Academic literature on the topic 'Quadratic Service Costs'

As the farmland transfer market in China develops, moderate-scale operations increasingly grow but without much improvement in fertilizer use efficiency. This study theoretically analyzes the mechanism and effect of rising farmland costs on fertilizer use efficiency using multiple quadratic regression and mediating effects models. It empirically tests a micro-sample of 806 farmers in Gansu and Jiangsu provinces in China from two dimensions: the full samples and farmer heterogeneity. The results showed 0.544 as the average fertilizer use efficiency (hereinafter, fe) of farmers in Gansu and Jiangsu, highlighting the severe loss of fe caused by excessive fertilizer inputs. The multiple quadratic regression model further revealed an inverted U-shaped relationship between farmland costs and fe, with the U-shaped curve showing a remarkable inflection point at the USD 708/mu mark. When farmland costs are excessive (cost > CNY 708/mu), the increase in farmland costs inhibits the fe. An investigation of the corresponding impact mechanism for this scenario (i.e., cost > USD 708/mu) revealed that farmland costs directly suppress fe (−0.485) by distorting the fertilizer factor substitution effect and indirectly suppress fe (−0.037) by impeding the technology spillover effect of production specialization and production scale-up. We also found heterogeneity between two groups: ordinary farmers and new agricultural operators (e.g., large grain and family farmers), with the peak kernel density function of fe of new agricultural operators (0.85) being much higher than that of ordinary farmers (0.30). Moreover, the multiple quadratic regression between the groups revealed a lower inflection point for ordinary farmers (CNY 638/mu) than new agricultural operators (CNY 823/mu), highlighting that the fe of ordinary farmers was more likely to be inhibited by the excessive rise in farmland costs. To promote the sustainable development of China’s agricultural production, we propose reducing the cost of farmland, promoting service-scale operations, and fostering new agricultural operators.

Maintaining a fleet of buses to transport students to school is a major expense for school districts. To reduce costs by reusing buses between schools, many districts spread start times across the morning. However, assigning each school a time involves estimating the impact on transportation costs and reconciling additional competing objectives. Facing this intricate optimization problem, school districts must resort to ad hoc approaches, which can be expensive, inequitable, and even detrimental to student health. For example, there is medical evidence that early high school starts are impacting the development of an entire generation of students and constitute a major public health crisis. We present an optimization model for the school time selection problem (STSP), which relies on a school bus routing algorithm that we call biobjective routing decomposition (BiRD). BiRD leverages a natural decomposition of the routing problem, computing and combining subproblem solutions via mixed integer optimization. It significantly outperforms state-of-the-art routing methods, and its implementation in Boston has led to $5 million in yearly savings, maintaining service quality for students despite a 50-bus fleet reduction. Using BiRD, we construct a tractable proxy to transportation costs, allowing the formulation of the STSP as a multiobjective generalized quadratic assignment problem. Local search methods provide high-quality solutions, allowing school districts to explore tradeoffs between competing priorities and choose times that best fulfill community needs. In December 2017, the development of this method led the Boston School Committee to unanimously approve the first school start time reform in 30 years.

ObjectiveThis study aims to explore the relationship between slack resources and cost consumption index in tertiary and secondary hospitals and to provide targeted healthcare resource utilisation recommendations for tertiary and secondary hospital managers.DesignThis is a panel data study of 51 public hospitals in Beijing from 2015 to 2019.SettingTertiary and secondary public hospitals in Beijing. Data envelope analysis was used to calculate the slack resources. Regression models were used to explore the relationship between slack resources and healthcare costs.ParticipantsA total of 255 observations were collected from 33 tertiary hospitals and 18 secondary hospitals.Outcome measuresSlack resources and healthcare costs in tertiary and secondary public hospitals in Beijing from 2015 to 2019. Linear or curve relationship between slack resources and healthcare costs in tertiary and secondary hospitals.ResultsThe cost of healthcare in tertiary hospitals has always been higher than in secondary hospitals, and the slack resources in secondary hospitals have always been worse than in tertiary hospitals. For tertiary hospitals, the cubic coefficient of slack resources is significant (β=−12.914, p<0.01) and the R2of cubic regression is increased compared with linear and quadratic regression models, so there is a transposed S-shaped relationship between slack resources and cost consumption index. For secondary hospitals, only the first-order coefficient of slack resources in the linear regression was significant (β=0.179, p<0.05), so slack resources in secondary hospitals were positively related to the cost consumption index.ConclusionsThis study shows that slack resources’ impact on healthcare costs differs in tertiary and secondary public hospitals. For tertiary hospitals, slack should be kept within a reasonable range to control excessive growth in healthcare costs. In secondary hospitals, keeping too many slack resources is not ideal, so managers should adopt strategies to improve competitiveness and service transformation.

