Existence of equilibria in nonconvex economies without free disposal

1992 ◽  
Vol 38 (1) ◽  
pp. 37-42 ◽  
Author(s):  
Elyes Jouini
Keyword(s):  
Free Disposal ◽  
Nonconvex Economies ◽  
Existence Of Equilibria

scholarly journals Truthful fair division without free disposal

2020 ◽  
Vol 55 (3) ◽  
pp. 523-545 ◽  
Author(s):  
Xiaohui Bei ◽  
Guangda Huzhang ◽  
Warut Suksompong
Keyword(s):  
Fair Division ◽  
Multiple Agents ◽  
Two Agents ◽  
Free Disposal ◽  
Cake Cutting ◽  
Strategic Agents ◽  
Additional Constraints

Abstract We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

scholarly journals Order Picking and E-Commerce: Introducing Non-Parametric Efficiency Measurement for Sustainable Retail Logistics

2021 ◽  
Vol 16 (4) ◽  
pp. 846-858
Author(s):  
Matthias Klumpp ◽  
Dominic Loske
Keyword(s):  
Goodness Of Fit ◽  
New Technologies ◽  
Order Picking ◽  
Free Disposal Hull ◽  
Free Disposal ◽  
Efficiency Assessment ◽  
Parametric Data ◽  
Proposed Model ◽  
Dea Models ◽  
Non Parametric

Order picking is a crucial but labor- and cost-intensive activity in the retail logistics and e-commerce domain. Comprehensive changes are implemented in this field due to new technologies like AI and automation. Nevertheless, human worker’s activities will be required for quite some time in the future. This fosters the necessity of evaluating manual picker-to-part operations. We apply the non-parametric Data Envelopment Analysis (DEA) to evaluate the efficiency of n = 23 order pickers processing 6109 batches with 865,410 stock keeping units (SKUs). We use distance per location, picks per location, as well as volume per SKU as inputs and picks per hour as output. As the convexity axiom of standard DEA models cannot be fully satisfied when using ratio measures with different denominators, we apply the Free Disposal Hull (FDH) approach that does not assume convexity. Validating the efficiency scores with the company’s efficiency assessment, operationalized by premium payments shows a 93% goodness=of-fit for the proposed model. The formulated non-parametric approach and its empirical application are promising ways forward in implementing empirical efficiency measurements for order picking operations within e-commerce operations.

scholarly journals Mathematical Analysis of an Epidemic-Species Hybrid Dynamical System

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jing Hui ◽  
Jian-Hua Pang ◽  
Dong-Rong Lin
Keyword(s):  
Dynamical System ◽  
Hopf Bifurcation ◽  
Local Stability ◽  
Orbital Stability ◽  
Species Hybrid ◽  
Hybrid Dynamical System ◽  
Mathematical Analyses ◽  
Existence Of Equilibria ◽  
Impulsive Releasing ◽  
Infected Prey

We consider an epidemic-species hybrid dynamical system. The disease is spread among the prey only and the infected prey can reproduce virus. The predator only eats the infected prey. Mathematical analyses are given for the system with regard to the existence of equilibria, local stability, Hopf bifurcation, and the orbital stability of the Hopf bifurcating limit cycle. We further analyse the system under impulsive releasing of virus and predator.

scholarly journals Full substitutability

2019 ◽  
Vol 14 (4) ◽  
pp. 1535-1590 ◽  
Author(s):  
John William Hatfield ◽  
Scott Duke Kominers ◽  
Alexandru Nichifor ◽  
Michael Ostrovsky ◽  
Alexander Westkamp
Keyword(s):  
Production Capacity ◽  
Limited Liability ◽  
Indivisible Goods ◽  
Exchange Economies ◽  
New Class ◽  
Existence Of Equilibria

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.

scholarly journals WHEN BIAS KILLS THE VARIANCE: CENTRAL LIMIT THEOREMS FOR DEA AND FDH EFFICIENCY SCORES

2014 ◽  
Vol 31 (2) ◽  
pp. 394-422 ◽  
Author(s):  
Alois Kneip ◽  
Léopold Simar ◽  
Paul W. Wilson
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Data Envelopment ◽  
Free Disposal Hull ◽  
Average Efficiency ◽  
Free Disposal ◽  
Monte Carlo Experiments ◽  
The Individual ◽  
Individual Scores

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that standard central limit theorems do not apply in the case of means of DEA or FDH efficiency scores due to the bias of the individual scores, which is of larger order than either the variance or covariances among individual scores. The main difficulty comes from the fact that such statistics depend on efficiency estimators evaluated at random points. Here, new central limit theorems are developed for means of DEA and FDH scores, and their efficacy for inference about mean efficiency levels is examined via Monte Carlo experiments.

scholarly journals Equilibrium with fixed budgets and superlinear connections

2001 ◽  
Vol 42 (4) ◽  
pp. 462-480
Author(s):  
A. M. Rubinov ◽  
B. M. Glover
Keyword(s):  
Extremal Problems ◽  
Economic Equilibrium ◽  
Differential Properties ◽  
Existence Of Equilibria

AbstractWe study models of economic equilibrium with fixed budgets and assuming superlinear connections between consumption and production. Extremal problems and the existence of equilibria are discussed for such models along with some related differential properties. Examples to illustrate the broad nature of the model are discussed.

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