Self-Selected Task Allocation

2020 ◽  
Author(s):  
Refael Hassin ◽  
Adam Nathaniel
Keyword(s):  
Task Allocation ◽  
Numerical Study ◽  
Fixed Number ◽  
Problem Definition ◽  
Independent Random Variables ◽  
Taxi Drivers ◽  
Closed Form Solutions ◽  
Allocation Method ◽  
Managerial Implications ◽  
The Common

Problem definition: Tasks sequentially arrive, and their values to the workers who are going to perform them are independent random variables. The common way to allocate tasks to workers is according to the first-in, first-out order. But this method both is inefficient and seems unfair to those who receive a low-valued task after a long wait. We are looking for a better allocation method. Academic/practical relevance: Finding a fair and efficient task allocation method is an aspiration of manpower firms that employ a pool of workers, such as salespersons, technicians, emergency medical stuff, nurses, or taxi drivers. We present many more implementations, such as turn taking and load management. Methodology: We propose a self-selected task allocation method and discuss its importance and implementations. The proposed method is defined as a cyclic queueing game with a fixed number of players. Every unit of time a prize with a random value is offered to the players according to their order in the queue, and a player who accepts a prize moves to the end of the queue. The process of choosing which prizes to accept in each position is presented as a noncooperative multiplayer game. We analyze strategies and symmetric equilibria for three variations. Results: We provide closed-form solutions and suggest a novel intuitive interpretation to find equilibria via calculating maximum-profit strategies. We complement the theoretical results by conducting a numerical study. Managerial implications: The proposed method is natural and easy to implement, its outcome is better than the common allocation by seniority, and the ratio of the expected value obtained under the two methods is unbounded.

Queues with Redundancy: Is Waiting in Multiple Lines Fair?

2021 ◽  
Author(s):  
Leela Nageswaran ◽  
Alan Scheller-Wolf
Keyword(s):  
Organ Transplantation ◽  
Numerical Study ◽  
Arrival Rate ◽  
Problem Definition ◽  
Service Systems ◽  
Equitable Access ◽  
Policy Makers ◽  
Managerial Implications ◽  
Shortest Queue ◽  
To Receive

Problem definition: We study service systems where some (so-called “redundant”) customers join multiple queues simultaneously, enabling them to receive service in any one of the queues, while other customers join a single queue. Academic/practical relevance: The improvement in overall system performance due to redundant customers has been established in prior work. We address the question of fairness—whether the benefit experienced by redundant customers adversely affects others who can only join a single line. This question is particularly relevant to organ transplantation, as critics have contended that multiple listing provides unfair access to organs for patients based on wealth. Methodology: We analyze two queues serving two classes of customers; the redundant class joins both queues, whereas the nonredundant class joins a single queue randomly. We compare this system against a benchmark wherein the redundant class resorts to joining the shortest queue (JSQ) if multiple queue joining were not allowed, capturing the most likely case if multilisting was prohibited: Affluent patients could still afford to list in the region with the shorter wait list. Results: We prove that when the arrival rate of nonredundant customers is balanced across both queues, they actually benefit under redundancy of the other class—that is, redundancy is fair. We also establish that redundancy may be unfair under some circumstances: Nonredundant customers are worse off if their arrival rate is strongly skewed toward one of the queues. We illustrate how these findings apply in the organ-transplantation setting through a numerical study using publicly available data. Managerial implications: Our analysis helps identify when, and by how much, multiple listing may be unfair and, as such, could be a useful tool for policy makers who may be concerned with trying to ensure equitable access to resources, such as organs, across patients with differing wealth levels.

scholarly journals Allocation of COVID-19 Vaccines Under Limited Supply

2020 ◽  
Author(s):  
Xin Chen ◽  
Menglong Li ◽  
David Simchi-Levi ◽  
Tiancheng Zhao
Keyword(s):  
New York ◽  
Numerical Study ◽  
Age Groups ◽  
Problem Definition ◽  
Dynamic Allocation ◽  
Effective Interventions ◽  
Managerial Implications ◽  
Myopic Policy ◽  
The Government ◽  
Age Structured

