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One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment. [ABSTRACT FROM AUTHOR]

In the context of Industry 4.0, industrial production equipment needs to communicate through the industrial internet to improve the intelligence of industrial production. This requires the current communication network to have the ability of large-scale equipment access, multiple communication protocols/heterogeneous systems interoperability, and end-to-end deterministic low-latency transmission. Time-sensitive network (TSN), as a new generation of deterministic Ethernet communication technology, is the main development direction of time-critical communication technology applied in industrial environments, and Wi-Fi technology has become the main way of wireless access for users due to its advantages of high portability and mobility. Therefore, accessing WiFi in the TSN is a major development direction of the current industrial internet. In this paper, we model the scheduling problem of TSN and WiFi converged networks and propose a scheme based on a greedy strategy distributed estimation algorithm (GE) to solve the scheduling problem. Compared with the integer linear programming (ILP) algorithm and the Tabu algorithm, the algorithm implemented in this paper outperforms the other algorithms in being able to adapt to a variety of different scenarios and in scheduling optimization efficiency, especially when the amount of traffic to be deployed is large. [ABSTRACT FROM AUTHOR]

This paper presents a method for identifying causal relationships between strategic objectives within a strategy map of a Balanced Scorecard. Strategy maps are modeled as a network of strategic objectives (nodes) and causal relationships (directed arcs). The nodes are also grouped into clusters that represent the perspectives of a Balanced Scorecard: (a) Finances, Clients, Internal Processes and Growth and Learning. The method uses the Analytic Network Process (ANP) to establish the importance of every relationship and uses a multi-objective integer linear programming model to select the relationships to be included within a strategy map of a company. The method provides a method that optimizes the selection of the relationships to be included in a strategy map. An illustration of the application of the method in a manufacturing company is presented. [ABSTRACT FROM AUTHOR]

In the multi-domain network scenario, in order to improve the survivability of service function chain (SFC) in the face of network failure, most methods solve this problem through virtual network function (VNF) backup mechanism. However, the traditional multi-domain SFC deployment method lacks a SFC partition mechanism for backup resource consumption and does not consider the isolation and privacy requirements between different network domains. In view of the above problems, this paper proposes a reliability partition scheme based on reinforcement learning in SFC partition stage, which can ensure that VNF is backed up while maintaining good load balancing and low inter-domain transmission delay, and improve the reliability of SFC. Then, this paper proposes a VNF backup mechanism with minimum resource fluctuation in the VNF mapping stage and uses the integer linear programming (ILP) model to determine the backup scheme of each VNF, so as to ensure the minimum fluctuation of resource occupancy of the entire network. Finally, this paper proposes a multi-domain SFC deployment and backup algorithm based on Federated learning (FA-MSDB). The experimental results indicate that FA-MSDB can effectively improve the survival rate of SFC, reduce the overall transmission delay, and ensure good inter-domain and intra-domain load balance. [ABSTRACT FROM AUTHOR]

Under the modern environment, the reconstruction of enterprise's core competitiveness depends not only on capital and technical strength, but also on the overall strength of its human resources. At the same time, effective allocation and rational use of talents are needed to create good performance for enterprises. Enterprise human resource management is the key part of the whole enterprise management. At the same time, it is also a necessary preparation for the continuous development and innovation of enterprises. In the whole process of human resource management, the core work is person-post matching. Only by promoting the reasonable implementation of person-post matching can other management work be carried out smoothly. This paper expounds two major elements in human resource management, namely, the concept and measurement of person-post matching and the principle of person-post matching. And the factors in the matching of people and posts are analyzed. This paper probes into the implementation of person-post matching in enterprise human resource management. Based on this, this paper puts forward a depth model of accurate matching between people and posts based on ability perception. On the basis of studying the optimization of human resource scheduling, this paper takes into account three factors: resource constraints, heterogeneity of employee efficiency and time sequence relationship, and uses integer linear programming theory to model the system with the shortest construction period as the goal. The research shows that the accuracy of this algorithm can reach about 94%, which is about 8% higher than the traditional algorithm. It has certain superior performance. This will provide some reference for related researchers. [ABSTRACT FROM AUTHOR]

Many papers in the field of integer linear programming (ILP, for short) are devoted to problems of the type max { c ⊤ x : A x = b , x ∈ Z ≥ 0 n } , where all the entries of A, b, c are integer, parameterized by the number of rows of A and ‖ A ‖ max . This class of problems is known under the name of ILP problems in the standard form, adding the word "bounded" if x ≤ u , for some integer vector u. Recently, many new sparsity, proximity, and complexity results were obtained for bounded and unbounded ILP problems in the standard form. In this paper, we consider ILP problems in the canonical form max { c ⊤ x : b l ≤ A x ≤ b r , x ∈ Z n } , where b l and b r are integer vectors. We assume that the integer matrix A has the rank n, (n + m) rows, n columns, and parameterize the problem by m and Δ (A) , where Δ (A) is the maximum of n × n sub-determinants of A, taken in the absolute value. We show that any ILP problem in the standard form can be polynomially reduced to some ILP problem in the canonical form, preserving m and Δ (A) , but the reverse reduction is not always possible. More precisely, we define the class of generalized ILP problems in the standard form, which includes an additional group constraint, and prove the equivalence to ILP problems in the canonical form. We generalize known sparsity, proximity, and complexity bounds for ILP problems in the canonical form. Additionally, sometimes, we strengthen previously known results for ILP problems in the canonical form, and, sometimes, we give shorter proofs. Finally, we consider the special cases of m ∈ { 0 , 1 } . By this way, we give specialised sparsity, proximity, and complexity bounds for the problems on simplices, Knapsack problems and Subset-Sum problems. [ABSTRACT FROM AUTHOR]

