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The Flexible Job shop Scheduling Problem (FJSP), as a Production Scheduling Problem (PSP), is generally an extension of the Job shop Scheduling Problem (JSP). In this paper, the FJSP with reverse flow consisting of two flows of jobs (direct and reverse) at each stage is studied; the first flow initiates in Stage 1 and goes to Stage C (the last stage), and the second flow starts with Stage c and ends up in Stage 1. The aim is to minimize the makespan of the jobs (the maximum completion time). A Mixed Integer Programming (MIP) is presented to model the problem and the Branch and Bound (B&B) method is used to solve the problem. A numerical small-size problem is presented to demonstrate the applicability, for which the Lingo16 software is employed for a solution. Due to the NPhardness of the problem, a meta-heuristic, namely the Vibration Damping Optimization (VDO) algorithm with tuned parameters using the Taguchi method, is utilized to solve large-scale problems. To validate the results obtained using the proposed solution algorithm in terms of the solution quality and the required computational time, they are compared with those obtained by the Lingo 16 software for small-size problems. Finally, the performance of the proposed algorithm is compared with a Genetic Algorithm (GA) by solving some randomly generated larger-size test problems, based on which the results are analyzed statistically. Computational results confirm the efficiency and effectiveness of the proposed algorithm and show that the VDO algorithm performs well. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a new model called the stochastic green capacitated p-median problem with a simulation-based optimisation approach. An integer linear programming mathematical model is built considering the total emission produced by vehicles and the uncertain parameters including the travel cost for a vehicle to travel from a particular facility to a customer and the amount of CO2 emissions produced. We also develop a simulation-based optimisation algorithm for solving the problem. Design/methodology/approach: The authors proposed new algorithms to solve the problem. The proposed algorithm is a hybridisation of Monte Carlo simulation and a Variable Neighbourhood Search matheuristic. The proposed model and method are evaluated using instances that are available in the literature. Findings: Based on the results produced by the computational experiments, the developed approach can obtain interesting results. The obtained results display that the proposed method can solve the problems within a short computational time and the solutions produced have good quality (small deviations). Originality/value: To the best of our knowledge, there is no paper in the previous literature investigating the simulation-based optimisation for the stochastic green capacitated p-median problem. There are two main contributions in this paper. First, to build a new model for the capacitated p-median problem taking into account the environmental impact. Second, to design a simulation-based optimisation approach to solve the stochastic green capacitated p-median problem incorporating VNS-based matheuristic and Monte Carlo simulation. [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]

Background: Farm-level models have become an important tool for agricultural economists as there is a growing demand for microsimulation and analysis of farms at the individual level. Objectives: In this paper, we present a mathematical model with the main objective of assessing the effectiveness of production and various possible strategies for agricultural holdings by reducing risks. At the same time, we were also interested in the environmental impacts of such strategies. The latter was measured using the indicator of GHG emissions. Methods/Approach: The model applied is based on linear programming and upgraded with QRP for risk analysis. The approach was tested on medium size mixed agricultural holding, which often faces challenges in light of the structural changes taking place in Slovenia. Results: The results suggest that such a farm could improve financial results with a more efficient risk management strategy. With a slightly modified production plan, the expected gross margin (EGM) can be increased by up to 10% at more or less the same risk. However, if the farmer is willing to diversify the production plan and take a higher risk (+23%), the farm's EGM could increase by up to 18%. This kind of change in the production plan would also generate 17% more GHG emissions in total, calculated as kg equivalent of CO2 at the farm level, as both BL and C scenarios have the same relative ratio at 3.12 GHG CO2 eq. /EUR. Conclusions: Through this research, we concluded that diversification has a positive potential on a mixed farm, and the farm could achieve better financial results. With flexibility in management, the farmer could also achieve higher risk management efficiency and better farm results. [ABSTRACT FROM AUTHOR]

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam's opinion diffusion model. For a given selection of the coefficients in our model, this proposal yields the original Galam's model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow it to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided. [ABSTRACT FROM AUTHOR]

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In view of the traditional branch line end express delivery centralized mode cannot adapt to the growing demand of high-speed rail (HSR) express, resulting in poor connection between trunk and branch line, high cost and poor timeliness. In this paper, the problem of scheduling optimization of branch-line flexible distribution vehicles relying on intermodal transportation of trunk and branch lines is proposed. Considering the number of vehicles, vehicle capacity, customer service time window and other constraints, an integer linear programming mathematical model with the minimum total cost of vehicle transportation cost, usage cost and time window penalty cost as the optimization objective is established. A two-level nested heuristic algorithm with two-level coding structure is proposed to solve the problem. Finally, a simulation example is given to verify the effectiveness of the model and the algorithm. The results show that the vehicle scheduling optimization problem studied in this paper can effectively improve the timeliness and accuracy of HSR express delivery, and can significantly reduce the total vehicle delivery cost. [ABSTRACT FROM AUTHOR]

