecological and logistical details. The model is comprised of equality constraints grounded in discretized dynamic population equations, inequality constraints representative of operational limitations including resource restrictions, and an objective function that jointly minimizes the count of competent mosquito vectors and the number of transgenic organisms released to mitigate them over a specified time period. We explore how nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) can advance the state of the art in designing the operational implementation of three distinct transgenic public health interventions, two of which are presently in active use around the world. [ABSTRACT FROM AUTHOR]

This paper presents two novel formulations for scheduling problems, namely order-position hybrid formulation (OPH) and order-disjunctive hybrid formulation (ODH), which extend and combine parts of existing formulation strategies. The first strategy (OPH) is based on sequence position and linear ordering formulations, adding relationships between constraints that allow relaxing some decision variables. The second approach (ODH) is based on linear ordering and disjunctive formulations. In this work, we prove ODH to be the most efficient formulation known so far. The experiments have been carried out with a large set of problems, which consider single machines and identical parallel machines. Computational results show that OPH is better than the rest of the existing formulations for the case of weighted completion objectives, while ODH turns out to be the best approach for most scenarios studied. [ABSTRACT FROM AUTHOR]

Haplotype inference is an important issue in computational biology due to its various applications in diagnosing and treating genetic diseases such as diabetes, Alzheimer, and heart defects. There are different criteria to choose the solution from the alternatives. Parsimony is one of the most important criteria according to which the problem is known as Pure Parsimony Haplotyping (PPH) problem. The approaches to solve PPH are classified to two groups: exact and non-exact. The exact approaches often model the problem as a Mixed Integer Linear Programming (MILP) problem. Although in solving the small instances, these models generate the optimal solution in a reasonable time, because of the NP-hardness characteristic of PPH problem, they are ineffective in solving very large instances. This deficiency is compensated by non-exact algorithms. In this paper, we present a non-exact algorithm for large instances of PPH problem based on the divide-and-conquer technique. This algorithm, first, divides the problem into small sub-problems, which are solved by one of the previous exact approaches, and finally the solutions of the sub-problems are combined through solving an MILP. The appeared MILPs for solving the sub-problems and those for combining the solutions are so small that are solved rapidly. The performance of this algorithm has been evaluated by implementing it on real and simulated instances and in comparison with two well-known methods of PHASE and WinHap2. [ABSTRACT FROM AUTHOR]

Most studies of shared autonomous vehicles (SAVs) have assumed established automated driving technology. In contrast, this study assumes that automated driving technology is not yet mature; it proposes two types of models to optimize the number of SAVs and the sections they travel. The first model (i.e., the 'actual depot model') does not consider the travel distance from the depot to the service start and end points. The second (i.e., the 'virtual depot model') considers the as-described travel distance. We showed in the actual depot model that under mild assumptions, the continuity condition of the SAV travel segments can be described by a simple constraint condition. The models were then applied to a hypothetical network; the performances of the models confirmed that the evaluation indicators for the virtual depot model tended to be better than the indicators for the actual depot model. [ABSTRACT FROM AUTHOR]

Mathematical modeling is a suitable method for solving agricultural production planning problems due to the restriction of resources available. In this study, we tried to use a generalized assignment problem in the form of mixed integer programming to model the best harvesting time of sugarcane farms in a 7-month horizon. Before the model can be applied to optimize the farms' harvesting time, two critical parameters of sugarcane yield and recoverable sugar percentage were predicted by a fuzzy c-means clustering system. The results of model optimization using GAMS software based on CPLEX solver showed that the most suitable period for obtaining the highest gross harvest profit at peak varietal maturity was during February, with an average of 10.5% recoverable sugar for the five major sugarcane varieties planted in Khuzestan province. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of scheduling independent jobs on identical parallel machines with a single server to minimise the makespan. We propose mixed integer programming (MIP) formulations to solve this problem. Each formulation reflects a specific concept on how the decision variables are defined. Moreover, we present inequalities that can be used to improve those formulations. A computational study is performed on benchmark instances from the literature to compare the proposed MIP formulations with other known formulations from the literature. It turns out that our proposed time-indexed variables formulation outperforms by far the other formulations. In addition, we propose a very efficient MIP formulation to solve a particular case of the problem with a regular job set. This formulation is able to solve all regular instances for the case of 500 jobs and 5 machines in less than 5.27 min, where all other formulations are not able to produce a feasible solution within 1 h. [ABSTRACT FROM AUTHOR]