The cloud service provider market has recently expanded its offerings by providing edge as a service. This involves offering resources equivalent to those already available in the cloud, but through data centers located closer to the end user, with the goal of improving service latencies. Application providers face the challenge of selecting appropriate resources, both from the edge and cloud, to deploy their applications in a way that minimizes deployment costs while satisfying latency requirements. This paper presents Edarop (EDge ARchitecture OPtimization), an innovative orchestration mechanism for the optimal allocation of virtual machines in geographically distributed edge and cloud infrastructures. Edarop is capable of handling different edge and cloud vendors, each offering various types of VMs in different regions, with different prices, and network latencies. It also supports multiple simultaneous applications with different latency requirements and load profiles. Edarop employs Integer Linear Programming (ILP) to ensure the globally optimal solution within a reasonable time frame for the considered use cases. Several variants of the mechanism are provided, depending on whether the objective is to minimize cost, response times, or both. These variants are compared to each other and to alternative approaches, with the results showing that, unlike other methods, Edarop consistently respects latency constraints while minimizing the proposed objectives. [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]

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]

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]

As a novel network architecture, network function virtualization (NFV) greatly improves the flexibility and scalability of service provision. Deploying the service function chain (SFC) in an NFV environment needs to coordinate the instantiation of the virtual network function descriptor, network function embedding, and traffic steering, which also improves the complexity of the problem. Although heuristic algorithms are widely used to optimize this problem, due to the lack of complete SFC deployment solution space and digital coding scheme, the time complexity of the algorithm is difficult to meet the requirements. Therefore, this paper studies the digital coding scheme of the heuristic SFC deployment to improve time efficiency without reducing performance. Firstly, we model the SFC deployment as a 0–1 integer linear programming, considering the above factors, and then design a continuous digital solution space construction scheme based on N-Base coding (NBACO-SS) to optimize the above problems. NBACO-SS uses integer size and carry to map the complex SFC deployment to simple digital coding, evaluates the continuity of solution space through the Manhattan distance, and optimizes the continuity through the ant colony algorithm. Based on NBACO-SS, we reconstruct two heuristic algorithms to solve the SFC deployment problem. Experimental results demonstrate that NBACO-SS can improve the time efficiency by 20% without reducing the total network service traffic. [ABSTRACT FROM AUTHOR]

We address three variants of the two-dimensional cutting stock problem in which the guillotine cutting of large objects produces a set of demanded items. The characteristics of the variants are the rectangular shape of the objects and items; the number of two or three orthogonal guillotine stages; and a sequencing constraint that limits the number of open stacks to a scalar associated with the number of automatic compartments or available space near the cutting machine. These problems arise in manufacturing environments that seek minimum waste solutions with limited levels of work-in-process. Despite their practical relevance, we are not aware of mathematical models for them. In this paper, we propose an integer linear programming (ILP) formulation for each of these variants based on modelling strategies for the two-dimensional guillotine cutting stock problem and the minimisation of the open stacks problem. The first two variants deal with exact and non-exact 2-stage patterns, and the third with a specific type of 3-stage patterns. Using a general-purpose ILP solver, we performed computational experiments to evaluate these approaches with benchmark instances. The results show that several equivalent solutions of the cutting problem allow obtaining satisfactory solutions with a reduced number of open stacks. [ABSTRACT FROM AUTHOR]

It is a critical issue to allocate redundancy to critical smart grid infrastructure for disaster recovery planning. In this study, a framework to combine statistical prediction methods and optimization models for the optimal redundancy allocation problem is presented. First, statistical simulation methods to identify critical nodes of very large-scale smart grid infrastructure based on the topological features of embedding networks are developed, and then a linear integer programming model based on generalized assignment problem (GAP) for the redundancy allocation of critical nodes in smart grid infrastructure is presented. This paper aims to contribute to the field by employing a general redundancy allocation problem (GRAP) model from high-order nonlinear to linear model transformation. The model is specifically implemented in the context of smart grid infrastructure. The innovative linear integer programming model proposed in this paper capitalizes on the logarithmic multiplication property to reframe the inherently nonlinear resource allocation problem (RAP) into a linearly separable function. This reformulation markedly streamlines the problem, enhancing its suitability for efficient and effective solutions. The findings demonstrate that the combined approach of statistical simulation and optimization effectively addresses the size limitations inherent in a sole optimization approach. Notably, the optimal solutions for redundancy allocation in large grid systems highlight that the cost of redundancy is only a fraction of the economic losses incurred due to weather-related outages. [ABSTRACT FROM AUTHOR]