The transition towards climate neutrality will result in an increase in electrical vehicles, as well as other electric loads, leading to higher loads on electrical distribution grids. This paper presents an optimisation algorithm that enables the integration of more loads into distribution grid infrastructure using information from smart meters and/or smart meter gateways. To achieve this, a mathematical programming formulation was developed and implemented. The algorithm determines the optimal charging schedule for all electric vehicles connected to the distribution grid, taking into account various criteria to avoid violating physical grid limitations and ensuring non-discriminatory charging of all electric vehicles on the grid while also optimising grid operation. Additionally, the expandability of the infrastructure and fail-safe operation are considered through the decentralisation of all components. Various scenarios are modelled and evaluated in a simulation environment. The results demonstrate that the developed optimisation algorithm allows for higher transformer loads compared to a P(U) control approach, without causing grid overload as observed in scenarios without optimisation or P(U) control. [ABSTRACT FROM AUTHOR]

Linear matching (LM) is a simple and effective method for solving image matching problems. In many cases, image matching problems are nonlinear due to involvement of the geometric transformations; therefore, an essential step for utilizing linear models for image matching is to linearize the geometric transformation matrices that introduce nonlinear terms into image matching problems. Existing LM methods usually use low-order transformations to artificially initialize a linear model. In this paper, we propose a residual-consensus driven LM algorithm that generalizes existing LM methods by allowing higher order transformations to automatically initialize a linear model. Based on the observation that transformation models generated from inlier subsets exhibit correlated behaviors (termed residual consensus hereafter), we develop a residual-consensus robust estimation algorithm to project the nontrivial linear transformation problem into a much smaller subspace, and thus enable efficient optimizations through linear programming. The experimental results on synthetic and real databases demonstrate the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

In the present paper, a multiobjective linear programming problem under uncertainty, particularly when parameters are given in interval forms, is investigated. In this case, it is assumed that objective coefficients and constraints parameters have arrived in interval numbers. Considering a suitable order relation for interval numbers, a solution procedure for dealing with such a problem is developed. A numerical example is provided to illustrate the efficiency of the solution procedure. [ABSTRACT FROM AUTHOR]

A linear problem of regression analysis is considered under the assumption of the presence of noise in the output and input variables. This approximation problem may be interpreted as an improper interpolation problem, for which it is required to correct optimally the positions of the original points in the data space so that they all lie on the same hyperplane. The use of the quadratic approximation criterion for such a problem led to the appearance of the total least squares method. In this paper, we use the minimax criterion to estimate the measure of correction of the initial data. It leads to a nonlinear mathematical programming problem. It is shown that this problem can be reduced to solving a finite number of linear programming problems. However, this number depends exponentially on the number of parameters. Some methods for overcoming this complexity of the problem are proposed. [ABSTRACT FROM AUTHOR]

In this paper, an airport ground service task assignment problem is studied. A task represents a service, which must be performed by one or multiple ground crew of a shift with required qualification/proficiency within a prescribed time period. For every assigned task, define "task priority" times "task duration" as the "benefit" generated. The objective is to maximize the summation of "benefit" for all the assigned tasks. The problem is modeled as an integer linear programming problem with mathematical formulation. A branch-and-price algorithm is proposed for solving the problem instances to optimality. To expedite the column generation process, an acceleration strategy is proposed. The computational results show that our proposed branch-and-price algorithm is capable of solving large-sized instances and the acceleration strategy is quite effective in reducing the computational time. Moreover, the impact of changing various characteristics of tasks and shifts on the performance of the algorithm is studied in detail with supporting computational experiments. In particular, the impact of reducing the qualifications is significant with 20.82% improvement in the objective value. [ABSTRACT FROM AUTHOR]

This paper addresses the Capacitated Vehicle Routing Problem (CVRP), which is a widely studied optimization problem due to its relevance to the field of transportation, distribution, and logistics. We present a matheuristic method for CVRP that adopts the main idea of the Kernel Search algorithm (KS) based on decomposing the original problem into sub-problems that are easier to solve. Unlike the original scheme of KS, our approach uses the Clarke–Wright savings algorithm to construct a sequence of smaller sub-problems, which are subsequently solved using mathematical programming strategies. The computational experiments performed on a set of benchmark instances showed that the proposed matheuristics achieves good results in acceptable computational time. [ABSTRACT FROM AUTHOR]

This paper introduces a proposed method for identifying the left and right Returns to Scales (RTS) and the overall RTS of frontier units based on the theoretical framework of data envelopment analysis (DEA). This paper first proposes an alternative definition for Left RTS (L-RTS) and Right RTS (R-RTS) of frontier units and then by focusing on this definition, provides two new DEA models to present a proposed method for identifying the L-RTS and R-RTS of frontier units. The major advantages of these two models include that they are feasible in all situations. Also, these models are capable to properly and accurately identify frontier units and their type of L-RTS and R-RTS, without any plurality in their judgment. The proposed method is compared -theoretically and experimentally- with other methods presented in the literature. Moreover, the theoretical correlation between the concepts of overall RTS and L&R-RTS of frontier units is analyzed. Then, this analysis is used to propose an alternative method for categorizing overall RTS of frontier units. Experimental application of this method shows that the results of evaluation of overall RTS of frontier units obtained by the proposed method is completely consistent with the results of the method presented by Banker and Thrall (Eur J Oper Res 62(1):74-84, 1992). The proposed methods in this paper can be easily used by the existing codes of DEA. [ABSTRACT FROM AUTHOR]

