Multi-issue bankruptcy problems with crossed claims

In this paper, we introduce a novel model of multi-issue bankruptcy problem inspired from a real problem of abatement of emissions of different pollutants in which pollutants can have more than one effect on atmosphere. In our model, therefore, several perfectly divisible goods (estates) have to be allocated among certain set of agents (claimants) that have exactly one claim which is used in all estates simultaneously. In other words, unlike of the multi-issue bankruptcy problems already existent in the literature, this model study situations with multi-dimensional states, one for each issue and where each agent claims the same to the different issues in which participates. In this context, we present an allocation rule that generalizes the well-known constrained equal awards rule from a procedure derived from analyzing this rule for classical bankruptcy problems as the solution to a sucession of linear programming problems. Next, we carry out an study of its main properties, and we characterize it using the well-known property of consistency.

Process Simulation Integrated Life Cycle Net Energy Analysis and GHG Assessment of Fuel-Grade Bioethanol Production from Unutilized Rice Straw

The life cycle stage of paddy rice cultivation can be excluded with a zero-inventory allocation rule for the life cycle scenario of bioethanol production from unutilized rice straw, i.e., rice straw with no applied valorization in current practice. Accordingly, this study evaluates the life cycle net energy analysis and greenhouse gas (GHG) assessment for a scaled-up bioethanol production plant using unutilized rice straw as the feedstock. The process simulation technique is integrated to model a scaled-up production plant to produce bioethanol at 99.7 vol% purity from unutilized rice straw, and the simulation results are retrieved to calculate inventory data for life cycle assessment (LCA). The simulated mass flow and energy flow results are comparable with that of real plants, reported in the published literature, which validates the process simulations in this study. Inclusive of energy generation using the waste flows in the process (i.e., wastewater and solid residues), the life cycle net energy analysis results show a net energy gain of 7,804.0 MJ/m3 of bioethanol with a net renewable energy gain of 38,230.9 MJ/m3 of bioethanol that corresponds to a net energy ratio of 1.20 and renewability factor of 5.49. The life cycle GHG assessment exhibits a net global warming potential of 584.8 kg CO2 eq./m3 of bioethanol. The effect of system boundary expansion up to the end-of-life stage as gasohol (E10), the sensitivity of the key process parameters, and the economic benefit via valorization of unutilized rice straw are further analyzed and discussed.

The Myth and Reality of Teacher Shortage in India: An Investigation Using 2019-20 Data

This paper examines the widespread perception in India that the country has an acute teacher shortage of about one million teachers in public elementary schools, a view repeated in India’s National Education Policy 2020. Using official DISE data, we show that teacher vacancies cannot be equated with teacher shortages: while the number of teacher vacancies (in teacher-deficit schools) is 766,487, the number of teacher surpluses (in surplus-teacher schools) is 520,141, giving a net deficit of only 246,346 teachers in the country. Secondly, removing estimated fake student numbers from enrolment data greatly reduces the required number of teachers and raises the number of surplus teachers, converting the net deficit of 246,346 teachers into an estimated net surplus of 98,371 teachers. Thirdly, if we both remove estimated fake enrolment and also make a hypothetical change to the teacher allocation rule to adjust for the phenomenon of emptying public schools (which has slashed the national median size of public schools to a mere 63 students, and rendered many schools ‘tiny’), the estimated net teacher surplus rises to 239,800 teachers. Fourthly, we show that if government does fresh recruitment to fill the supposed approximately one-million vacancies as promised in National Education Policy 2020, the already modest national mean pupil-teacher-ratio of 25.1 would fall to 19.9, at a permanently increased fiscal cost of nearly Rupees 637 billion (USD 8.7 billion) per year in 2019-20 prices, which is higher than the individual GDPs of 50 countries that year. The paper highlights the major efficiencies that can result from evidence-based policy on minimum viable school-size, teacher allocation norms, permissible maximum pupil teacher ratios, and teacher deployment.

Research on Energy Efficiency of NOMA–SWIPT Cooperative Relay Network Using GS-DinkelBach Algorithm

In order to improve the energy efficiency (EE) performance of cooperative networks, this study combines non-orthogonal multiple access (NOMA) with simultaneous wireless information and power transfer (SWIPT) technologies to construct a cooperative relay network composed of one base station (BS), multiple near users, and one far user. Based on the network characteristics, a time-division resource allocation rule is proposed, and EE formulas regarding direct-link mode and cooperative mode are derived. Considering user selection and decoding performance, to obtain the optimal EE, this study utilizes a DinkelBach iterative algorithm based on the golden section (GS-DinkelBach) to solve the EE optimization problem, which is affected by power transmitted from the BS, achievable rates under three communication links, and quality of service (QoS) constraints of users. The simulation results show that the GS-DinkelBach algorithm can obtain precise EE gains with low computational complexity. Compared with the traditional NOMA–SWIPT direct-link network model and the relay network model, the optimal EE of the established network model could be increased by 0.54 dB and 1.66 dB, respectively.