With the quickly developing data centers in smart cities, reducing energy consumption and improving network performance, as well as economic benefits, are essential research topics. In particular, Data Center Networks do not always run at full capacity, which leads to significant energy consumption. This paper experiments with a range of optimization tools to find the optimal solutions for the Integer Linear Programming (ILP) model of network power consumption. The study reports on experiments under three communication patterns (near, long, and random), measuring runtime and memory consumption in order to evaluate the performance of different ILP solvers. While the results show that, for near traffic pattern, most of the tools rapidly converge to the optimal solution, CP-SAT provides the most stable performance and outperforms the other solvers for the long traffic pattern. On the other hand, for random traffic pattern, Gurobi can be considered to be the best choice, since it is able to solve all the benchmark instances under the time limit and finds solutions faster by 1 or 2 orders of magnitude than the other solvers do. [ABSTRACT FROM AUTHOR]

Numerous research works has focused on the positioning multiple mobile sinks in the network area to improvise the lifetime of wireless sensor network. The experimental results of the research works clearly indicates that the lifetime of the network will be increased several folds on exploiting multiple mobile sinks in the network rather than static sinks. The proposed paper employs multiple mobile sinks to increase the lifetime of network. The research work focuses on finding the best energy rich locations for placing multiple mobile sinks in a way it delays the expiry of one hop sensor nodes. The paper contributes an Integer Linear Programming (ILP) formulation for the positioning of mobile sinks. In an attempt to find the best location to place the mobile sinks, the paper discretizes the solution space as a replacement for the entire network. The energy rich positions for positioning the mobile sinks are found through the solution ofthe ILP formulation. As an alternative of running the ILP on a continuous search space, the solution space is discretized and ILP is implemented on the discretized space. Experimental results indicate that the proposed ILP model maximizes the network lifetime to a great extent in comparison with the static sink method. [ABSTRACT FROM AUTHOR]

AbstractLet c: V(G) → {1, . . . , ℓ} = [ℓ] be a proper vertex coloring of G and C(i) = {u ∈ V(G): c(u) = i} for i ∈ [ℓ]. The k-color code rk(v|c) of vertex v is the ordered ℓ-tuple (aG(v,C(1)), . . . , aG(v,C(ℓ))) whereIf every two vertices have different color codes, then c is a (k, ℓ)-locating coloring of G. The k-locating chromatic number of graph G, denoted by , is the smallest integer ℓ such that G has a (k, ℓ)-locating coloring. In this paper, we propose this concept as an extension of diam(G)-locating chromatic number and 2-locating chromatic number which are known as the locating chromatic number, denoted χL(G), and neighbor-locating chromatic number, denoted , respectively. In this paper, we give sharp bounds for and where G◦H and are the corona and edge corona of G and H, respectively. We formulate an integer linear programming model to determine , noting that almost all graphs have diameter 2 and for every graph G of diameter 2. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the daily berth planning problem for Xiamen Hai-Tian Container Terminal (XHCT) at the Port of Xiamen, China, and propose the development and implementation of a berth planning system. The aim of the berth planning problem is to optimize daily berth plans by considering various decisions, including berth allocation, quay crane assignment, fairway traffic control, and berthing safety requirements. Among these decisions, the berthing safety requirement is a novel but practical problem in berth allocation that concerns the resource allocation related to berthing safety and interrelation with other decisions. A mathematical programming-driven methodological framework is designed with a 0-1 integer linear programming model for problem formulation and a highly efficient decomposition heuristic algorithm for solving the problem. This framework establishes the core for the berth planning system. The adoption of the berth planning system contributes to the increase of container throughput and berth capacity by transforming the planning process of XHCT. Moreover, the mathematical programming-driven daily berth planning informs further intelligent operations development in the Port of Xiamen and other container ports. History: This paper was refereed. Funding: This research was supported by the National Natural Science Foundation of China [Grants 72394360, 72394362, 72025103, 71831008, 72361137001, 72071173, and 72371221]. [ABSTRACT FROM AUTHOR]

Edge computing provides task offloading services to extend the computational capacity of mobile users and reduce task latency. Prior studies mainly focus on tasks with strict deadlines. However, in the real world, some tasks may not always have to be finished before hard deadlines, e.g., multimedia tasks. Tasks with soft deadlines can miss their primary deadlines, but not by too much, and still be timely. This has not been properly considered by existing offloading approaches. In this paper, we propose CONFECT, a novel offloading approach that handles tasks with mixtures of hard deadlines and soft deadlines. Specifically, we first formulate the problem as an integer linear programming and prove its hardness. Then, we propose two online algorithms with proven competitive ratios to solve the problem collectively, including an algorithm that assigns tasks to edge servers to maximize the task completion ratio and an algorithm that adjusts the task execution order to maximize the task completion revenue. Moreover, to balance the fairness among tasks and system revenue elastically, we extend CONFECT by using a tunable fairness knob. Finally, extensive experiments show that CONFECT outperforms five baseline algorithms in terms of task completion ratio and completion revenue. [ABSTRACT FROM AUTHOR]