Focusing on the dynamic improvement of the underlying service network configuration, this paper aims to address a specific challenge of redesigning a multi-echelon city logistics distribution network. By considering the intra-echelon connection of facilities within the same layer of echelon, we propose a new distribution network design model by reformulating the classical quadratic assignment problem (QAP). To minimize the overall transportation costs, the proposed model jointly optimizes two types of decisions to enable agile distribution with dynamic “shortcuts”: (i) the allocation of warehouses to supply the corresponding distribution centers (DCs), and (ii) the demand coverage decision from distribution centers to delivery stations. Furthermore, a customized branch-and-bound algorithm is developed, where the lower bound is obtained by adopting Gilmore and Lawler lower Bound (GLB) for QAP. We conduct extensive computational experiments, highlighting the significant contribution of GLB-oriented lower bound, to obtain practical solutions; this type of efficient mathematical lower bounds offers a powerful tool for balancing theoretical research ideas with practical and industrial applicability.

IntroductionHypertension (HT) and diabetes mellitus (DM) and are major disease burdens in all healthcare systems. Given their high impact on morbidity, premature death and direct medical costs, we need to optimise effectiveness and cost-effectiveness of primary care for patients with HT/DM. This study aims to find out the association of trajectories in disease patterns and treatment of patients with HT/DM including multimorbidity and continuity of care with disease outcomes and service utilisation over 10 years in order to identify better approaches to delivering primary care services.Methods and analysisA 10-year retrospective cohort study on a population-based primary care cohort of Chinese patients with documented doctor-diagnosed HT and/or DM, managed in the Hong Kong Hospital Authority (HA) public primary care clinics from 1 January 2006 to 31 December 2019. Data will be extracted from the HA Clinical Management System to identify trajectory patterns of patients with HT/DM. Complications defined by ICPC-2/International Classification of Diseases-Ninth Revision, Clinical Modification diagnosis codes, all-cause mortality rates and public service utilisation rates are included as independent variables. Changes in clinical parameters will be investigated using a growth mixture modelling analysis with standard quadratic trajectories. Dependent variables including effects of multimorbidity, measured by (1) disease count and (2) Charlson’s Comorbidity Index, and continuity of care, measured by the Usual Provide Continuity Index, on patient outcomes and health service utilisation will be investigated. Multivariable Cox proportional hazards regression will be conducted to estimate the effect of multimorbidity and continuity of care after stratification of patients into groups according to respective definitions.Ethics and disseminationThis study was approved by the institutional review board of the University of Hong Kong—the HA Hong Kong West Cluster, reference no: UW 19–329. The study findings will be disseminated through peer-reviewed publications and international conferences.Trial registration numberNCT04302974.

P u r p o s e s. When designing a system of urban electric transport that charges while driving, including autonomous trolleybuses with batteries of increased capacity, it is important to optimize the charging infrastructure for a fleet of such vehicles. The charging infrastructure of the dedicated routes consists of overhead wire sections along the routes and stationary charging stations of a given type at the terminal stops of the routes. It is designed to ensure the movement of trolleybuses and restore the charge of their batteries, consumed in the sections of autonomous running.The aim of the study is to create models and methods for developing cost-effective solutions for charging infrastructure, ensuring the functioning of the autonomous trolleybus fleet, respecting a number of specific conditions. Conditions include ensuring a specified range of autonomous trolleybus running at a given rate of energy consumption on routes, a guaranteed service life of their batteries, as well as preventing the discharge of batteries below a critical level under various operating modes during their service life.M e t ho d s. Methods of set theory, graph theory and linear approximation are used.Re s u l t s. A mathematical model has been developed for the optimization problem of the charging infrastructure of the autonomous trolleybus fleet. The total reduced annual costs for the charging infrastructure are selected as the objective function. The model is formulated as a mathematical programming problem with a quadratic objective function and linear constraints.Co n c l u s i o n. To solve the formulated problem of mathematical programming, standard solvers such as IBM ILOG CPLEX can be used, as well as, taking into account its computational complexity, the heuristic method of "swarm of particles". The solution to the problem is to select the configuration of the location of the overhead wire sections on the routes and the durations of charging the trolleybuses at the terminal stops, which determine the corresponding number of stationary charging stations at these stops.

