Total Absolute Deviation Research Articles

An asymptotically optimal solution for the minimization of the variation of job completion times in two-stage proportionate no-wait flow shops

We propose an asymptotically optimal solution for the two-stage no-wait proportionate flow shop scheduling problem with the objective of minimizing the total absolute deviation of job completion times. The proposed solution is within 1% of the optimum for problems with more than 20 jobs. We also show that the problem is solved optimally in constant time for the special case where the two smallest jobs have equal processing times. Our results provide answers to most of the outstanding research questions for this problem.

Development of a machine learning finite-range nonlocal density functional.

Kohn-Sham density functional theory has been the most popular method in electronic structure calculations. To fulfill the increasing accuracy requirements, new approximate functionals are needed to address key issues in existing approximations. It is well known that nonlocal components are crucial. Current nonlocal functionals mostly require orbital dependence such as in Hartree-Fock exchange and many-body perturbation correlation energy, which, however, leads to higher computational costs. Deviating from this pathway, we describe functional nonlocality in a new approach. By partitioning the total density to atom-centered local densities, a many-body expansion is proposed. This many-body expansion can be truncated at one-body contributions, if a base functional is used and an energy correction is approximated. The contribution from each atom-centered local density is a single finite-range nonlocal functional that is universal for all atoms. We then use machine learning to develop this universal atom-centered functional. Parameters in this functional are determined by fitting to data that are produced by high-level theories. Extensive tests on several different test sets, which include reaction energies, reaction barrier heights, and non-covalent interaction energies, show that the new functional, with only the density as the basic variable, can produce results comparable to the best-performing double-hybrid functionals, (for example, for the thermochemistry test set selected from the GMTKN55 database, BLYP based machine learning functional gives a weighted total mean absolute deviations of 3.33kcal/mol, while DSD-BLYP-D3(BJ) gives 3.28kcal/mol) with a lower computational cost. This opens a new pathway to nonlocal functional development and applications.

Static term structure of interest rate construction with tension interpolation splines

<abstract><p>Traditional theories of term structure of interest rate consist of four major classical theories, including Pure Expectation Theory, Liquidity Preference Theory, Preferred Habitat Theory and Market Segmentation Theory. However, they cannot be well interpreted by the traditional static term structure of interest rate methods such as polynomial spline and exponential spline. To address problems on low precision and weak stability of traditional methods in constructing static interest rate term structure curve, in this paper, we introduce the tension interpolation spline based on a fourth-order differential equation with local tension parameters calculated by Generalized Reduced Gradient (GRG) algorithm. Our primary focus is to illustrate its better prediction effect and stability with an empirical study conducted using datum of treasury bonds. Then, we divided the datum into intra-sample datum for estimating tension parameters and out-of-sample datum for evaluating their robustness of predicting stochastics collected from Shanghai Stock Exchange on $ {2^{{\rm{nd}}}} $ February, 2019. According to the principle of total least squares and total least absolute deviations, the result shows that the tension interpolation spline model has better precision and stronger stability in prediction of out-of-sample treasury bonds prices compared with the model established by polynomial spline and exponential spline. In addition, it can better explain the Liquidity Preference Theory, which confirms that it is suitable for constructing the static term structure of interest rates in the securities exchange market.</p></abstract>

A double-hybrid density functional based on good local physics with outstanding performance on the GMTKN55 database.

In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn-Sham density functionals based on physical modeling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid density functional with the lowest GMTKN55 WTMAD2 "weighted total mean absolute deviation" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23."

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

In this work, we propose the idea of considering (∂p∂x)T, x→0 as an infinite dilution thermodynamic function. Our research shows that (∂p∂x)T,x→0 as a thermodynamic function is closely related to temperature, with the relation being simply expressed as: ln(∂p∂x)T, x→0=AT+B. Then, we use this equation to correlate the isothermal vapor−liquid equilibrium (VLE) data for 40 systems. The result shows that the total average relative deviation is 0.15%, and the total average absolute deviation is 3.12%. It indicates that the model correlates well with the experimental data. Moreover, we start from the total pressure expression, and use the Gibbs−Duhem equation to re-derive the relationship between (∂p∂x)T,x→0 and the infinite dilution activity coefficient (γ∞) at low pressure. Based on the definition of partial molar volume, an equation for (∂p∂x)T,x→0 and gas solubility at high pressure is proposed in our work. Then, we use this equation to correlate the literature data on the solubility of nitrogen, hydrogen, methane, and carbon dioxide in water. These systems are reported at temperatures ranging from 273.15 K to 398.15 K and pressures up to 101.325 MPa. The total average relative deviation of the predicted values with respect to the experimental data is 0.08%, and the total average absolute deviation is 2.68%. Compared with the Krichevsky−Kasarnovsky equation, the developed model provides more reliable results.