Optimal planning and design of microgrids are priorities in the electrification of off-grid areas. Indeed, in one of the Sustainable Development Goals (SDG 7), the UN recommends universal access to electricity for all at the lowest cost. Several optimization methods with different strategies have been proposed in the literature as ways to achieve this goal. This paper proposes a microgrid installation and planning model based on a combination of several techniques. The programming language Python 3.10 was used in conjunction with machine learning techniques such as unsupervised learning based on K-means clustering and deterministic optimization methods based on mixed linear programming. These methods were complemented by the open-source spatial method for optimal electrification planning: onsset. Four levels of study were carried out. The first level consisted of simulating the model obtained with a cluster, which is considered based on the elbow and k-means clustering method as a case study. The second level involved sizing the microgrid with a capacity of 40 kW and optimizing all the resources available on site. The example of the different resources in the Togo case was considered. At the third level, the work consisted of proposing an optimal connection model for the microgrid based on voltage stability constraints and considering, above all, the capacity limit of the source substation. Finally, the fourth level involved a planning study of electrification strategies based mainly on microgrids according to the study scenario. The results of the first level of study enabled us to obtain an optimal location for the centroid of the cluster under consideration, according to the different load positions of this cluster. Then, the results of the second level of study were used to highlight the optimal resources obtained and proposed by the optimization model formulated based on the various technology costs, such as investment, maintenance, and operating costs, which were based on the technical limits of the various technologies. In these results, solar systems account for 80% of the maximum load considered, compared to 7.5% for wind systems and 12.5% for battery systems. Next, an optimal microgrid connection model was proposed based on the constraints of a voltage stability limit estimated to be 10% of the maximum voltage drop. The results obtained for the third level of study enabled us to present selective results for load nodes in relation to the source station node. Finally, the last results made it possible to plan electrification using different network technologies and systems in the short and long term. The case study of Togo was taken into account. The various results obtained from the different techniques provide the necessary leads for a feasibility study for optimal electrification of off-grid areas using microgrid systems. [ABSTRACT FROM AUTHOR]

The optimal PMU placement problem is placing the minimum number of PMUs in the network to ensure complete network observability. It is an NP-complete optimization problem. PMU placement based on cost and critical nodes is solved separately in the literature. This paper proposes a novel approach, a degree of centrality in the objective function, to combine the effect of both strategies to place PMUs in the power network optimally. The contingency analysis and the effect of zero-injection buses are solved to ensure the reliability of network monitoring and attain a minimum number of PMUs. Integer linear programming is used on the IEEE 7-bus, IEEE 14-bus, IEEE 30-bus, New England 39-bus, IEEE 57-bus, and IEEE 118-bus systems to solve this problem. The results are evaluated based on two performance measures: the bus observability index (BOI) and the sum of redundancy index (SORI). On comparison, it is found that the proposed methodology has significantly improved results, i.e., a reduced number of PMUs and increased network overall observability (SORI). This methodology is more practical for implementation as it focuses on critical nodes. Along with improvement in the results, the limitations of existing indices are also discussed for future work. [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]

The distributionally robust chance constrained integer programming problems are notoriously hard to solve due to the stochastic feature and the discrete nature of integer variables. In this paper, an exact solution method is developed for linear integer programming problems with the distributionally robust chance constraint. By exploring the geometric properties, some domain cut techniques based on feasible points and infeasible points are derived. Thus cut off some sub-boxes which do not contain any optimal solution and the optimality gap is reduced successively in the solution iterations. Then the optimal solution will be found in a finite number of iterations. Encouraging computational results are also reported in the paper. [ABSTRACT FROM AUTHOR]

The paper presents a new method for solving the 0–1 linear programming problems (LPs). The general 0–1 LPs are believed to be NP-hard and a consistent, efficient general-purpose algorithm for these models has not been found so far. Cutting planes and branch and bound approaches were the earliest exact methods for the 0–1 LP. Unfortunately, these methods on their own failed to solve the 0–1 LP model consistently and efficiently. The hybrids that are a combination of heuristics, cuts, branch and bound and pricing have been used successfully for some 0–1 models. The main challenge with these hybrids is that these hybrids cannot completely eliminate the threat of combinatorial explosion for very large practical 0–1 LPs. In this paper, a technique to reduce the complexity of 0–1 LPs is proposed. The given problem is used to generate a simpler version of the problem, which is then solved in stages in such a way that the solution obtained is tested for feasibility and improved at every stage until an optimal solution is found. The new problem generated has a coefficient matrix of 0 s and 1 s only. From this study, it can be concluded that for every 0–1 LP with a feasible optimal solution, there exists another 0–1 LP (called a double in this paper) with exactly the same optimal solution but different constraints. The constraints of the double are made up of only 0 s and 1 s. It is not easy to determine this double 0–1 LP by mere inspection but can be obtained in stages as given in the numerical illustration presented in this paper. The 0–1 integer programming models have applications in so many areas of business. These include large economic/ financial models, marketing strategy models, production scheduling and labor force planning models, computer design and networking models, military operations, agriculture, wild fire fighting, vehicle routing and health care and medical models [ABSTRACT FROM AUTHOR]

Role assignment is an important and complex task in collaboration and management. Group role assignment (GRA) pursues the optimal team performance by assigning pertinent roles to agents in a team from the team’s viewpoint. There are many factors that should be considered when conducting role assignment. Budgets are such a factor. This paper presents a challenging role assignment problem in collaboration, called GRA with budget constraints (GRABC). This paper contributes a thorough investigation of the GRABC problem including: 1) the first formalization of the proposed problem; 2) a set of practical solutions to different forms of this problem by using the IBM ILOG CPLEX optimization package (CPLEX); 3) a set of necessary conditions for these problems to possess feasible solutions to improve the CPLEX solutions; and 4) a synthesized process to deal with GRABC problems. Contribution 2) actually clarifies a list of requirements in solving the GRABC problem. Simulations, experiments and a case study are used to verify the practicability and efficiency of the proposed solutions. [ABSTRACT FROM AUTHOR]