Problem definition: This paper considers how to allocate COVID-19 vaccines to different age groups when limited vaccines are available over time. Academic/practical relevance: Vaccine is one of the most effective interventions to contain the ongoing COVID-19 pandemic. However, the initial supply of the COVID-19 vaccine will be limited. An urgent problem for the government is to determine who to get the first dose of the future COVID-19 vaccine. Methodology: We use epidemic data from New York City to calibrate an age-structured SAPHIRE model that captures the disease dynamics within and across various age groups. The model and data allow us to derive effective static and dynamic vaccine allocation policies minimizing the number of confirmed cases or the numbers of deaths. Results: The optimal static policies achieve a much smaller number of confirmed cases and deaths compared to other static benchmark policies including the pro rata policy. Dynamic allocation policies, including various versions of the myopic policy, significantly improve on static policies. Managerial implications: For static policies, our numerical study shows that prioritizing the older groups is beneficial to reduce deaths while prioritizing younger groups is beneficial to avert infections. For dynamic policies, the older groups should be vaccinated at early days and then switch to younger groups. Our analysis provides insights on how to allocate vaccines to the various age groups, which is tightly connected to the decision-maker's objective.

Correlation analysis of radiation damage

1978 ◽  
Vol 36 (1) ◽  
pp. 214-215
Author(s):  
R. Hegerl ◽  
A. Feltynowski ◽  
B. Grill
Keyword(s):  
Electron Microscopy ◽  
Independent Random Variables ◽  
Optical Parameters ◽  
Bright Field Image ◽  
Bright Field ◽  
Expectation Value ◽  
All Optical ◽  
Image Element ◽  
Stochastic Series ◽  
The Common

Till now correlation functions have been used in electron microscopy for two purposes: a) to find the common origin of two micrographs representing the same object, b) to check the optical parameters e. g. the focus. There is a third possibility of application, if all optical parameters are constant during a series of exposures. In this case all differences between the micrographs can only be caused by different noise distributions and by modifications of the object induced by radiation.Because of the electron noise, a discrete bright field image can be considered as a stochastic series Pm,where i denotes the number of the image and m (m = 1,.., M) the image element. Assuming a stable object, the expectation value of Pm would be Ηm for all images. The electron noise can be introduced by addition of stationary, mutual independent random variables nm with zero expectation and the variance. It is possible to treat the modifications of the object as a noise, too.

Partial Completion as a Nonprofit Strategy

2021 ◽  
Author(s):  
Can Zhang ◽  
Atalay Atasu ◽  
Karthik Ramachandran
Keyword(s):  
Nonprofit Organizations ◽  
Service Provision ◽  
Problem Definition ◽  
Product Service ◽  
Service Portfolio ◽  
Wide Range ◽  
Partial Completion ◽  
Innovative Solution ◽  
Managerial Implications ◽  
Level 3

Problem definition: Faced with the challenge of serving beneficiaries with heterogeneous needs and under budget constraints, some nonprofit organizations (NPOs) have adopted an innovative solution: providing partially complete products or services to beneficiaries. We seek to understand what drives an NPO’s choice of partial completion as a design strategy and how it interacts with the level of variety offered in the NPO’s product or service portfolio. Academic/practical relevance: Although partial product or service provision has been observed in the nonprofit operations, there is limited understanding of when it is an appropriate strategy—a void that we seek to fill in this paper. Methodology: We synthesize the practices of two NPOs operating in different contexts to develop a stylized analytical model to study an NPO’s product/service completion and variety choices. Results: We identify when and to what extent partial completion is optimal for an NPO. We also characterize a budget allocation structure for an NPO between product/service variety and completion. Our analysis sheds light on how beneficiary characteristics (e.g., heterogeneity of their needs, capability to self-complete) and NPO objectives (e.g., total-benefit maximization versus fairness) affect the optimal levels of variety and completion. Managerial implications: We provide three key observations. (1) Partial completion is not a compromise solution to budget limitations but can be an optimal strategy for NPOs under a wide range of circumstances, even in the presence of ample resources. (2) Partial provision is particularly valuable when beneficiary needs are highly heterogeneous, or beneficiaries have high self-completion capabilities. A higher self-completion capability generally implies a lower optimal completion level; however, it may lead to either a higher or a lower optimal variety level. (3) Although providing incomplete products may appear to burden beneficiaries, a lower completion level can be optimal when fairness is factored into an NPO’s objective or when beneficiary capabilities are more heterogeneous.