Optimizing Agricultural Input and Production for Different Types of at-Risk Peasant Households: An Empirical Study of Typical Counties in the Yimeng Mountain Area of Northern China.

Using typical counties in the Yimeng Mountain area of northern China as an example, this paper analyzed the household and agricultural input characteristics of different types of peasant households using survey data from 262 farm households. The target minimization of the total absolute deviations (MOTAD) model was applied to determine the optimal combinations in the allocation of agricultural input factors and production for different types of at-risk peasant households to obtain the ideal agricultural income. The relevant results are twofold. (1) The agricultural input behaviors of different types of peasant households vary significantly. The highest levels of agricultural land, labor, and yield-increasing and labor-saving inputs included I part-time peasant households (I PTPH), followed by full-time peasant households (FTPH), while the input levels of II part-time peasant households (II PTPH) and non-agricultural peasant households (NAPH) with higher levels of non-agricultural employment gradually decreased. In general, an increase in peasant households' part-time employment revealed an inverted U-shaped trend in the agricultural input level, with a trajectory of I PTPH > FTPH > II PTPH > NAPH. (2) The current agricultural inputs and production combinations of different types of peasant households have room for improvement. It is necessary to adjust agricultural inputs and optimize production combinations to obtain target incomes. Overall, all types of peasant households must streamline labor inputs and increase capital inputs, except for I PTPH, for which capital inputs should be reduced. Following optimization, economic crops gradually replace grain crops, and the optimal agricultural incomes of peasant households will be improved. The study results provide practical policy insights for reducing agricultural production risks and improving agricultural production incomes.

Drivers of climate variability and increasing water salinity impacts on the farmer’s income risk with future outlook mitigation

PurposeThe main aim of this study is to investigate the impact of climate change and water salinity on farmer’s income risk with future outlook mitigation. Salinity and climate change are a threat to agricultural productivity worldwide. However, the combined effects of climate change and salinity impacts on farmers' income are not well understood, particularly in developing countries.Design/methodology/approachThe response-yield function and general maximum entropy methods were used to predict the impact of temperature, precipitation and salinity on crop yield. The target minimization of total absolute deviations (MOTAD)-positive mathematical programming model was used to simulate the impact of climate change and salinity on socioeconomic and environmental indicators. In the end, a multicriteria decision-making model was used, aiming at the selection of suitable climate scenarios.FindingsThe results revealed that precipitation shows a significantly decreasing trend, while temperature and groundwater salinity (EC) illustrate a significantly increasing trend. Climate change and EC negatively impact the farmer's income and water shadow prices. Maximum reduction in income and water shadow prices was observed for A2 scenario (−12.4% and 19.4%) during 2050. The environmental index was the most important, with priority of 43.4% compared to socioeconomic indicators. Subindex amount of water used was also significant in study area, with 28.1% priority. The technique for order preference by similarity to ideal solution ranking system found that B1 was the best climatic scenario for adopting climate change adaptation in the research region.Originality/valueIn this study, farmers' income threats were assessed with the aspects of different climate scenario (A1, A1B and B1) over the horizons of 2030, 2040 and 2050 and three different indicators (economic, social and environmental) in Northwestern region of Pakistan. Only in arid and semiarid regions has climate change raised temperature and reduced rainfall, which are preliminary symptoms of growing salinity.

Industrial Hemp Production and Market Risk Analysis in Oklahoma

Industrial hemp production has garnered producer attention as a potential summer crop alternative in Oklahoma. Farmers considering the inclusion of hemp, an emerging new crop, in their operations need to factor in risk and uncertainty. We conducted a risk analysis to determine the optimal allocation of land to conventional crops and hemp for a representative 1,000-acre wheat farm in northeastern Oklahoma under production and market risk. Target MOTAD (minimization of total absolute deviation) model was used to focus on downside risk and hemp market price uncertainty. Six double-cropping systems for double- cropped winter wheat were considered, including sorghum, sesame, hemp for grain, hemp for fiber, hemp for dual grain and fiber, and hemp for floral materials. Less than 4% of the 1,000-acre available land allocated to hemp for floral material and as much as 800 acres of hemp for grain and hemp for dual grain and fiber, were profit- maximizing allocations depending on the producer’s tolerance for downside risk, target profit levels, control of cross-pollination, and market conditions.