Generally, when optimizing a rolling stock schedule, the locations of the depots, or places in the network where the composition changes and maintenance occurs, are assumed known. The locations where maintenance is performed naturally influence the quality of any resulting rolling stock schedules. In this paper, the problem of selecting new depot locations and their corresponding capacities is considered. A two-stage mixed integer programming approach for rolling stock scheduling with maintenance requirements is extended to account for depot selection. First, a conventional flow-based model is solved, ignoring maintenance requirements, to obtain a variety of rolling stock schedules with multiple depot locations and capacity options. Then, a maintenance feasible rolling stock schedule can be obtained by solving a series of assignment problems by using the schedules found in the first stage. The proposed methodology is tested on real-life instances, and the numerical experiments of different operational scenarios are discussed. [ABSTRACT FROM AUTHOR]

Computerized adaptive testing (CAT) has gained deserved popularity in the administration of educational and professional assessments, but continues to face test security challenges. To ensure sustained quality assurance and testing integrity, it is imperative to establish and maintain multiple stable item pools that are consistent in terms of psychometric characteristics and content specifications. This study introduces the Honeycomb Pool Assembly (HPA) framework, an innovative solution for the construction of multiple parallel item pools for CAT that maximizes item utilization in the item bank. The HPA framework comprises two stages—cell assembly and pool assembly—and uses a mixed integer programming modeling approach. An empirical study demonstrated HPA's effectiveness in creating a large number of parallel pools using a real‐world high‐stakes CAT assessment item bank. The HPA framework offers several advantages, including (a) simultaneous creation of multiple parallel pools, (b) simplification of item pool maintenance, and (c) flexibility in establishing statistical and operational constraints. Moreover, it can help testing organizations efficiently manage and monitor the health of their item banks. Thus, the HPA framework is expected to be a valuable tool for testing professionals and organizations to address test security challenges and maintain the integrity of high‐stakes CAT assessments. [ABSTRACT FROM AUTHOR]

Identifying seismic risk factors and determining necessary resources are critical for effective post-earthquake mitigation planning. This usually involves field assessments, data collection, and disaster scenario simulations. After an earthquake, the focus is on providing medical services and although hospitals are vital in saving lives, they may become overwhelmed with injured patients. As a result, it is essential to establish post-disaster strategies to ensure continued access to medical services. This study introduces a framework that analyses an earthquake's temporal effect on a hospital network's emergency response capabilities under various casualty transfer strategies. The framework initially evaluates the seismic vulnerability of buildings to estimate the medical demand and subsequently assesses the resilience of the hospital network based on patients waiting times for ambulance arrivals and treatment in the emergency departments of the hospitals. The model determines the optimal allocation of emergency department capacity across the hospital network and evaluates each hospital's performance. The framework is implemented in Bayrakli, a metropolitan district in Izmir, Turkey, which has a unique building inventory dataset. The study demonstrated how various casualty transfer decisions can expedite the transportation process, providing valuable insights for creating effective emergency management and mitigation strategies in areas that are prone to earthquakes. [ABSTRACT FROM AUTHOR]

Yarn dyeing is a critical link in the textile production chain that consumes the most time and energy. Today's dyeing shops receive hundreds of demands with thousands of different colors, different due dates, and different production requirements. This situation has made it very difficult for the human brain to create a minimum‐cost production plan by complying with the due dates. In this study, a real‐life problem of a company operating in the textile industry is discussed and a solution has been developed for the planning of yarn‐dyeing boilers. The application was held in Bursalı Textile, which is the major towel manufacturer operating in Turkey. The problem dealt with is basically in the nature of the variable‐size bin‐packing problem (VSBPP). The limited availability of bins (boilers) of different sizes and the packing of the items (yarn work orders) with due date constraints are the original aspects of this study. Multi‐objective mixed integer programming model is developed to minimize two objectives. For the solution, the preemptive method called the lexicographic approach, in which the objectives are solved in order, is preferred. As the first objective, the overcapacity usage is minimized and then the second objective, which is the boiler usage cost, is minimized. Given that the VSBPP is strongly NP‐hard, an iterated greedy algorithm with two different decoding approaches is proposed. Computational experiments were conducted on 20 randomly generated benchmark instances and a real‐world industrial dataset. The numerical results show that good solutions can be obtained in seconds using the proposed approaches. [ABSTRACT FROM AUTHOR]