The authors analyze 925 town highway departments in New York to determine potential economies from consolidation and the degree of cost efficiency. Only 15% of departments would reduce costs by merging, resulting in an average 13% reduction in expenditures. In addition, all of the towns are cost inefficient by an average 17%. Size economies are estimated using a log quadratic stochastic frontier regression model. The estimated cost curve is a textbook U shape with a mean cost elasticity of 0.97, indicating that most towns are operating at the minimum point of the curve. The composed error model is used to estimate cost inefficiency, which is not systematically linked to size inefficiency. However, 14 very small departments are quite cost inefficient.

Virtualization is one of the core technologies used in cloud computing to provide services on demand for end users over the Internet. Most current research allocates virtual machines to physical machines based on CPU utilization. However, for many applications that require communication between services running on different servers, communication costs influence the overall performance. Therefore, this study focuses on the optimal allocation of virtual machines across multiple geographically dispersed data centers, with the objective of minimizing communication costs. The original problem can be constructed as a quadratic assignment problem that is a classical NP-hard combinatorial optimization problem. This study adopts an efficient deterministic optimization approach to reformulate the original problem as a mixed-integer linear program that may be solved to obtain a globally optimal solution. Since the required bandwidth matrix and communication cost matrix are symmetric, the mathematical model of virtual machine placement can be simplified. Several numerical examples drawn from the literature are solved to demonstrate the computational efficiency of the proposed method for determining the optimal virtual machine allocation in cloud computing.

This paper integrates Discrete Particle Swarm Optimization (DPSO) and Sequential Quadratic Programming (SQP) to propose a DPSO-SQP method for solving unit commitment problems for ancillary services. Through analysis of ancillary services, including Automatic Generation Control (AGC), Real Spinning Reserve (RSR), and Supplemental Reserve (SR), the cost model of unit commitment was developed. With the requirements of energy balance, ancillary services, and operating constraints considered, DPSO-PSO was used to calculate the energy supply of each source, including the associated AGC, RSR, and SR, and the operating cost of a day-ahead power market was calculated. A study case using the real data from thermal units of Taipower Company (TPC) and Independent Power Producers (IPPs) demonstrated effective results for the “summer” and “non-summer” seasons, as classified by TPC for the two charging rates. According to the test cases in this research, costs without ancillary services in non-summer and summer seasons are higher than those with ancillary services. The simulation results are also compared with the Genetic Algorithm (GA), Evolutionary Programming (EP), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). DPSO-PSO shows effectiveness in solving unit commitment problems with enhanced sorting efficiency, and a higher probability of reaching the global optimum.

Walkability has been associated with urban development and political plans, contributing to more connected cities with improvements in communication, shopping, and pedestrian base. Among these services, fitness centers are becoming important elements for communities due to their impact on the health and welfare of citizens. The present study aims to examine how an area’s Walk Score® affects fitness center services, specifically membership costs, opening hours, and aquatic services. Data from 193 fitness centers were retrieved, representing all the areas of the municipality of Madrid, Spain, including fitness centers in the 21 city districts. A nonlinear relationship between an area’s Walk Score® and fitness centers’ monthly fees is observed. Only in premium fitness centers, a weak curvilinear model is observed, following a quadratic equation, showing that fitness centers with higher prices are in less walkable areas. Additionally, the association between Walk Score® and a fitness center’s opening hours reveals that fitness centers with wider hours of operation tend to be in moderately to highly walkable locations. Lastly, the existence of a swimming pool is related to a lower Walk Score®. Thus, fitness centers in less walkable areas try to offer additional services as differentiation from competitors, whereas centers in walkable locations use this advantage as a strength.

