Efficiency and stability under substitutable priorities with ties

Many assignment mechanisms appeal to a priority structure to determine how over-subscribed indivisible goods are assigned to unit-demand individuals. We study substitutable priorities with ties which not only nest important classes of priorities and preferences studied in the literature, but also allow us to formalize plausible priority structures not captured in previous literature. Efficiency is typically in conflict with respecting priorities (i.e., stability), and therefore the natural welfare objective is constrained efficiency. A generalization of the deferred acceptance process yields a stable assignment, but this outcome is not necessarily constrained efficient. We identify an easily verifiable sufficient condition for a stable assignment to be constrained efficient, which then leads to an algorithm to compute a constrained efficient assignment. Finally we illustrate practical applications of our framework and algorithm, including a widely studied matching problem with distributional constraints

Priority-based intersection management with kinodynamic constraints

We consider the problem of coordinating a collection of robots at an intersection area taking into account dynamical constraints due to actuator limitations. We adopt the coordination space approach, which is standard in multiple robot motion planning. Assuming the priorities between robots are assigned in advance and the existence of a collision-free trajectory respecting those priorities, we propose a provably safe trajectory planner satisfying kinodynamic constraints. The algorithm is shown to run in real time and to return safe (collision-free) trajectories. Simulation results on synthetic data illustrate the benefits of the approach.Comment: to be presented at ECC2014; 6 page

Welfare theorems for random assignments with priorities

Motivated by the application of designing fair and efficient school choice lotteries, we consider constrained efficiency notions for random assignments under priorities. We provide a constrained (priority respecting) version of the ordinal efficiency welfare theorem for random assignments. Moreover, we show that a constrained version of a cardinal second welfare theorem fails to hold

A greedy heuristic approach for the project scheduling with labour allocation problem

Responding to the growing need of generating a robust project scheduling, in this article we present a greedy algorithm to generate the project baseline schedule. The robustness achieved by integrating two dimensions of the human resources flexibilities. The first is the operators’ polyvalence, i.e. each operator has one or more secondary skill(s) beside his principal one, his mastering level being characterized by a factor we call “efficiency”. The second refers to the working time modulation, i.e. the workers have a flexible time-table that may vary on a daily or weekly basis respecting annualized working strategy. Moreover, the activity processing time is a non-increasing function of the number of workforce allocated to create it, also of their heterogynous working efficiencies. This modelling approach has led to a nonlinear optimization model with mixed variables. We present: the problem under study, the greedy algorithm used to solve it, and then results in comparison with those of the genetic algorithms

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the classical simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.Comment: 18 pages, 1 figur

Respecting priorities versus respecting preferences in school choice: When is there a trade-off?

A classic trade-off that school districts face when deciding which matching algorithm to use is that it is not possible to always respect both priorities and preferences. The student-proposing deferred acceptance algorithm (DA) respects priorities but can lead to inefficient allocations. We identify a new condition on school choice markets under which DA is efficient. Our condition generalizes earlier conditions by placing restrictions on how preferences and priorities relate to one another only on the parts that are relevant for the assignment. Whenever there is a unique allocation that respects priorities, our condition captures all the environments for which DA is efficient. We show through stylized examples and simulations that our condition significantly expands the range of known environments for which DA is efficient. We also discuss how our condition sheds light on existing empirical findings

Efficient Priority Rules

We study the assignment of indivisible objects with quotas (houses, jobs, or offices) to a set of agents (students, job applicants, or professors). Each agent receives at most one object and monetary compensations are not possible. We characterize efficient priority rules by efficiency, strategy-proofness, and renegotiation-proofness. Such a rule respects an acyclical priority structure and the allocations can be determined using the deferred acceptance algorithm.L. Ehlers gratefully acknowledges financial support from the SSHRC (Canada). B. Klaus's research was partly supported by a Ramón y Cajal contract and Research Grant BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and by the Barcelona Economics Program of CREA