Intense global competition, dynamic product variations, and rapid technological developments force manufacturing systems to adapt and respond quickly to various changes in the market. Such responsiveness could be achieved through new paradigms such as Reconfigurable manufacturing systems (RMS). In this paper, the problem of configuration design for a scalable reconfigurable RMS that produces different products of a part family is addressed. In order to handle demand fluctuations of products throughout their lifecycles with minimum cost, RMS configurations must change as well. Two different approaches are developed for addressing the system configuration design in different periods. Both approaches make use of modular reconfigurable machine tools (RMTs), and adjust the production capacity of the system, with minimum cost, by adding/removing modules to/from specific RMTs. In the first approach, each production period is designed separately, while in the second approach, future information of products' demands in all production periods is available in the beginning of system configuration design. Two new mixed integer linear programming (MILP) and integer linear programming (ILP) formulations are presented in the first and the second approaches respectively. The results of these approaches are compared with respect to many different aspects, such as total system design costs, unused capacity, and total number of reconfigurations. Analyses of the results show the superiority of both approaches in terms of exploitation and reconfiguration cost. [ABSTRACT FROM AUTHOR]

We address the facility location problem for firms that sell an homogeneous product and compete on delivered prices. If the firms set equilibrium prices at each market, the problem can be seen as a location game for which there exists a Nash equilibrium if demand is inelastic. However, this equilibrium may be Pareto-inefficient and the firms could decide to collude if they can guarantee themselves higher payoffs than those prescribed by the equilibrium. The aim of this paper is to study the joint profit maximization problem to obtain a collusive solution of the location game (Pareto-efficient) and determine if such a solution is also a Nash equilibrium. We develop Integer Linear Programming models to find Pareto-efficient solutions for multiple and single facility location. Nash equilibria are obtained by the best response procedure. An empirical investigation is performed to compare the joint profit of the firms and the profit of each one of the firms, got through the Pareto-efficient locations, with those got through the Nash equilibrium. [ABSTRACT FROM AUTHOR]

Due to the high pollution of the transportation sector, nowadays the role of electric vehicles has been noticed more and more by governments, organizations, and environmentally friendly people. On the other hand, the problem of electric vehicle routing (EVRP) has been widely studied in recent years. This paper deals with an extended version of EVRP, in which electric vehicles (EVs) deliver goods to customers. The limited battery capacity of EVs causes their operational domains to be less than those of gasoline vehicles. For this purpose, several charging stations are considered in this study for EVs. In addition, depending on the operational domain, a full charge may not be needed, which reduces the operation time. Therefore, partial recharging is also taken into account in the present research. This problem is formulated as a multi-objective integer linear programming model, whose objective functions include economic, environmental, and social aspects. Then, the preemptive fuzzy goal programming method (PFGP) is exploited as an exact method to solve small-sized problems. Also, two hybrid meta-heuristic algorithms inspired by nature, including MOSA, MOGWO, MOPSO, and NSGAII_TLBO, are utilized to solve large-sized problems. The results obtained from solving the numerous test problems demonstrate that the hybrid meta-heuristic algorithm can provide efficient solutions in terms of quality and non-dominated solutions in all test problems. In addition, the performance of the algorithms was compared in terms of four indexes: time, MID, MOCV, and HV. Moreover, statistical analysis is performed to investigate whether there is a significant difference between the performance of the algorithms. The results indicate that the MOSA algorithm performs better in terms of the time index. On the other hand, the NSGA-II-TLBO algorithm outperforms in terms of the MID, MOCV, and HV indexes. [ABSTRACT FROM AUTHOR]

Efficiently managing retail space is critical as the increase in product variety is in conflict with limited shelf space and instore replenishment constraints. This paper develops a general framework for retail space management and presents a decision support model with the related problems within the framework of optimizing assortment, shelf space assignment and replenishment. An integrative approach to these planning problems becomes particularly relevant for fast-moving consumer goods and groceries, where stores are regularly replenished from distribution centers. The planning problem at hand is a multi-product shelf space allocation problem where demand is a composite function of the shelf space allocated and assortment-related demand substitution, and actual replenishment practices from retail are incorporated. The model developed extends existing models of shelf space management by jointly considering space-elastic demand and assortment-based substitution and integrating restocking constraints. For the latter, we consider real-world replenishment processes of retailers that distinguish between period-based and ad-hoc replenishment from the backroom. We develop three solution approaches that are based on efficient pre-processing and a nonlinear binary integer programming formulation of the problem. The computation tests based on retail data show the efficiency of the solution approaches in terms of computation time and solution quality. We reveal the improvement in profit levels that can be achieved from integrating assortments, shelf space planning and replenishment where challenges arise in obtaining feasible solutions with limited shelf space and replenishment constraints. We also use sensitivity analyses to demonstrate the high impact of replenishment constraints on profits and solution structures. [ABSTRACT FROM AUTHOR]