The Effects of Patent Extension and Take-Back Regulation on Green Pharmacy

2021 ◽  
Author(s):  
Tianqin Shi ◽  
Nicholas C. Petruzzi ◽  
Dilip Chhajed
Keyword(s):  
Pharmaceutical Industry ◽  
Social Welfare ◽  
Technical Information ◽  
Problem Definition ◽  
Theoretic Model ◽  
Innovative Company ◽  
Take Back ◽  
Starting Point ◽  
European Environmental Agency ◽  
Managerial Implications

Problem definition: The eco-toxicity arising from unused pharmaceuticals has regulators advocating the benign design concept of “green pharmacy,” but high research and development expenses can be prohibitive. We therefore examine the impacts of two regulatory mechanisms, patent extension and take-back regulation, on inducing drug manufacturers to go green. Academic/practical relevance: One incentive suggested by the European Environmental Agency is a patent extension for a company that redesigns its already patented pharmaceutical to be more environmentally friendly. This incentive can encourage both the development of degradable drugs and the disclosure of technical information. Yet, it is unclear how effective the extension would be in inducing green pharmacy and in maximizing social welfare. Methodology: We develop a game-theoretic model in which an innovative company collects monopoly profits for a patented pharmaceutical but faces competition from a generic rival after the patent expires. A social-welfare-maximizing regulator is the Stackelberg leader. The regulator leads by offering a patent extension to the innovative company while also imposing take-back regulation on the pharmaceutical industry. Then the two-profit maximizing companies respond by setting drug prices and choosing whether to invest in green pharmacy. Results: The regulator’s optimal patent extension offer can induce green pharmacy but only if the offer exceeds a threshold length that depends on the degree of product differentiation present in the pharmaceutical industry. The regulator’s correspondingly optimal take-back regulation generally prescribes a required collection rate that decreases as its optimal patent extension offer increases, and vice versa. Managerial implications: By isolating green pharmacy as a potential target to address pharmaceutical eco-toxicity at its source, the regulatory policy that we consider, which combines the incentive inherent in earning a patent extension on the one hand with the penalty inherent in complying with take-back regulation on the other hand, serves as a useful starting point for policymakers to optimally balance economic welfare considerations with environmental stewardship considerations.

The effect of the roller profile oncave-in defect in reshaping processby considering nonlinear combine strain hardening

2021 ◽  
pp. 095440542110368
Author(s):  
Siamak Mazdak ◽  
Hassan Moslemi Naeni ◽  
Mohammad Reza Sheykholeslami ◽  
Manabo Kiuchi ◽  
Hesam Validi
Keyword(s):  
Numerical Study ◽  
Contact Model ◽  
Slab Method ◽  
Incremental Method ◽  
Circular Pipes ◽  
Meaningful Relationship ◽  
Numerical Software ◽  
Combined Hardening ◽  
The Common ◽  
Roller Profile

The reshaping process of pipes is an important method in producing non-circular pipes. Desired profile products are produced by passing round pipe through the rotating rollers. Cave-in defect is one of the common defects in the reshaping process. Roller design issues can decrease this kind of defect. In this paper, a method based on the slab method and the incremental plasticity has been presented to the numerical study of a 2D reshaping process. For investigating the Cave-in defect, the contact model has been developed. The concept of element elongation has been introduced to increase the accuracy of the contact model. Based on the presented method, numerical software has been developed to simulate the 2D reshaping process. Elastic-plastic equations for this subject have been driven based on the incremental method, J yielding criterion, and non-linear combined hardening. The effects of the radius of the roller profile on cave-in defects have been investigated by using the presented software (DARF). A set of experiments has been conducted in a forming station to verify the results. Results show that the presented model has higher accuracy than the Abaqus commercial software in predicting the cave-in defect. Based on the results of the model, the local increase of yielding stress directly affects the cave-in defect. Also, a meaningful relationship between the radius of the roller and the amount of the cave-in has been observed.