A lion optimization algorithm for an integrating maintenance planning and production scheduling problem with a total absolute deviation of completion times objective

A lion optimization algorithm for an integrating maintenance planning and production scheduling problem with a total absolute deviation of completion times objective

Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection

We consider two-stage no-wait proportionate flow shops with the objective of minimizing service time variation measured by defining the mid-processing point of a job and minimizing the Total Absolute Deviation of mid-processing Points (TADZ). We show that the two-stage no-wait proportionate flow shop with the TADZ objective is solvable in O(nlogn) time. Our findings provide an affirmative answer to an open research question posed by Kovalev et al. (2019) regarding existence of a solvable variant of the two-stage no-wait proportionate flow shop problem with the Total Absolute Deviation of Completion Times (TADC) objective. Moreover, we show when a generic two-stage no-wait proportionate flow shop scheduling problem is solvable in O(nlogn) time. We present practical applications where TADZ is more suitable than TADC as a scheduling objective. We also introduce a new metric defined as the sum of all partial schedule lengths SPSL and show that the two-stage no-wait proportionate flow shop with the SPSL objective is solvable in O(nlogn) time; thus, an additional solvable variant of the two-stage no-wait proportionate flow shop with the SPSL objective is identified and solved. Finally, we consider the option of rejecting a job from the schedule by paying a job-specific penalty for each rejected job and solve the resulting problem with the TADZ objective and the rejection option in O(n3) time by dynamic programming.

Resilient airline scheduling to minimize delay risks

Airlines tend to design their flights schedules with the primary concern of the minimization of operational costs. However, the recently emerging idea of resilient scheduling defined as staying operational in case of unexpected disruptions and adaptability should be of great importance for airlines as well due to the high opportunity costs caused by the flight cancellations and passenger inconvenience caused by delays in the schedule. In this study, we integrate resilient airline schedule design, aircraft routing and fleet assignment problems with uncertain non-cruise times and controllable cruise times. We follow a data-driven method to estimate flight delay probabilities to calculate the airport congestion coefficients required for the probability distributions of non-cruise time random variables. We formulate the problem as a bi-criteria nonlinear mixed integer mathematical model with chance constraints. The nonlinearity caused by the fuel consumption and CO2 emission function associated with the controllable cruise times in our first objective is handled by second order conic inequalities. We minimize the total absolute deviation of the aircraft path variability’s from the average in our second objective to generate balanced schedules in terms of resilience. We compare the recovery performances of our proposed schedules to the minimum cost schedules by a scenario-based posterior analysis.

A temperature-independent prediction model predicts the vapor-liquid equilibrium of CO2-based binary mixtures

CO2-based binary mixtures are considered good alternative working fluids in the refrigeration and power cycle due to their excellent performance and environmental friendliness. The vapor-liquid phase equilibrium of CO2-based binary mixtures is the basis for calculating mixing enthalpy and heat capacity, which is essential for thermodynamic analysis. In this work, based on the vdW mixing rules, we proposed a kij model (kij=θjki-θikj). In the proposed model, ki and kj are defined as pure interaction factors of the pure components, θj is the influence factor of component j to component i, and θi is the influence factor of component i to component j. After continuous fitting and trial calculation, we developed a semi-empirical formula, which is called a temperature-independent prediction model. The model does not have any adjustable parameters, which are only related to the physical properties (critical pressure (kPa), critical temperature (K), and acentric factor) and molecular structure (carbon-carbon double bonds, carbon-fluorine, chlorine, iodine, and oxygen atoms) of the components. The temperature-independent prediction model can predict the bubble-point pressures, vapor phase molar fractions, and relative volatilities very well, which is better than the prediction model based on the vdW mixing rules by others and the group contribution model based on the excess free energy (GE) mixing rules (PR+MHV1+UNIFAC). The total average absolute relative deviation of pressures, the total average absolute deviation of vapor phase molar fractions, and the total average absolute relative deviation of relative volatilities by the temperature-independent prediction model are 2.23%, 0.0095, and 5.21%, respectively.

