A note on object allocation under lexicographic preferences

Sabán, Daniela; Sethuraman, Jay

doi:10.1016/j.jmateco.2013.12.002

Cited by 31 publications

(24 citation statements)

References 4 publications

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“…A lexicographic approach allows decision makers to introduce decision rules in which they select more objects impacting on their most-preferred criteria. According to Saban and Sethuraman (2014), when two objects have the same impact on the most-preferred criteria, decision makers prefer the one with the highest impact on the second most-preferred criteria, and so forth. This lexicographic representation models the problems where decision makers strictly prefer one criterion over another or they are managing noncompensatory aggregation (Pulido, Mandow, & de la Cruz, 2014;Yaman, Walsh, Littman, & Desjardins, 2011).…”

Section: Lexicographic Approachmentioning

confidence: 99%

Risk-based ROI, capital budgeting, and portfolio optimization in the Department of Defense

Mun

2020

Defense ARJ

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This article shows a reusable, extensible, adaptable, and comprehensive advanced analytical modeling process to help the U.S. Department of Defense (DoD) with risk-based capital budgeting and optimizing of acquisition and program portfolios with multiple stakeholders while subject to budgetary, risk, schedule, and strategic constraints. The article covers traditional capital budgeting methodologies in industry and explains how these methods can be applied in the DoD by using DoD-centric, noneconomic, logistic, readiness, capabilities, and requirements variables. Portfolio optimization for the purposes of selecting the best combination of programs and capabilities is also addressed, as are alternative methods such as average ranking, risk metrics, lexicographic methods, PROMETHEE, ELECTRE, and others. Finally, an illustration from the Program Executive Office Integrated Warfare Systems (PEO-IWS) and Naval Sea Systems Command (NAVSEA) showcases the methodology’s application in developing a comprehensive and analytically robust case study that senior leadership at the DoD may utilize to make optimal decisions.

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Section: Lexicographic Approachmentioning

confidence: 99%

Risk-based ROI, capital budgeting, and portfolio optimization in the Department of Defense

Mun

2020

Defense ARJ

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“…Thus, we examine the properties of RSD and PS in the space of all possible preference profiles as well as under lexicographic preferences. Lexicographic preferences are present in various applications and have been extensively studied in artificial intelligence and multiagent systems as a means of assessing allocations based on ordinal preferences [18,21,44]. Under lexicographic preferences, an allocation that assigns a higher probability to the top ranked object is always preferred to any other allocation, regardless of the probabilities assigned to objects in the next positions.…”

Section: General and Lexicographic Preferencesmentioning

confidence: 99%

Investigating the characteristics of one-sided matching mechanisms under various preferences and risk attitudes

Hosseini

Larson

Cohen

2018

Auton Agent Multi-Agent Syst

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One-sided matching mechanisms are fundamental for assigning a set of indivisible objects to a set of self-interested agents when monetary transfers are not allowed. Two widely-studied randomized mechanisms in multiagent settings are the Random Serial Dictatorship (RSD) and the Probabilistic Serial Rule (PS). Both mechanisms require only that agents specify ordinal preferences and have a number of desirable economic and computational properties. However, the induced outcomes of the mechanisms are often incomparable and thus there are challenges when it comes to deciding which mechanism to adopt in practice.In this paper, we first consider the space of general ordinal preferences and provide empirical results on the (in)comparability of RSD and PS. We analyze their respective economic properties under general and lexicographic preferences. We then instantiate utility functions with the goal of gaining insights on the manipulability, efficiency, and envyfreeness of the mechanisms under different riskattitude models. Our results hold under various preference distribution models, which further confirm the broad use of RSD in most practical applications.

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“…Responsiveness is a very mild requirement and responsive preferences form a very wide and variable class. Therefore we shall restrict our attention to two specific examples, namely additive [5,9,11] and lexicographic [17,5,34,33,36] preferences. Although lexicographic preferences can be modelled as additive preferences by choosing appropriate weights [9], we would like to avoid this approach as it requires very large numbers, moreover, assuming lexicographic preferences from the outset leads to more straightforward algorithms.…”

Section: Prerequisites and Corequisitesmentioning

confidence: 99%

Pareto optimal matchings of students to courses in the presence of prerequisites

Cechlárová

Klaus

Manlove

2018

Discrete Optimization

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We consider the problem of allocating applicants to courses, where each applicant has a subset of acceptable courses that she ranks in strict order of preference. Each applicant and course has a capacity, indicating the maximum number of courses and applicants they can be assigned to, respectively. We thus essentially have a many-tomany bipartite matching problem with one-sided preferences, which has applications to the assignment of students to optional courses at a university.We consider additive preferences and lexicographic preferences as two means of extending preferences over individual courses to preferences over bundles of courses. We additionally focus on the case that courses have prerequisite constraints: we will mainly treat these constraints as compulsory, but we also allow alternative prerequisites. We further study the case where courses may be corequisites.For these extensions to the basic problem, we present the following algorithmic results, which are mainly concerned with the computation of Pareto optimal matchings (POMs). Firstly, we consider compulsory prerequisites. For additive preferences, we show that the problem of finding a POM is NP-hard. On the other hand, in the case of lexicographic preferences we give a polynomial-time algorithm for finding a POM, based on the well-known sequential mechanism. However we show that the problem of deciding whether a given matching is Pareto optimal is co-NP-complete. We further prove that finding a maximum cardinality (Pareto optimal) matching is NP-hard. Under alternative prerequisites, we show that finding a POM is NP-hard for either additive or lexicographic preferences. Finally we consider corequisites. We prove that, as in the case of compulsory prerequisites, finding a POM is NP-hard for additive preferences, though solvable in polynomial time for lexicographic preferences. In the latter case, the problem of finding a maximum cardinality POM is NP-hard and very difficult to approximate.

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A note on object allocation under lexicographic preferences

Cited by 31 publications

References 4 publications

Risk-based ROI, capital budgeting, and portfolio optimization in the Department of Defense

Risk-based ROI, capital budgeting, and portfolio optimization in the Department of Defense

Investigating the characteristics of one-sided matching mechanisms under various preferences and risk attitudes

Pareto optimal matchings of students to courses in the presence of prerequisites

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