This paper presents a nonintrusive load monitoring (NILM) algorithm based on mixed-integer linear programming. The formulation deals with the problem of multiple switching that arises when disaggregating individual appliance’s consumptions from a compound power measurement. Mixed-integer linear constraints are used to efficiently represent the load signatures of each appliance. Also, a window-based strategy is used to enhance the computational performance of the proposed NILM algorithm. The disaggregation can be made using only active power measurements at a low sampling rate, which is available in most energy meters. Moreover, if available, other signatures can be added to the model to improve its accuracy, such as reactive power signatures or harmonics. The performance of the algorithm is evaluated using three test cases from the almanac of minutely power dataset. The proposed method is also compared with a disaggregation method called aided linear integer programming. Results demonstrate the ability of the proposed method to accurately identify and allocate individual energy signatures in a computationally efficient manner, which makes it suitable for inexpensive home energy management. [ABSTRACT FROM AUTHOR]

The search of separation hyperplanes is an efficient way to find rules with classification purposes. This paper presents an alternative mathematical programming formulation to existing methods to find a discriminant hyperplane. The hyperplane H is found by minimizing the sum of all the distances to the area assigned to the group each individual belongs to. It results in a convex optimization problem for which we find an equivalent linear programming problem. We demonstrate that H exists when the centroids of the two groups are not equal. The method is effective dealing with low and high dimensional data where reduction of the dimension is proposed to avoid overfitting problems. We show the performance of this approach with different data sets and comparisons with other classifications methods. The method is called LPDA and it is implemented in a R package available in https://github.com/mjnueda/lpda. [ABSTRACT FROM AUTHOR]

An enormous challenge for state estimation (SE) in power distribution networks with high penetration of photovoltaic generators lies in how to deal with measurement uncertainty. Driven by this motivation, an interval arithmetic (IA) based SE is proposed in this paper, which considers interval modeling for measurement uncertainty. The proposed SE is formulated as two interval optimization models based on the unknown-but-bounded theory, and solution bounds of state variables are obtained using a two-stage linear programming approach. In particular, the proposed SE is extended to realistic power distribution networks with mixed microphasor measurement units (μPMU), voltage magnitude, smart meters and feeder terminal units. Case studies and results are illustrated and discussed to demonstrate the performance of the proposed IA-based SE. It could provide the operators intuitive and effective bounds of system states for advanced power industrial applications under consideration of uncertainty. [ABSTRACT FROM AUTHOR]

This paper is devoted to the management of advance admission requests for obstetric care. Pregnant women in China select one hospital and request admission for both antenatal and postnatal care after nine weeks of pregnancy. Schedulers must make the admission decision instantly based on the availability of the most critical resource, that is, hospital beds for postnatal care. The random delay between admission requests and postnatal care has created a distinct advance admission control problem. To address this issue, we propose a basic model that assumes a unit bed requirement for one day. Each admission generates a unit of revenue and each unit of overcapacity use incurs an overcapacity cost. With the objective of maximizing the expected net revenue, we establish an optimal policy for unlimited requests, that is, an expected arrival time quota (EATQ) policy that accepts a fixed quota of advance admission requests with the same expected date of confinement. We then propose an extended model for general capacity requirements. Using the Poisson approximation, we establish the optimality of the EATQ policy, which is shown to be solvable by a simple linear programming model. We compare the numerical results from the different policies and conduct a sensitivity analysis. The EATQ policy is demonstrated to be the best option in all test instances and notably outperforms the current admission rules used in hospitals, which usually accept admission requests according to some empirical monthly quota of the expected delivery month. The Poisson approximation is shown to be effective for determining the optimal EATQ policy for both stationary and nonstationary arrivals. Summary of Contribution: First, this paper investigates the advance admission control problem for obstetric care. Pregnant women in China choose one hospital and request admission for both antenatal and postnatal care after nine weeks of pregnancy but the most critical resource is hospitalization beds needed for postnatal care. The random delay between admission request and postnatal care makes the problem unique and challenging to solve. It belongs to the scope of computing and operations research. Second, this paper formulates a dynamic programming model, analyzes the structural properties of the optimal control policy, and finally proposes a mathematical programming model to determine the optimal quota. Numerical experiments show the validity of the proposed approach. It covers the research contents of theories on dynamic stochastic control, mathematic programming model, and experiments. Moreover, this paper is motivated by the practical problem (advance admission control) in obstetric units of Shanghai. Using these optimality properties, solution approaches, and numerical results, this paper provides guidance on how to manage advance obstetric admission requests. [ABSTRACT FROM AUTHOR]

This paper deals with the mixed-model assembly line balancing problem. This type of line is applied to more than one similar model of a product in an intermixed order. Despite their widespread use, these lines have received little attention in the literature. Metaheuristics, heuristics, and mathematical programming techniques are developed to solve these types of assembly line balancing problems. However, linear physical programming method has never been used. In this paper, a linear physical programming model is proposed for balancing a mixed-model assembly line. The performance of the proposed model is applied to a numerical example to analyze the usage of the methodology. Five objectives are considered in the model, and the outperformance of the methodology is demonstrated by comparing it to a different approach. According to the results, it has been seen that the proposed linear physical programming model is practical and useful approach for mixed-model assembly line balancing problems. [ABSTRACT FROM AUTHOR]