The extensive consumption of energy in manufacturing has led to a large amount of greenhouse gas emissions that have caused an enormous effect on the environment. Therefore, investigating how to reduce energy consumption in manufacturing is of great significance to cleaner production. This paper considers an energy-conscious unrelated parallel batch processing machine scheduling problem under time-of-use (TOU) electricity prices. Under TOU, electricity prices vary for different periods of a day. This problem is grouping jobs into batches, assigning the batches to machines and allocating time to the batches so as to minimize the total electricity cost. A mixed-integer linear programming model and two groups of heuristics are proposed to solve this problem. The first group of heuristics first forms batches, assigns the batches to machines and finally allocates time to the batches, while the second group of heuristics first assigns jobs to machines, batches the jobs on each machine and finally allocates time to each batch. The computational results show that the SPT-FBLPT-P1 heuristic in the second group can provide high-quality solutions for large-scaled instances in a short time, in which the jobs are assigned to the machines based on the shortest processing time rule, the jobs on each machine are batched following the full-batch longest processing time algorithm, and the time is allocated to each batch following an integer programming approach. The MDEC-FBLPT-P1 heuristic that uses the minimum difference of the power consumption algorithm to assign the jobs also performed well. [ABSTRACT FROM AUTHOR]

Multi-robot task assignment is one of the main processes in an intelligent warehouse. This paper models multi-robot task assignment in an intelligent warehouse as an open-path multi-depot asymmetric traveling salesman problem (OP-MATSP). A two-objective integer linear programming (ILP) model for solving OP-MDTSP is proposed. The theoretical bound on the computational time complexity of this model is O (n !) . We can solve the small multi-robot task assignment problem by solving the two-objective ILP model using the Gurobi solver. The multi-chromosome coding-based genetic algorithm has a smaller search space, so we use it to solve large-scale problems. The experiment results reveal that the two-objective ILP model is very good at solving small-scale problems. For large-scale problems, both EGA and NSGA3 genetic algorithms can efficiently obtain suboptimal solutions. It demonstrates that this paper's multi-robot work assignment methods are helpful in an intelligent warehouse. [ABSTRACT FROM AUTHOR]

This paper addresses serialized approaches of the routing, modulation level, and spectrum assignment (RMLSA) problem in elastic optical networks, using multiple sequential sub-sets of requests, under Integer Linear Programming (ILP). The literature has reported two-stage serial optimization methods referred to as RML+SA, which retain computational efficiency when the problem grows, compared to the classical one-stage RMLSA optimization approach. However, there still remain numerous issues in terms of the spectrum used that can be improved when compared to the RMLSA solution. Consequently, this paper proposes RML+SA solutions considering multiple sequential sub-sets of requests, split traffic flow, as well as path-oriented and link-oriented routing models. Simulation results on different test scenarios determine that: (a) the multiple sequential sub-sets of request-based models improve computation time without worsening the spectrum usage when compared to just one set of requests optimization approaches, (b) divisible traffic flow approaches show promise in cases where the number of request sub-sets is low compared to the non-divisible counterpart, and (c) path-oriented routing succeeds in improving the used spectrum by increasing the number of candidate routes compared to link-oriented routing. [ABSTRACT FROM AUTHOR]

This paper studies optimal micro-PMU (µPMU) placement problem in active distribution networks (ADNs) for complete observability. Minimum procurement cost of μPMUs in extensive distribution networks and minimum loss of observability (LOB) during islanding operations are two important aspects of observability analysis. Because of complexities, modern ADNs require maximum observability during islanding operations. Therefore, this paper proposes a novel objective function considering μPMU-channel cost and risk of operation (RoOP) of system nodes in the integer linear programming framework. The index RoOP is incorporated as a metric for node reliability. A novel zero-injection bus (ZIB) modeling is proposed using topology transformation. Consideration of RoOP is essential for active distribution networks, where islanding operations may appear due to unreliable branch and node outages. Incorporation of RoOP ensures minimum total system operation risk (TSOR), minimum LOB, and higher total system observability in ADNs. Accurate RoOP is evaluated using Markov chain model and Monte Carlo simulation. The proposed objective function considering only channel cost is tested first on IEEE 34-, 69-, and 123-bus systems and found substantial savings compared to existing literature. Situations like single μPMU outage, existence of ZIB effect, and conventional meters are considered to validate the effectiveness of the proposed formulation. Further, simulation conducted on the IEEE 34-bus system considering channel cost and RoOP depicts that the proposed method successfully achieves 13.21% lesser TSOR and 2.44% higher measurement redundancy compared to the case without considering RoOP. Eventually, 0% LOB is ensured for the maximum number of possible islanding situations. [ABSTRACT FROM AUTHOR]

The Resource-Constrained Project Scheduling Problem (RCPSP) is a significant and important issue in the field of project management. It arises during project planning when resources must be allocated among tasks with specific time constraints. Solving this problem enables the optimization of project execution time, minimization of resource costs, and increased efficiency of the entire team's work. Due to the increasing complexity of projects, the development of new methods and algorithms to solve RCPSP is relevant nowadays. The existing methods for obtaining approximate solutions with guaranteed accuracy are characterized by high computational complexity and are often ineffective in considering the specific constraints of the problem. Fast heuristic approaches also have several drawbacks related to fine-tuning algorithm parameters and strong dependence on the quality of the initial solution. This paper investigates the features of the linear integer programming (LIP) model to solve RCPSP. The proposed LIP model is universal and scalable, enabling it to fully consider all specific aspects of the problem. The paper provides a construction algorithm of a functional space of the model and discusses the estimation of complexity. From the estimation of the mentioned algorithm's complexity, it is observed that the general complexity of the proposed approach is proportional to a controlled parameter of the LIP. Increasing this controlled parameter can significantly reduce the dimensionality of the initial problem, thus leading to the effectiveness of the LIP model-based approach in terms of computational resources. An upper bound for the value of this parameter is obtained for a special case of the RCPSP. Using the obtained balanced value, a numerical experiment was carried out on real-world samples. [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]