Service or job scheduling problems arise in many contexts such as cloud computing, task scheduling in CPUs, traffic routing and scheduling, production scheduling in plants, scheduling charging of electric vehicles (EVs), etc. For instance, in cloud computing, server power consumption increases as a convex function of the load. Hence, delay-tolerant jobs need to be deferred in order to save on long-term average power cost. The jobs, while being delay tolerant, may not be delay-insensitive and may also have hard deadlines. In all such cases it is crucial to schedule jobs or services to minimize a weighted sum of service and waiting costs, the latter capturing delay sensitivity of the jobs. In several systems, jobs are admitted only at slot boundaries, but they can leave as soon as their services are complete, e.g., consider EVs at EV Charging stations. Then the waiting period of an agent can depend on the amount of deferred service. To capture the disutility due to waiting in such cases, we introduce waiting costs that are linear in the amount of deferred services. We study service scheduling problems with quadratic service costs and linear waiting costs. We frame the problems as average cost Markov decision processes. While the studied system is a linear system with quadratic costs, it has state-dependent control and a non-standard cost function structure, rendering the optimization problem complex. We obtain explicit optimal policies in the case when all the jobs are of the same size. In particular, we show that the optimal policy is linear or piece-wise linear in the system state, depending on the system parameters. We extend our study to a scenario where job sizes can take distinct values and job arrivals constitute a Markov chain. We provide an algorithm that yields the optimal scheduling policy but has exponential complexity. Hence, we propose an approximate policy of linear complexity and derive its performance bound. We also study systems with maximum sojourn time of three slots. To account for higher user sensitivity to incremental delays, we also study job scheduling problems with quadratic service costs and quadratic waiting costs – quadratic waiting costs can be employed to capture higher job sensitivity to delays. Job arrivals and sojourn times are as in the previous problem. Our problem is a constrained optimization linear quadratic control Markov decision problem. However, unconstrained problem of our formulation can be cast as a standard linear quadratic control Markov decision problem. We obtain explicit optimal policies in the case when all the jobs are of same size. In particular, we show that the optimal policy is linear in the system state. When the job sizes can take two or more distinct values, we provide an algorithm that yields the optimal policy. We propose a policy to cater to the cases with unknown parameters. In several systems of interest, agents can enter the system or leave only at slot boundaries, e.g., compute tasks derive utility only at slot boundaries. In such tasks that complete only at slot boundaries, the current operating job will be present in the system until its next slot boundary irrespective of the amount of pending service. Thus, the waiting involved is fixed and does not depend on the amount of deferred service. We study service scheduling problems in a slotted system where jobs arrive according to a Bernoulli process and have to leave within two slots after arrival. The service cost is quadratic in service rate, and a job also incurs a fixed waiting cost if it is not completed in the first slot after its arrival. We provide the optimal policy when the parameters satisfy certain conditions. We also propose an approximate policy that enables us to characterize the optimal policy. In all the above setups, we also consider scenarios where each service request comes from a rational agent interested in optimizing his/her own service and waiting costs. For example, in the context of EV charging, EV owners being rational agents would be interested in minimizing their own cost instead of the total system cost. In such scenarios we can frame service-scheduling problem as a non-cooperative dynamic game among the agents. Finally, we characterize symmetric Nash equilibria in all these cases. We next consider a more general scenario where job arrival statistics are unknown, jobs’ sojourn times are arbitrary, and service costs are convex increasing functions. We study job or service scheduling as a continuous-time problem with convex increasing service costs and linear waiting costs with focus on minimizing service and job waiting costs. We first consider the offline version of the problem where arrival times, requirements and deadlines of all the jobs are known a priori. We propose job scheduling algorithms that minimize the total accrued cost. We then consider the online version of the problem and propose two heuristics. Our problem can be seen as an extension of the well studied speed scaling problem with a waiting cost also included. Finally, we study service scheduling problems with service cost being a piecewise linear convex function of service rate. We now assume that service rates are upper bounded. Here, the central facility is not bound to serve of every job by its deadline. Hence, we do not consider waiting cost but consider a dissatisfaction cost instead. We model disutility for not serving the required amount in the form of dissatisfaction cost. We study the following variants of the service scheduling problem: (a) Stochastic arrivals with common departure epoch, (b) Common arrival epoch but distinct departure epochs, (c) Stochastic arrivals with maximum sojourn time of two slots, and (d) Stochastic arrivals with arbitrary sojourn times. We derive slot dependent optimal policies for cases (a), (b). We derive slot independent optimal policy for (c). We propose a heuristic for case (d) based on the optimal policy of common arrival epoch but distinct departure epochs.