Biochar application and enhanced weathering are negative emission technologies (NETs) with the potential for large-scale deployment for the removal of CO2 from the atmosphere. Biochar is a solid product of pyrolysis that can permanently store carbon when applied in soil due to its chemical recalcitrance. Enhanced weathering is based on the acceleration of the natural reaction of moisture, CO2, and alkaline minerals. Both of these NETs rely on the application of pulverized material to different types of terrestrial sinks, which can include marginal and agricultural land. These two NETs can be used separately or concurrently, depending on local sink conditions. In some cases, simultaneous application of biochar and mineral powder to soil has the advantage of attaining additional beneficial effects of soil amendment. Although recent papers have reported the development of process integration models for optimizing carbon management networks based on either biochar application or enhanced weathering, none have reported models integrating these two NETs in the same system. To address this gap, a fuzzy mixed-integer linear programming model is developed that integrates biochar application and enhanced weathering for large-scale carbon sequestration. Fuzzy set theory provides a well-tested framework for integration of both subjectivity and uncertainty into mathematical programming. The model determines the optimal allocation of biochar and/or alkaline minerals from each source to each sink, while considering the application limits and CO2 sequestration potential. An illustrative case study is solved that clearly demonstrates the application of the model. The case study shows interesting results that can guide how the full sustainable potential of these two technologies can be utilized in a carbon management network. [ABSTRACT FROM AUTHOR]

This paper studies the energy efficiency optimization problem for coordinated multipoint (CoMP)-enabled and backhaul-constrained ultra-dense small-cell networks (UDNs). Energy efficiency is an eternal topic for future wireless communication networks; however, taking actual bottleneck of the backhaul link and the coordinated network architecture into consideration, it is difficult to find an effective way to improve the energy efficiency of the network. Aiming at this problem, we propose to combine cell association, subchannel allocation, backhaul resource allocation, and sleep/on of the cells together to develop an optimization algorithm for energy efficiency in UDN and then solve the formulated energy efficiency optimization problem by means of improved modified particle swarm optimization (IMPSO) and linear programming in mathematics. Simulation results indicate that nearly 13 % energy cost saving and 21 % energy efficiency improvement can be obtained by combining IMPSO with linear programming, and the backhaul link data rate can be improved by 30 % as the number of small cells increases. From the results, it can be found that by combining IMPSO with linear programming, the proposed algorithm can improve the network energy efficiency effectively at the expense of limited complexity. [ABSTRACT FROM AUTHOR]

Given an edge weighted tree T(V, E), rooted at a designated base vertex r∈V, and a color from a set of colors C={1,…,k} assigned to every vertex v∈V, All Colors Shortest Path problem on trees (ACSP-t) seeks the shortest, possibly non-simple, path starting from r in T such that at least one node from every distinct color in C is visited. We show that ACSP-t is NP-hard, and also prove that it does not have a constant factor approximation. We give an integer linear programming formulation of ACSP-t. Based on a linear programming relaxation of this formulation, an iterative rounding heuristic is proposed. The paper also explores genetic algorithm and tabu search to develop alternative heuristic solutions for ACSP-t. The performance of all the proposed heuristics are evaluated experimentally for a wide range of trees that are generated parametrically. [ABSTRACT FROM AUTHOR]

Purpose: In recent years, significant energy consumption and facing global warming have led to concern worldwide. Therefore, governments have turned to deterrent actions such as imposing daily tariffs in different intervals to tackle energy consumption. This article addresses unrelated parallel machine energy-efficient scheduling problems by considering sequence-independent setup times and energy consumption tariffs. The objective function is that jobs should be assigned to machines and processed in different intervals so that the cost of consumed energy becomes as less as possible. It should be noted that the assumed sequence-independent setup times are addressed in two different modes, setup times jointed to processing time and setup times disjointed from processing time. Design/methodology/approach: To optimize the total energy consumption cost in unrelated parallel machine scheduling problems with sequence-independent setup times jointed to processing time and disjointed from processing time, mixed-integer linear programming (MILP) models have been proposed from two different points of view. The first model has been formulated according to the predecessor jobs of a special job, while the second model has been conducted based on the immediate predecessor job. Also, a fix and relax heuristic (FRH) algorithm has been conducted to solve large-scale instances. All mathematical models and the heuristic algorithm have been coded in the Visual C# 2017 environment and implemented using the CPLEX 12.8 Concert Technology on a PC with 32GB RAM and Intel Corei7 4.0 GHz CPU (4 cores). Also, a sizeable number of instances have been solved to evaluate the efficiency of mathematical models and the heuristic algorithm and to ensure their accuracy. Findings: According to numerical analysis, both mathematical models solved the instances of up to 20 jobs and 80 machines optimally for sequence-independent setup-times jointed to processing time, and sequence-independent disjointed from processing time problems. However, generally speaking, the mathematical model based on predecessor jobs was more efficient than another mathematical model, especially in terms of run time. Moreover, the proposed fix and relax-based heuristic algorithm solved instances of up to 20 machines and 190 jobs for the disjointed setup times problem, and up to 20 and 220 instances for the jointed setup times problem. It should be noted that all instances were generated analogously to the literature. Research limitations/implications: A vast number of exogenous factors contributed to the scheduling problems in the real world, which can disturb the scheduling process easily, frequent power outages, machine breakdown, and operator absence. Besides, considering all the real world's possibilities raises extreme complexity in problems. Therefore, similar to other studies, some assumptions were considered as follows: - machines are always available at all times; - idle is allowable for machines; - the energy consumption rate of various machines is different for each job; - each machine's energy consumption rate during processing and setups is different for each job, it is assumed as constant; - preemption is not allowed in the job's processing and setups; - all jobs are available at the beginning of the planning horizon; and - each machine can process or do the setup for only one job at a time. Practical implications Given that unrelated parallel machines are one of the most practical scheduling environments, this article can be effective in production sites and operation lines that contain such a kind of machine. Besides, unrelated parallel machines cover identical and related parallel machines. Consequently, this paper is the building blocks of cost-effective and environmentally friendly scheduling programs. Also, the application of unrelated parallel machines is not merely restricted to production problems. In other words, unrelated parallel machine scheduling problems can be used in other real-world cases, such as airplane scheduling and elevator scheduling. Originality/value - In this paper, unrelated parallel machine energy-efficient scheduling has been addressed considering sequence-independent setup times. Since it was a common belief that sequence-independent setup times could be included in processing times, sequence-independent setup times have been neglected so far. However, in this innovative study for the first time, an unrelated parallel machine energy efficient problem was investigated with sequence-independent setup times. Mathematical programming models and a heuristic algorithm were proposed for such a practical problem. [ABSTRACT FROM AUTHOR]