Some Scheduling Problems With Job Rejection And A Learning Effect

AbstractIn this paper, we examined single and parallel machine scheduling problems with a learning effect and job rejection simultaneously. In real life, job processing times decrease when there is a learning effect. In some cases, producers cannot process all the jobs and pay the penalty cost for these jobs that they do not process. In our study, learning effect and job rejection are considered at the same time. We examined four different objective functions. Our objectives for single-machine scheduling problems are makespan and rejection cost minimization, total completion time and rejection cost minimization and total absolute deviation of completion times (TADC) and rejection cost minimization. Our objective for parallel machines is makespan and rejection cost minimization. The problems are solved by mathematical models, and four different algorithms are proposed for the problems. From these algorithms, the same results are obtained with single-machine makespan and rejection cost minimization, parallel machine makespan and rejection cost minimization and total completion time and rejection cost minimization. The accuracy for these models is obtained as 100%. The proposed algorithm for TADC and rejection cost minimization yielded close-to-optimal results. Mathematical model and algorithm results for 10 jobs, 20 jobs and 30 jobs are compared and the results are presented. The obtained solutions are obtained in polynomial time.

Results of Parallel-Machine Scheduling Model with Maintenance Activity considering Time-Dependent Deterioration, Delivery Times, and Resource Allocation

This paper investigates parallel-machine scheduling models with maintenance activity, delivery times, time-dependent deterioration, and resource allocation. We consider two forms of the problem: the first is to minimize the sum of total completion times, total machine loads, the total absolute deviation of job completion times, and the total resource allocation; the second is to minimize the sum of total waiting times, total machine loads, the total absolute deviation of job waiting times, and the total resource allocation. The problems are proved to be solvable in polynomial time.

Surprisingly Good Performance of XYG3 Family Functionals Using a Scaled KS-MP3 Correlation

By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E3 to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wave function ab initio approaches. Intriguingly, (a) the introduction of E3 makes an empirical dispersion correction redundant; (b) generalized gradient approximation (GGA) or meta-GGA semilocal correlation functionals offer no advantage over the local density approximation (LDA) in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a six-parameter functional with WTMAD2 = 1.42 that has no post-LDA density functional theory components and no dispersion correction in the final energy.

OPTIMUM ENTERPRISE MIX UNDER RISK AND LIMITED RESOURCE CONDITIONS AMONG SMALLHOLDER LIVESTOCK FARMERS IN KWARA STATE, NIGERIA

The study developed optimum and a set of risk efficient livestock enterprise mix for smallholder farmers in Kwara State, Nigeria. Multi-stage sampling procedure was used to select 127 smallholder livestock farmers. A structured questionnaire complimented with interview schedule was used to obtain cross-sectional data from the farmers. Data were analyzed using descriptive statistics, farm budgeting technique, LP (linear programming) and T-MOTAD (Target minimization of total absolute deviation) models. The LP result prescribed 0.25TLU of cattle/goat/sheep, 0.37TLU of broiler and 0.47TLU of broiler/layer for optimum gross margin in plan I; and 0.29TLU of cattle/goat/sheep, 0.37TLU of broiler and 0.47TLU of broiler/layer were prescribed in plan II under the limited resource condition. A set of feasible risk efficient farm plans I, II and III were obtained with the T-MOTAD model. The plan I prescribed 0.25TLU of cattle/goat/sheep, 0.37TLU of broiler and 0.47TLU of broiler/layer. Plan II prescribed 0.07TLU of cattle/goat/sheep, 0.28TLU of broiler and 0.79TLU of broiler/layer; and plan III prescribed 0.36TLU of cattle/goat/sheep, 0.05TLU of broiler, 0.48TLU of cockerel and 0.23TLU of broiler/layer. Gross margin increased from ₦218,170.75/TLU in the existing plan to ₦242,662.30/TLU and ₦247,676.00/TLU in optimum plans I and II, respectively, and to ₦242,670.60/TLU, ₦235,065.60/TLU and ₦222,897.90/TLU in risk efficient plans I, II and III, respectively. Gross margin was more sensitive to variation in the prices of output than other variables. Labour and capital were the major limiting resource across all the plans for the livestock enterprises. It was concluded that the livestock farmers had the potential to maximize gross margins per unit enterprise in the optimum and risk efficient farm plans as resources were not optimally allocated in the existing plan for livestock activities. Farmers should therefore adopt the prescribed optimum and risk efficient farm plans.