Device-to-device (D2D) communication is a promising technique to enhance the spectrum efficiency of a cellular network. However, one of the major challenges in D2D communications is to select appropriate communication modes for all possible D2D pairs in a D2D network. In this paper, we study the mode selection problems in a multi-mode and multi-pair D2D network, where the eNB can assign one of the three D2D communication modes (including local route mode, direct D2D mode, and relay D2D mode) to each D2D pair. To achieve the maximal cell-wise capacity, an optimal mode selection algorithm is proposed in this paper with the aim to share cellular users’ uplink channels. The optimal mode selection problem can be modeled by an integer programming problem. Particularly, in a fully loaded cell, we discover that the optimal mode selection problem can be solved using a linear programming algorithm with a significantly reduced complexity. [ABSTRACT FROM AUTHOR]

This paper proposes a fast optimization method for synthesizing thinned planar antenna arrays. A 0-1 integer linear programming (ILP) model was proposed for the antenna array optimization. This model mainly aims to minimize the peak sidelobe level (PSLL) and consider the design requirements of narrow beamwidth and high directivity, finally obtaining the optimal distribution of the turned "ON" element positions in the aperture. Several cases of planar array designs with different aperture sizes and scan angles were provided in the paper and compared with other popular algorithms. Numerical results showed that the new method can effectively optimize the thinned planar arrays, including large-scale arrays, while significantly reducing the computational cost and time. [ABSTRACT FROM AUTHOR]

The multi-row facility layout problem (MRLP) is an important design problem often encountered in real life. Existing studies on MRLPs typically either ignore clearances between adjacent machines or consider only the minimum clearances. However, separating adjacent machines with clearances greater than the minimum ones may achieve lower material flow cost. In addition, current studies on MRLPs ignore the optimisation of layout area. In this paper, we study a multi-row facility layout problem with extra clearances (MRLP-EC), with the objectives of minimising material flow cost and layout area. A mixed integer programming formulation is established for MRLP-EC. A hybrid approach combining an improved multi-objective greedy randomised adaptive search procedure (mGRASP) and linear programming (LP) is proposed for the problem. The mGRASP is used to optimise machine sequences to obtain a set of non-dominated machine sequences. A segments-based dominance method is suggested to measure the dominance relationship of any pair of machine sequences. LP is used to optimise extra clearances between adjacent machines (i.e. the exact location of each machine) for each non-dominated machine sequence. The proposed approach is compared against an exact method and two multi-objective heuristics. Experiments show that the approach is effective for MRLP-EC and outperforms comparative approaches. [ABSTRACT FROM AUTHOR]

Channel reciprocity is the foundation for physical layer key generation, which is influenced by noise, hardware impairments, and synchronization offsets. Weak channel reciprocity will result in a high key disagreement rate (KDR). The existing solutions for improving channel reciprocity cannot achieve satisfactory performance improvements. Furthermore, the existing quantization algorithms generally use one-dimensional channel features to quantize and generate secret keys, which cannot fully utilize channel information. The multidimensional vector quantization technique also needs to improve in terms of randomness and time complexity. This paper proposes a physical layer key generation scheme based on deep learning and balanced vector quantization. Specifically, we build a channel reciprocity compensation network (CRCNet) to learn the mapping relationship between Alice and Bob's channel measurements. Alice compensates for channel measurements via a trained CRCNet to reduce channel measurement errors between legitimate users and enhance channel reciprocity. We also propose a balanced vector quantization algorithm based on integer linear programming (ILP-BVQ). ILP-BVQ reduces the time complexity of quantization on the basis of ensuring key randomness and a low KDR. Simulation results showed that the proposed CRCNet performs better in terms of channel reciprocity and KDR, while the proposed ILP-BVQ algorithm improves time consumption and key randomness. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose an integrated centralized data envelopment analysis (CDEA)-balanced scorecard (BSC) model to provide a selective approach to determine the most efficient indicators for evaluating the four perspectives of the BSC. Design/methodology/approach: An integer linear programming model based on the efficiency concept of the CDEA method is presented to select the best indicators for evaluating four perspectives of the BSC. The basis for selecting indicators in this method is to maximize the overall performance of each BSC perspective. The modeling is performed on a real case. The considered model is solved using a general algebraic modeling system software for the data set of the real case. Findings: A real-world case is solved using the proposed method. The integration of the CDEA and the BSC seems to be advantageous because it sheds more light on the complexity and tradeoffs inherent in actual performance measurement. It is important to note that there cannot be a unique and universal model of performance measurement applicable in every situation, in every organization and at any time. Research limitations/implications: The data set of a single organization in the manufacturing industry is used to show the performance of the proposed mathematical model; therefore, generalization of the results should be done cautiously. This framework is based on the Iranian community and experts' viewpoints; therefore, different results may be obtained if it is applied elsewhere, and the importance of perspectives and their indicators might show different results in other populations and other countries. In addition, because the data is collected in a specific period of time, the results cannot be extended to other periods of time. Originality/value: The main contribution of this paper lies in the adaption of a new integrated CDEA-BSC model to performance measurement in the industrial sector that technology improves the ultimate results of performance measurement and provides wider opportunities for decision-makers. This paper aids managers and decision-makers to control the efficient indicators in perspectives. [ABSTRACT FROM AUTHOR]