The problem of optimal flow production planning at the operational scheduling stage is being studied, using the example of the out-of-furnace department of a converter-based steel-making production in the iron metallurgy industry. To solve this problem, a linear integer programming model is proposed, which fully describes the specifics of the investigated technological processes. A major advantage of this approach is its scalability for solving related optimization problems in the industry of plant logistics, as well as flexibility in adapting to changes and fine-tuning the system of constraints and objective function. The software implementation of the developed model forms the basis of the operational scheduling module of the optimal flow production planning system, which is used for a large-scale computational experiment on real-world data. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present an optimization model for planning the distribution of materials in earthmoving operations, considering possible interferences between cut-and-fill sections such as rivers, vegetation, topographical features, or expropriations. The earth allocation problem incorporating interferences was modeled as a linear programming problem, aiming to minimize the total earthmoving cost while considering the constraints related to volume balance, construction project duration, and time for the release of traffic. The proposed linear programming model was run by an integrated system, using Excel for data analysis and IBM CPLEX as the optimizer. The mathematical model was evaluated by a sensitivity analysis and validated by a real-world project of a dam access road in the state of Ceará, Brazil. The unit costs and productivity rates used in the fictional example and in the real-world application followed the referential cost system created by Ceará's Secretariat of Infrastructure (SEINFRA-CE). The proposed optimization model achieved reasonable processing times for all tested applications, presenting itself as a viable and efficient option for planning earthmoving operations. Furthermore, the linear programming approach provided a 2.12% cost reduction for the real-world case study, when comparing the optimized solution and original budget. This study explored the problem of earth allocation with interferences using a linear programming approach, while avoiding complex modeling issues found in recent literature. As a result, this paper proposes a user-friendly optimization system that can be easily utilized by construction companies and departments. [ABSTRACT FROM AUTHOR]

Generation capacity expansion planning (GCEP) is the process of deciding on a set of optimal new investments in generation capacity to adequately supply future loads, while satisfying technical and reliability constraints. This paper shows the application of stochastic mixed-integer programming (SMIP) to account for hydrological uncertainty in GCEP for the Chilean Central Interconnected System, using a two-stage SMIP multi-period model with investments and optimal power flow (OPF). The substantial computational challenges posed by GCEP imply compromising between the detail of the stochastic hydrological variables and the detail of the OPF. We selected a subset of hydrological scenarios to represent the historical hydro variability using moment-based scenario reduction techniques. The tradeoff between modeling accuracy and computational complexity was explored both regarding the simplification of the MIP problem and the differences in the variables of interest. Using a simplified OPF model, we found the difference of using a subset of hydro scenarios to be small when compared with using a full representation of the stochastic variable. Overall, SMIP with scenario reduction provided optimal capacity expansion plans whose investment plus expected operational costs were between 1.3% and 1.9% cheaper than using a deterministic approach and proved to be more robust to hydro variability. [ABSTRACT FROM PUBLISHER]

This paper presents a mixed-integer linear mathematical programming model for the integrated planning problem of the part quality inspection and preventive maintenance activities in serial multi-stage manufacturing system. The model concurrently determines the right time and place for performing the above-mentioned activities while the production stages are linearly deteriorating. These two decisions are made while the model is to minimize the total cost including the production, maintenance, inspection, scrap, replacement, and the penalty of shipped defective items to customer(s). A numerical example and a real case study are investigated to validate and verify the proposed model. The results show that the determination of inspection locations along a manufacturing line in different periods of time regarding the impact of preventive maintenance activities on defective production probability results in a more efficient manufacturing system. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the index tracking strategy using mathematical programming. First, we use a non-linear programming formulation for the index tracking problem, considering a limited number of assets. Since the problem is difficult to be solved in reasonable time by commercial mathematical packages, we apply a hybrid solution approach, combining mathematical programming and genetic algorithm. We show the efficiency of the proposed approach comparing the results with optimal solutions, with previous developed methods, and from real-world market indexes. The computational experiments focus on Ibovespa (the most important Brazilian market index), but we also present results for consolidated markets such as S&P 100 (USA), FTSE 100 (UK) and DAX (Germany). The proposed framework shows its ability to obtain very good results (gaps from the optimal solution smaller than 5 % in 8 min of CPU time) even for a highly volatile index from a developing country. [ABSTRACT FROM AUTHOR]