For successful industrial scale-up and effective cost analysis of transesterification process, presentation of complimentary research data from process optimization using statistical design techniques, chemical kinetics and thermodynamics are essential. Full factorial central composite design (FFCCD) was applied for the statistical optimization of base methanolysis of sea almond (Terminalia catappa) seed oil using response surface methodology (RSM) coupled with desirability function analysis on quadratic model. Reaction time had the most significant impact on the biodiesel yield. Optimum conditions for biodiesel yield of 93.09 wt% validated at 92.58 wt% were 50.03°C, 2.04 wt% catalyst concentration, 58.5 min and 4.66 methanol/oil molar ratio with overall desirability of 1.00. Ascertained fuel properties of the FAME were in compliance with international limits. GC–MS, FTIR and NMR characterizations confirmed unsaturation and good cold-flow qualities of the biodiesel. Based on power rate law, second-order kinetic model out-performed first-order kinetic model. Rate constants of the triglyceride (TG), diglycerides (DG) and monoglycerides (MG) hydrolysis were in the range of 0.00838–0.0409 wt%/min while activation energies were 12.76, 15.83 and 22.43 kcal/mol respectively. TG hydrolysis to DG was the rate determining step. The optimal conditions have minimal error and would serve as a springboard for industrial scale-up of biodiesel production from T. catappa seed oil.

ABSTRACT: Conventional PDC cutters are prone to get broken when drilling through conglomerate formations and soft-hard interbedded heterogeneous layers, leading to serious fatigue wear, short bit life, and small bit footage. Compared to the conventional PDC cutter, axe-shaped PDC cutter can dig out gravel and pebbles through crushing and shearing, which significantly reduces energy consumption for rock-breaking. Thus, this paper proposed to study effects of axe-shaped PDC cutter cutting parameters on rock-breaking characteristics of conglomerates. Using PDC cutter cutting equipment, the research quantitatively revealed the effects of cutting depth, back rake angle, and cutting speed on the cutting force, cutting size distribution, and the groove morphological characteristics of axe-shaped PDC cutter. Also, mechanical modeling was used to describe the mechanical dynamics of the axeshaped PDC cutter in the cutting process. Then, an axe-shaped PDC bit was designed and manufactured, for the purpose of field application. According to the testing data, the cutting force of the axe-shaped PDC cutter increases with increasing back rake angle and increasing cutting depth. The larger the cutting angle, the more complicated the relationship between the cutting force amplitude and the cutting depth, from linear relation to quadratic and cubic functions. Meanwhile, the mechanical specific energy for rock-breaking remains at a small level in a cutting angle range of 10 to 20 °. Compared with the conventional PDC bit, the bit footage of PDC bit with ASP-cutter increased by 399m and the average ROP increased by 24.22%. These findings are expected to provide theoretical guidance on the rock-breaking characteristics of axe-shaped PDC cutter, especially for the drilling process in conglomerate formation. INTRODUCTION Since PDC bit was introduced into the oil and gas drilling industries in 1970s by GENERAL Electric of the United States, it has been widely used in drilling soft to medium-hard formations with high rock-breaking efficiency and long service life (Yang and Guo 2018). However, in the drilling process of conglomerates and other heterogeneous layers (e.g. soft-hard interbedded layers), conventional PDC cutters are easily to get broken and prone to crack, leading to premature failure of drill bit, low drilling efficiency and high drilling cost (He et al. 2021; Zeng et al. 2021).