Influence maximization (IM) is a challenging combinatorial optimization problem on (social) networks given a diffusion model and limited choice for initial seed nodes. In a recent paper by Keskin and Güler (Turkish J of Electrical Eng & Comput Sci 26:3383–3396, 2018) an integer programming formalization of IM using the so-called deterministic linear threshold diffusion model was proposed. In fact, it is a special 0-1 linear program in which the objective is to maximize influence while minimizing the diffusion time. In this paper, by rigorous analysis, we show that the proposed algorithm can get stuck in locally optimal solution or cannot even start on certain input graphs. The identified problems are resolved by introducing further constraints which then leads to a correct algorithmic solution. Benchmarking results are shown to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The optimization of the layout of the surface gathering and transportation pipe network in the oil and gas field can effectively reduce the total investment in the pipe network. Currently, based on the constraints of fixed station capacity in the star-tree pipe network topology, hierarchical optimization strategies are often used to optimize the pipe network layout. Aiming at the overall optimization of the layout of the star-tree ground gathering and transportation pipe network, this paper constructs a special mixed-integer linear programming (MILP) mathematical model considering the station capacity allocation problem, which can simultaneously obtain the optimal pipe network topology, pipe connection relationship, station location and quantity, station type, central station [central processing plant (CPP)] location and investment of each part. Numerical analysis of gas fields of different scales is used to discuss the influence of station capacity allocation and different station capacity combinations on the optimization of pipe network layout. The optimization effect of star-tree and star-star pipe network layout is compared and analyzed. The results not only prove the correctness and effectiveness of the model and algorithm proposed in this paper but also reduce the total investment of the pipe network. It can be seen that the optimization scheme has guiding significance for the surface engineering construction of the oil and gas fields. [ABSTRACT FROM AUTHOR]

Community structures are critical towards understanding not only the network topology but also how the network functions. However, how to evaluate the quality of detected community structures is still challenging and remains unsolved. The most widely used metric, normalized mutual information (NMI), was proven to have finite size effect, and its improved form relative normalized mutual information (rNMI) has reverse finite size effect. Corrected normalized mutual information (cNMI) was thus proposed and has neither finite size effect nor reverse finite size effect. However, in this paper, we show that cNMI violates the so-called proportionality assumption. In addition, NMI-type metrics have the problem of ignoring importance of small communities. Finally, they cannot be used to evaluate a single community of interest. In this paper, we map the computed community labels to the ground-truth ones through integer linear programming, and then use kappa index and F-score to evaluate the detected community structures. Experimental results demonstrate the advantages of our method. [ABSTRACT FROM AUTHOR]

This paper presents an optimization framework for sequential reconfiguration using an assortment of switching devices and repair process in distribution system restoration. Compared to existing studies, this paper considers types, capabilities and operational limits of different switching devices, making it applicable in practice. We develop a novel multi-phase method to find the optimal sequential operation of various switching devices and repair faulted areas. We consider circuit breakers, reclosers, sectionalizers, load breaker switches, and fuses. The switching operation problem is decomposed into two mixed-integer linear programming (MILP) subproblems. The first subproblem determines the optimal network topology and estimates the number of steps to reach that topology, while the second subproblem generates a sequence of switching operations to coordinate the switches. For repairing the faults, we design an MILP model that dispatches repair crews to clear faults and replace melted fuses. After clearing a fault, we update the topology of the network by generating a new sequence of switching operations, and the process continues until all faults are cleared. To improve the computational efficiency, a network reduction algorithm is developed to group line sections, such that only switchable sections are present in the reduced network. The proposed method is validated on the IEEE 123-bus and 8500-bus systems. [ABSTRACT FROM AUTHOR]

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered when solving an optimization problem. Standard floating-point algorithms are highly efficient but remain susceptible to the accumulation of round-off errors, which can lead solvers to return feasibility and optimality claims that are actually invalid. This paper introduces a novel direct solution approach for solving sequences of closely related SLEs encountered in nonlinear programming efficiently and without round-off errors. Specifically, it introduces rank-one update algorithms for the round-off error–free factorization framework, a tool set built on integer-preserving arithmetic that has led to the development and implementation of extremely reliable subroutines for solving SLEs occurring in linear programming. The formal guarantees of the presented algorithms are established through the derivation of theoretical insights. Their advantages are supported with computational experiments, which demonstrate upward of 75× improvements over exact factorization runtimes on fully dense matrices with more than one million entries. A significant advantage of the featured integer-preserving framework is that the length of any matrix coefficient produced by its algorithms is bounded polynomially in the size of the inputs without having to resort to greatest common divisor operations, which are required by and thereby hinder an efficient implementation of exact rational arithmetic approaches. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. 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.2021.0331) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0331). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]