A multi-mode resource-constrained project scheduling problem (MRCPSP) with multiple skills is investigated in this paper. Unlike the traditional form of this problem, and considering the real-world project circumstances, project activities can be preempted. In this paper, a new multi-objective mixed-integer linear programming (MILP) model with three objective functions is extended. These objectives are: (1) minimizing the project makespan, (2) minimizing the total resource costs, and (3) minimizing the total project risk. Based on real-life projects, non-renewable resources are represented as an uncertain stochastic parameter. To cope with the uncertain environment, chance-constrained programming with a confidence level is considered. A real-world construction project of a sports center in Tehran is utilized to demonstrate the applicability of the presented formulation. A well-known lexicographic optimization method, namely AUGMECON2, is applied to solve the proposed formulation with three objectives. Ultimately, for the case study and two datasets J30 and MM50, the proposed lexicographic optimization algorithm is compared with an efficient multi-objective mathematical programming technique known as the AUGMECON method. The comparison is based on performance metrics (i.e., IGD and HV) commonly used in multi-objective optimization. The results show the relative dominance of the proposed lexicographic optimization algorithm over the AUGMECON method in all sizes of the problem instances. [Display omitted] • Considering a multi-skill multi-mode resource-constrained project scheduling problem with preemption. • Presenting a new multi-objective mixed-integer linear programming model for problem with a time lag between activities. • Minimizing three objectives: the total project risk, project makespan, and total project cost simultaneously. • Investigating the real project of building a sports center in a prominent engineering company to validate the model. • Proposing chance-constrained programming with the stochastic parameter and AUGMECON2 method for the first time. [ABSTRACT FROM AUTHOR]

Manufacturing process optimization is an ever-actual goal. Within this goal, machining parameters optimization is a very important task. Machining parameters strongly influence the manufacturing costs, process productivity and piece quality. Literature presents a series of optimization methods. The results supplied by these methods are comparable and it is difficult to establish which method is the best. For machining parameters optimization, this paper proposes a novel, simple and efficient method, without additional costs related to new software packages. This approach is based on linear mathematical programming. The optimization mathematical models are, however, nonlinear. Therefore, mathematical model linearization is required. The major and difficult problem is the linearization of the objective function. This represents the key element of the proposed optimization method. In this respect, the paper proposes an original mathematical procedure for calculating the part of the objective function that refers to the analytical integration of the tool life into the model. This calculus procedure was transposed into an original software tool. For demonstrating the validity of the method, a comparison is presented among the results obtained by certain optimization techniques. It results that the proposed method is simple and as good as those presented by the literature. [ABSTRACT FROM AUTHOR]

Linear programming problems in fuzzy environment have been investigated by many researchers in the recent years. Some researchers have solved these problems by using primal-dual method with linear and exponential membership functions. These membership functions are particular form of the reference functions. In this paper, we introduce a pair of primal-dual PPs in Atanassov's intuitionistic fuzzy environment (AIFE) in which the membership and non-membership functions are taken in the form of the reference functions and prove duality results in AIFE by using an aspiration level approach with different view points, viz., optimistic, pessimistic and mixed. Since fuzzy and AIF environments cause duality gap, we propose to investigate the impact of membership functions governed by reference functions on duality gap. This is specially meaningful for fuzzy and AIF programming problems, when the primal and dual objective values may not be bounded. Finally, the duality gap obtained by the approach has been compared with the duality gap obtained by existing approaches. [ABSTRACT FROM AUTHOR]

This paper proposes to address the problem of the simultaneous optimization of the liner shipping route and ship schedule designs by incorporating port time windows. A mathematical programming model was developed to minimize the carrier's total operating cost by simultaneously optimizing the port call sequence, ship arrival time per port of call, and sailing speed per shipping leg under port time window constraints. In view of its structure, the nonlinear nonconvex optimization model is further transformed into a mixed-integer linear programming model that can be efficiently solved by extant solvers to provide a global optimal solution. The results of the numerical experiments performed using a real-world case study indicated that the proposed model performs significantly better than the models that handle the design problems separately. The results also showed that different time windows will affect the optimal port call sequence. Moreover, port time windows, bunker price, and port efficiency all affect the total operating cost of the designed shipping route. [ABSTRACT FROM AUTHOR]

The global scientific community has intensified efforts to develop, test, and commercialize pharmaceutical products to deal with the COVID-19 pandemic. Trials for both antivirals and vaccines are in progress; candidates include existing repurposed drugs that were originally developed for other ailments. Once these are shown to be effective, their production will need to be ramped up rapidly to keep pace with the growing demand as the pandemic progresses. It is highly likely that the drugs will be in short supply in the interim, which leaves policymakers and medical personnel with the difficult task of determining how to allocate them. Under such conditions, mathematical models can provide valuable decision support. In particular, useful models can be derived from process integration techniques that deal with tight resource constraints. In this paper, a linear programming model is developed to determine the optimal allocation of COVID-19 drugs that minimizes patient fatalities, taking into account additional hospital capacity constraints. Two hypothetical case studies are solved to illustrate the computational capability of the model, which can generate an allocation plan with outcomes that are superior to simple ad hoc allocation. [ABSTRACT FROM AUTHOR]