A Proportional-Egalitarian Allocation Policy for Public Goods Problems with Complex Network

How free-riding behavior can be avoided is a constant topic in public goods problems, especially in persistent and complex resource allocation situations. In this paper, a novel allocation policy for public goods games with a complex network, called the proportional-egalitarian allocation method (PEA), is proposed. This allocation rule differs from the well-studied redistribution policies by following a two-step process without paying back into the common pool. A parameter is set up for dividing the total income into two parts, and then they are distributed by following the egalitarianism and proportional rule, respectively. The first part of total income is distributed equally, while the second part is allocated proportionally according to players’ initial payoffs. In addition, a new strategy-updating mechanism is proposed by comparing the average group payoffs instead of the total payoffs. Compared with regular lattice networks, this mechanism admits the difference of cooperative abilities among players induced by the asymmetric network. Furthermore, numerical calculations show that a relatively small income for the first distribution step will promote the cooperative level, while relatively less income for the second step may harm cooperation evolution. This work thus enriches the knowledge of allocation policies for public goods games and also provides a fresh perspective for the strategy-updating mechanism.

Axiomatic and Dynamic Processes for a Symmetric Allocation Rule

It has recently become imperative to analyze relevant issues to improve the efficiency of resource allocation by means of different perspectives and ways of thinking. There exist numerous decisive factors, such as changes in forms of allocation, reactive behavior, and the interaction and functional effectiveness of strategies, that need to be complied. In contrast to expert meetings, rules of thumb, or other existing concepts, this article aims to offer a different and efficient resource allocation approach by applying game-theoretical methods to resource-allocation situations. Our major investigative procedures are as follows: (1) after comparing our method with pre-existing allocation rules from pre-existing allocation rules, a symmetric allocation rule is proposed that considers both units and their energy grades; (2) based on the properties of grade completeness, criterion for models, unmixed equality symmetry, grade synchronization, and consistency, some axiomatic outcomes are used to examine the mathematical accuracy and the applied rationality of this symmetric allocation rule; (3) based on a symmetrical revising function, a dynamic process is applied to show that this symmetric allocation rule can be reached by units that start from an arbitrary grade completeness situation; and (4) these axiomatic and dynamic results and related meanings are applied to show that this symmetric allocation rule can present an optimal alternative guide for resource-allocation processes. Related applications, comparisons, and statements are also offered throughout this article.

Genetic Algorithm for the Retailers’ Shelf Space Allocation Profit Maximization Problem

This paper discusses the problem of retailers’ profit maximization regarding displaying products on the planogram shelves, which may have different dimensions in each store but allocate the same product sets. We develop a mathematical model and a genetic algorithm for solving the shelf space allocation problem with the criteria of retailers’ profit maximization. The implemented program executes in a reasonable time. The quality of the genetic algorithm has been evaluated using the CPLEX solver. We determine four groups of constraints for the products that should be allocated on a shelf: shelf constraints, shelf type constraints, product constraints, and virtual segment constraints. The validity of the developed genetic algorithm has been checked on 25 retailing test cases. Computational results prove that the proposed approach allows for obtaining efficient results in short running time, and the developed complex shelf space allocation model, which considers multiple attributes of a shelf, segment, and product, as well as product capping and nesting allocation rule, is of high practical relevance. The proposed approach allows retailers to receive higher store profits with regard to the actual merchandising rules.

The Efficient Proportional Myerson Values for Hypergraph Games

This study deals with a class of efficient extensions of Myerson value for games with hypergraph communication situations in which the surplus is allocated proportionally. We introduce w -fairness of surplus and provide axiomatic characterizations of the new allocation rule. Furthermore, we give an example of research fund distribution amongst researchers, compare the numerical results with several values, and realize other efficient extensions of Myerson value can be obtained depending on the different measure function w on the hypergraph.

Derived Storage Allocation Rules to Meet Shared Water Demands for Optimal Operation of an Inter-basin Multi-reservoir Water Supply System

The priority principle of storage allocation rules of serial cascade reservoirs within an inter-basin water supply can reduce water loss and reduce water supply times. Reasonable balancing curves for reservoirs in parallel are proposed and the proportional distribution of water is determined to illustrate the optimal allocation rule for different scheduling periods of reservoirs. The mutation point and slope are used to describe the segmentation of reservoirs in parallel. In addition, the optimization model is established with the objective function to minimize times of water shortage while the particle swarm optimization algorithm based on the immune evolutionary algorithm is applied to calibrate the balancing curves. Finally, the relative optimal water supply rule is obtained, providing a larger water supply capacity and higher storage synchronization of member reservoirs. The reservoir groups downstream of Luan River are used as an example, with the results showing that the suggested method can effectively improve the operational performance and meet shared water demands in an inter-basin multi-reservoir. This article highlights the superior results obtained compared to the current storage allocation rules to meet shared water demands.