Numerical Study on Progressive Failure of the Marble Plate Based on the Thin-Layer Tri-Node Jointed Element

2011 ◽  
Vol 255-260 ◽  
pp. 1867-1872
Author(s):  
Jing Hua Qi ◽  
Zhen Nan Zhang ◽  
Xiu Run Ge
Keyword(s):  
Crack Propagation ◽  
Thin Layer ◽  
Numerical Study ◽  
Progressive Failure ◽  
Triangular Element ◽  
Compressive Loads ◽  
Joint Element ◽  
The Common ◽  
Edge Cracks ◽  
Good Agreement

In order to model the mechanical behavior of joints efficiently, a thin-layer tri-node joint element is constructed. The stiffness matrix of the element is derived in the paper. For it shares the common nodes with the original tri-node triangle element, the tri-node joint element can be applied to model the crack propagation without remeshing or mesh adjustment. Another advantage is that the cracked body is meshed without consideration of its geometry integrity and existence of the joints or pre-existed crack in the procedure of mesh generation, and then the triangular element intersected by the crack or joint is automatically transformed into the tri-node joint element to represent pre-existed cracks. These make the numerical simulation of crack propagation highly convenient and efficient. After CZM is chosen to model the crack tip, the mixed- energy simple criterion is used to determine whether the element is intersected by the extended crack or not, the extended crack is located in the model. By modeling the marble plates with two edge cracks subjected to the uniaxial compressive loads, it is shown that the numerical results are in good agreement with the experimental results, which suggests that the present method is valid and feasible in modeling rock crack propagation.

Truthful Mechanisms for Medical Surplus Product Allocation

2020 ◽  
Vol 22 (4) ◽  
pp. 735-753 ◽  
Author(s):  
Can Zhang ◽  
Atalay Atasu ◽  
Turgay Ayer ◽  
L. Beril Toktay
Keyword(s):  
Private Information ◽  
Value Added ◽  
Information Provision ◽  
Problem Definition ◽  
Preference Ranking ◽  
Additional Increase ◽  
Healthcare Facilities ◽  
Selection Decisions ◽  
Managerial Implications ◽  
Recipient Selection

Problem definition: We analyze a resource allocation problem faced by medical surplus recovery organizations (MSROs) that recover medical surplus products to fulfill the needs of underserved healthcare facilities in developing countries. The objective of this study is to identify implementable strategies to support recipient selection decisions to improve MSROs’ value provision capability. Academic/practical relevance: MSRO supply chains face several challenges that differ from those in traditional for-profit settings, and there is a lack of both academic and practical understanding of how to better match supply with demand in this setting where recipient needs are typically private information. Methodology: We propose a mechanism design approach to determine which recipient to serve at each shipping opportunity based on recipients’ reported preference rankings of different products. Results: We find that when MSRO inventory information is shared with recipients, the only truthful mechanism is random selection among recipients, which defeats the purpose of eliciting information. Subsequently, we show that (1) eliminating inventory information provision enlarges the set of truthful mechanisms, thereby increasing the total value provision; and (2) further withholding information regarding other recipients leads to an additional increase in total value provision. Finally, we show that under a class of implementable mechanisms, eliciting recipient valuations has no value added beyond eliciting preference rankings. Managerial implications: (1) MSROs with large recipient bases and low inventory levels can significantly improve their value provision by appropriately determining the recipients to serve through a simple scoring mechanism; (2) to truthfully elicit recipient needs information to support the recipient selection decisions, MSROs should withhold inventory and recipient-base information; and (3) under a set of easy-to-implement scoring mechanisms, it is sufficient for MSROs to elicit recipients’ preference ranking information. Our findings have already led to a change in the practice of an award-winning MSRO.

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