Stochastic Programming (SP) has long been considered a well-justified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large number of scenarios by using a small number of scenarios to be processed via deterministic solvers, or running Sample Average Approximation on some genre of high performance machines so that statistically acceptable bounds can be obtained. In this paper we show that for a class of stochastic linear programming problems, an alternative approach known as Stochastic Decomposition (SD) can provide solutions of similar quality in far less computational time using ordinary desktop or laptop machines of today. In addition to these compelling computational results, we provide a stronger convergence result for SD, and introduce a new solution concept that we call the compromise decision. This new concept is attractive for algorithms that call for multiple replications in sampling-based convex optimization algorithms. For such replicated optimization, we show that the difference between an average solution and a compromise decision provides a natural stopping rule. We discuss three stopping criteria that enhance the reliability of the compromise decision, reducing bias and variance associated with the result. Finally our computational results cover a variety of instances from the literature, including a detailed study of SONET Switched Network (SSN), a network planning instance known to be more challenging than other test instances in the literature. [ABSTRACT FROM AUTHOR]

Optimization solvers include many options that allow users to control algorithmic aspects that may have a considerable impact on solver performance. Tuning solver options is often necessary to reduce execution time and improve solution quality. Previous studies of solver tuning techniques have focused on mixed-integer linear programming and local nonlinear programming solvers. In this paper, we investigate the potential of tuning a global optimization solver for nonlinear and mixed-integer nonlinear programming problems. In particular, derivative-free optimization (DFO) algorithms are used to find optimal values for options of the global optimization solver BARON. A set of 126 problems from the GLOBALLib and MINLPLib collections are utilized in a computational study from which we conclude that tuning options can improve the default performance of BARON for individual problems and an entire library. Additionally, we present a systematic comparison of 27 DFO solvers in terms of their ability to improve the performance of the global solver. We find that several DFO implementations are much better than others in terms of finding optimal tuning parameters. [ABSTRACT FROM AUTHOR]

In this paper, a new technique has been developed for solving stochastic programming problems by using the idea of decomposition based pricing method. A computer code has also been developed by using a mathematical programming language AMPL and a real life oriented model has been developed. The technique has been demonstrated by analyzing the model for different data sets which has been collected for different scenarios. To our knowledge, this is the first work for solution procedure of stochastic programming problems by using decomposition based pricing method. [ABSTRACT FROM AUTHOR]

One of the most important Distribution System Operators (DSO) schemes addresses the Volt/Var control (VVC) problem. Developing a cost-based reactive power dispatch model for distribution systems, in which the reactive powers are appropriately priced, can motivate Distributed Energy Resources (DERs) to participate actively in VVC. In this paper, new reactive power cost models for DERs, including synchronous machine-based DGs and wind turbines (WTs), are formulated based on their capability curves. To address VVC in the context of competitive electricity markets in distribution systems, first, in a day-ahead active power market, the initial active power dispatch of generation units is estimated considering environmental and economic aspects. Based on the results of the initial active power dispatch, the proposed VVC model is executed to optimally allocate reactive power support among all providers. Another novelty of this paper lies in the pricing scheme that rewards transformers and capacitors for tap and step changing, respectively, while incorporating the reactive power dispatch model. A Benders decomposition algorithm is employed as a solution method to solve the proposed reactive power dispatch, which is a mixed integer non-linear programming (MINLP) problem. Finally, a typical 22-bus distribution network is used to verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce total dual integrality of the linear complementarity problem (LCP) by analogy with the linear programming problem. The main idea of defining the notion is to propose the LCP with orientation, a variant of the LCP whose feasible complementary cones are specified by an additional input vector. Then we naturally define the dual problem of the LCP with orientation and total dual integrality of the LCP. We show that if the LCP is totally dual integral, then all basic solutions are integral. If the input matrix is sufficient or rank-symmetric, and the LCP is totally dual integral, then our result implies that the LCP always has an integral solution whenever it has a solution. We also introduce a class of matrices such that any LCP instance having the matrix as a coefficient matrix is totally dual integral. We investigate relationships between matrix classes in the LCP literature such as principally unimodular matrices. Principally unimodular matrices are known that all basic solutions to the LCP are integral for any integral input vector. In addition, we show that it is coNP-hard to decide whether a given LCP instance is totally dual integral. [ABSTRACT FROM AUTHOR]