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This paper studies the assignment problem of multi product assembly jobs to days. The problem aims to minimize the amount of overtime while avoiding assembly delays for jobs that can be fragmented into smaller sub-tasks. When sequencedependent setup times are negligible, the problem considered transforms into the bin packing problem with restricted item fragmentation where jobs represent items and days stand for bins. We present a mixed integer programming model of the problem by extending earlier formulations in the literature. Computational experiments show that the mathematical model obtained optimal solutions for majority of instances tested within reasonable computation times. [ABSTRACT FROM AUTHOR]

This paper examines the recovery of a three-level manufacturing supply chain under supply and demand disruptions. The paper proposes new combined recovery strategies, which aim to cope with interruption by adjusting the supply chain structure and material flows. This study integrates both supply chain performance and supply chain capability dimensions. We develop a bi-criteria mixed integer linear programming model with profit and resilience maximization as the objective. The model combines supply-side supply expansion, manufacturer capacity impairment, and demand regulation on the demand side. In a numerical example, we find that a "reciprocal disruption overlay" occurs when supply and demand disruptions, but the supply chain still loses some profit. The results suggest that the combined recovery strategies reduce profit loss and increase supply chain resilience. Furthermore, the strategies are also the optimal recovery strategies under unilateral disruptions. This model facilitates the coordination of a disrupted supply chain and can help managers decide on the best recovery plan. [ABSTRACT FROM AUTHOR]

To reduce human resource costs, the part-to-picker order fulfilment systems may have a single picker in charge of multiple workstations. And the picking speed of the picker becomes faster as the picking number increases due to the learning effect in the picking operation. In this paper, the scheduling problem to optimizing picking sequence of the picker is presented to minimize the maximum picking time, where one picker is responsible for multiple workstations. The learning effect and travel time between workstations are taken into account to improve scheduling accuracy. Two mixed integer programming (MIP) models are proposed to solve the problem, namely the rank-based model and disjunctive model. The performance of the two Mixed Integer Programming (MIP) models has been evaluated, and it has been found that they are only capable of solving small-scale problems. The rank-based model is limited to solving problems with up to 9 groups, whereas the disjunctive model can handle up to 20 groups. Therefore, the disjunctive model outperforms the rank-based model. Moreover, this paper proposes Interval Insertion NEH (IINEH) and iterative greedy (IG) algorithm to solve the large-scale problem. Numerical experiments demonstrate the effectiveness of the two methods to solve the problem, where IINEH operates faster while IG gives better results. Therefore, when faced with a large-scale problem, IINEH is recommended if a quick solution is needed. If better optimization results are needed, the decision maker can choose IG. [ABSTRACT FROM AUTHOR]

This article examined the issue of selection heuristics for the ABB algorithm, a branch-and-bound method for determining the optimal solution structure in P-graphs. Previous studies have not investigated the possible effects of different heuristics on the running time of the ABB algorithm. In this study, we represent the results of applying three basic heuristics in randomly generated P-graphs. In particular, for P-graphs with matrix patterns, the LIFO heuristic is recommended because it performed the best, while the FIFO heuristic had the slowest running time. [ABSTRACT FROM AUTHOR]

Two-stage precoding schemes have been developed to reduce the channel estimation overhead in FDD systems. By integrating user scheduling into these schemes, it becomes possible to meet the quality-of-service requirements of high-density wireless communication systems, despite the limitations on spatial resources and transmit power budget. In this paper, we propose a user scheduling and dynamic beam allocation method for neighbor-based joint spatial division multiplexing (N-JSDM) transmission. The user scheduling problem is formulated as a 0–1 quadratic programming problem to maximize effective spectral efficiency (ESE) using directional channel properties. To address the complexity issue, convex relaxation and linearization methods are employed to transform the problem into a 0–1 mixed integer linear programming, and a dimensionality reduction method is introduced. The proposed user scheduling-aided N-JSDM scheme reduces downlink training length and feedback of channel state information. Additionally, a dynamic configuration form is used for pre-beamforming matrix design based on user distribution, outperforming conventional approaches. Simulation results demonstrate higher ESE achieved by the proposed scheme compared to previous methods. [ABSTRACT FROM AUTHOR]