Minimizing total absolute deviation of job completion times on a single machine with maintenance activities using a Lion Optimization Algorithm

Scheduling is a decision-making process that plays an important role in the service and production industries. Effective scheduling can assist companies to survive in the competitive market. Single machine scheduling is an important optimization problem in the scheduling research area. It can be found in a wide range of real-world engineering problems, from manufacturing to computer science. Due to the high complexity of single machine scheduling problems, developing approximation methods, particularly metaheuristic algorithms, for solving them have absorbed considerable attention. In this study, a Lion Optimization Algorithm (LOA) is employed to solve a single machine with maintenance activities, where the objective is to minimize the Total Absolute Deviation of Compilation Times (TADC). In the scheduling literature, TADC as an objective function has hardly been studied. To evaluate the performance of the LOA, it was compared against a set of well-known metaheuristics. Therefore, a set of problem was generated, and a comprehensive experimental analysis was conducted. The results of computational experiments indicate the superiority of the proposed optimization method.

Calculation of interfacial tension of binary systems containing water and an organic component by group contribution methods

This work proposes a predictive method for estimating liquid-liquid interfacial tension (IFT) by group contribution methods of systems containing water and an organic component. The model for calculating the interfacial tension of liquid–liquid systems was derived using a general thermodynamic framework that was empirically extended by the introduction of an effective interfacial area. The effective interfacial area is defined for each component and takes into account the effects of groups of the other component present at the liquid-liquid interface. In addition, the interfacial molar volume was estimated by a mixing rule, using the molar volume of pure components in the liquid phase, weighted by the equilibrium compositions calculated by the UNIFAC model. The corresponding thermophysical properties were obtained by a group contribution method, in which a temperature-dependent binary parameter was proposed. This parameter is given by the sum of contributions related to each group present in the molecule, with values estimated from an experimental database of interfacial tension of water and different organic compounds. Therefore, the model can be used to predict the interfacial tension of binary mixtures in different temperatures through the knowledge of the structure of the organic component. The values of the model parameters were determined by a parameter estimation procedure based on an extensive database, covering 546 interfacial tension data of liquid-liquid binary systems containing water and an organic component. The model predicts interfacial tension data for binary systems containing organic compounds with different chemical functions in equilibrium with water, including oxygenated organic compounds, which are rarely predicted with good accuracy. The total mean absolute deviation obtained from this method was 1.20 mN⋅m−1, better than other predictive model and also better than some correlative models available in the literature.

Single-machine slack due-window assignment scheduling with multiple maintenance activities and position-and-resource-dependent processing times

This paper studies the slack due-window assignment method for single-machine scheduling problems with position-and resource-dependent processing times, for which the actual processing time is a continuous bivariate non-increasing convex function involving position and resource allocation. Only the slack due-window assignment method will be used. Two linear combination problems concerning position-dependent effects and resource allocation will be studied, in which the machine requires multiple maintenance activities. We present the optimal properties or design optimal algorithms to minimise the combination of the makespan, the total completion time and the total absolute deviation of completion time and to minimise the combination of the total costs of tardiness, the slack due date, the earliness cost, and the resource amount. Finally, we also consider the bi-criteria scheduling problem with nonmaintenance activities to minimise the combination of the total resource allocation cost, the weighted number of tardy jobs, and slack due-window assignment costs. A pseudo-polynomial time algorithm is designed to solve the bi-criteria scheduling problem.

Appraisal of Dimensional Accuracy in Five Brands of Extended Pour Irreversible Hydrocolloid Materials for FDP Impression

Aim. The purpose of this study was to assess and compare the dimensional accuracies of five brands ofextended pour irreversible hydrocolloid materials for fixed dental prosthesis impression.Materials and methods. Impressions of a master stainless steel model were made with five extended pourirreversible hydrocolloids and one addition silicone impression material. A total of ninety impressions(n=90) were made, with fifteen for each group of impression material. The stone dies retrieved fromthese impressions were analysed with Baty-Vision Systems - Venture 3D CNC machine, for dimensionalaccuracies. Comparison of continuous data between two groups was done with the Wilcoxon rank-sum test(Mann Whitney U test) and for more than two groups with the Kruskal Wallis test (? = .05)Results. All six impression materials showed some amount of error. On comparison of the median totalabsolute deviation of the various dimension of stone dies, the accuracies of impression materials in decreasingorder appeared to be Neocolloid >> Affinis >> Coltoprint >> Zelgan >> 3M ESPE >> Plastalgin. On thecontrary, a comparison of the impression materials, in terms of several dimensions of stone dies differingsignificantly from the stainless-steel model, the sequence in terms of accuracy was, Coltoprint > Affinis >3MESPE > Neocolloid > Plastalgin > Zelgan.Conclusions. Based on the dimensional accuracies of the stone dies retrieved from the impressions,Neocolloid was found to be the best impression material with the least possible deviation, followed byColtoprint and Affinis.