The paper proposes a type of secret sharing schemes called ramp assignment schemes (RAS's) to realize general access structures (AS's). In such a scheme, each participant is assigned a subset of primitive shares of an optimal $$(k,L,m)$$ -ramp scheme in such a way that the number of primitive shares assigned to each qualified subset is not less than $$k$$ whereas the one corresponding to any forbidden subset is not greater than $$k-L$$ . RAS's can be viewed as a generalization of multiple assignment schemes (MAS's). For a same AS, the minimum information rate achieved by MAS's can not be less than that achieved by RAS's. With our method, one can find efficient suitable decompositions for general AS's. And it provides a possibility to refine an existing $$(\lambda ,\omega )$$ -decomposition. We show that a RAS with minimal worst or/and average information rate can be obtained by linear programming (LP), which is in the complexity class P and much easier than the NP-hard integer programming (IP) applied to constructing optimal MAS's. Several well-designed algorithms are further presented to cut down the size of the LP/IP problems for optimal RAS's/MAS's. Other contributions of the paper include: (1) the current best upper bounds of information rates of two graph AS's on six participants are improved; (2) some specific AS's are recognized so that one can obtain the corresponding optimal RAS's directly, i.e., even without the need of solving LP problems; and (3) we characterize the AS's of ideal RAS's and of ideal MAS's. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Fuzzy Stochastic Linear Fractional Programming problem (FSLFP). In this problem, the coefficients and scalars in the objective function are the triangular fuzzy number and technological coefficients and the quantities on the right side of the constraints are fuzzy random variables with the specific distribution. Here we change an FSLFP problem to an equivalent deterministic Multi-objective Linear Fractional Programming (MOLFP) problem. Then by using Fuzzy Mathematical programming approach transformed MOLFP problem is reduced single objective Linear programming (LP) problem. A numerical example is presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Two-stage stochastic optimization, in which a long-term master problem is coupled with a family of short-term subproblems, plays a critical role in various application areas. However, most existing algorithms for two-stage stochastic optimization only work for special cases, and/or are based on the batch method, which requires huge memory and computational complexity. To the best of our knowledge, there still lack efficient and general two-stage online stochastic optimization algorithms. This paper proposes a two-stage online successive convex approximation (TOSCA) algorithm for general two-stage nonconvex stochastic optimization problems. At each iteration, the TOSCA algorithm first solves one short-term subproblem associated with the current realization of the system state. Then, it constructs a convex surrogate function for the objective of the long-term master problem. Finally, the long-term variables are updated by solving a convex approximation problem obtained by replacing the objective function in the long-term master problem with the convex surrogate function. We establish the almost sure convergence of the TOSCA algorithm and customize the algorithmic framework to solve three important application problems. Simulations show that the TOSCA algorithm can achieve superior performance over existing solutions. [ABSTRACT FROM AUTHOR]

Transmission power control has paramount importance in the design of energy-efficient wireless sensor networks (WSNs). In this paper, we systematically explore the effects of various transmission power control strategies on WSN lifetime with an emphasis on discretization of power levels and strategies for transmission power assignment. We investigate the effects of the granularity of power levels on energy dissipation characteristics through a linear programming framework by modifying a well known and heavily utilized continuous transmission power model (HCB model). We also investigate various transmission power assignment strategies by using two sets of experimental data on Mica motes. A novel family of mathematical programming models are developed to analyze the performance of these strategies. Bandwidth requirements of the proposed transmission power assignment strategies are also investigated. Numerical analysis of our models are performed to characterize the effects of various design parameters and to comparethe relative performance of transmission power assignment strategies. Our results show that the granularity of discrete energy consumption has a profound impact on WSN lifetime, furthermore, more fine-grained control of transmission power (i.e., link level control) can extend network lifetime up to 20% in comparison to optimally-assigned network-level single transmission power. [ABSTRACT FROM AUTHOR]

In this paper, a practical optimization framework and enhanced strategy within an industrial setting are proposed for solving large-scale structural optimization problems in aerospace. The goal is to eliminate the difficulties associated with optimization problems, which are mostly nonlinear with numerous mixed continuous-discrete design variables. Particular emphasis is placed on generating good initial starting points for the search process and in finding a feasible optimum solution or improving the chances of finding a better optimum solution when traditional techniques and methods have failed. The efficiency and reliability of the proposed strategy were demonstrated through the weight optimization of different metallic and composite laminated wingbox structures. The results show the effectiveness of the proposed procedures in finding an optimized solution for high-dimensional search space cases with a given level of accuracy and reasonable computational resources and user efforts. Conclusions are also inferred with regards to the sensitivity of the optimization results obtained with respect to the choice of different starting values for the design variables, as well as different optimization algorithms in the optimization process. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-stage stochastic programming formulation based on affine decision rules for the reservoir management problem. Our approach seeks to find a release schedule that balances flood control and power generation objectives while considering realistic operating conditions as well as variable water head. To deal with the non-convexity introduced by the variable water head, we implement a simple, yet effective, successive linear programming algorithm. We also introduce a novel non-linear inflow representation that captures serial correlation of arbitrary order. We test our method on a small real river system and discuss policy implications. Our results namely show that our method can decrease flood risk and increase production compared to the historical decisions, albeit at the cost of reduced final storages. [ABSTRACT FROM AUTHOR]

The problem ( LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for ( LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems. [ABSTRACT FROM AUTHOR]

The school bus routing problem (SBRP) is crucial because of its impact on economic and social objectives. A single bus is assigned to each route, picking up students and arriving at the school within a specified time window. SBRP aims to find the fewest buses needed to cover all of the routes while minimizing the total travel distance and meeting required constraints. We propose a mathematical formulation responding to the overbooking policies applied in a real-world school district. According to our empirical studies, the probability of a student riding a bus varies from 22% to 77%, opening the opportunity to overbook the buses to improve utilization of their capacity. However, SBRP with overbooking has not attracted much attention in previous studies. In this work, overbooking is modeled via chance constrained programming. Additionally, to account for the uncertainty of the total travel time of the buses, a constraint limiting the probability of being late to school is also proposed in this paper. As a result of the NP-hard nature of the problem, a cascade simplification algorithm is proposed to partition the multiple stage SBRP problems into multiple multi-depot and one-school subproblems that are solved sequentially, where the results for one are data inputs for the next. Furthermore, we develop column-generation-based algorithms to solve the scheduling problem, and different instances of the problem are examined. Our computational experiments on a real-world school district demonstrate desirable cost savings in terms of the total number of buses used. [ABSTRACT FROM AUTHOR]