Assignment Problem Research Articles

Solving the storage location assignment of large-scale automated warehouse based on dynamic vortex search algorithm

This paper establishes the mathematical model for Storage Location Assignment (SLA) problem in large-scale automated warehouses by combining three objectives: efficiency, shelf stability, and stacker load balancing. Along with a novel repair strategy to handle the complex constraints of large-scale problems. Additionally, a coding method and solution approach suitable for practical application scenarios are developed. In order to solve large-scale SLA problem, an improved vortex search algorithm is proposed based on attraction operation in flow field, dimension-by-dimension dynamic radius and leadership decision-making mechanism (FDVSA). In the experimental part, the algorithm effectiveness experiment of FDVSA was first conducted using the large-scale global optimization test sets IEEE congress on evolutionary computation 2010 and 2013 (CEC2010, CEC2013). The results show that: (1) Compared with other comparison algorithms, the comprehensive average optimization rate of FDVSA in CEC2010 and CEC2013 is 88 % and 78 %, respectively. (2) The experimental results of FDVSA showed that each improvement strategy has advantages in dealing with large-scale problems. (3) The post-hoc analysis showed that there are significant differences between FDVSA and other comparison algorithms, and FDVSA is significantly better. Finally, FDVSA and other comparison algorithms are solved on three different scale and complexity of SLA cases. The results show that: (1) FDVSA has significant advantages in solving large-scale SLA problem, and the comprehensive average optimization rate is 19 %. (2) The convergence curve and boxplot showed that FDVSA has good convergence speed and solving stability. (3) The effectiveness of the repair strategy was verified by experiments in the large-scale SLA problems.

A New Integer Model for Selecting Students at Higher Education Institutions: Preparatory Classes of Engineers as Case Study

This study addresses the challenge of selecting outstanding students at higher education institutions under multiple constraints. We propose a novel integer programming solution to manage this process, formulating it as a constrained assignment problem with a maximization objective function. This function prioritizes the fair selection of students while respecting criteria such as academic qualifications, required skills, and student preferences. The goal is to develop a decision support system that efficiently selects qualified students at higher education institutions within a reasonable time. The model was tested using real data from Moroccan preparatory classes, achieving important assignment rates across all student categories. Results demonstrate significance in execution time, fulfillment of student choices, and prioritization of outstanding students. This approach offers a flexible, efficient solution for managing academic merit-based selections, optimizing resource utilization, and enhancing fairness in the selection process.

A novel framework for production planning and class-based storage location assignment: Multi-criteria classification approach

Efficient warehouse management is essential for optimizing inventory, minimizing transportation costs, and enhancing overall performance. This research introduces a novel Mixed-Integer Nonlinear Programming (MINLP) model to address the Storage Location Assignment Problem (SLAP) in warehouse management. Integrating multi-criteria decision-making with strategic production planning, our model advances warehouse operations by allocating storage locations to products strategically, focusing on reducing transportation distances and maximizing storage efficiency. The distinctive innovation of this study is the nuanced application of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) results to strategic storage location assignments, enhancing the model's capability to consider a comprehensive evaluation of inventory attributes, including physical characteristics and perishability. This approach evolves TOPSIS's application in warehouse management, enabling it to consider both physical characteristics and perishability of products. The outcomes of TOPSIS, including product classifications and preferences, serve as vital inputs to the mathematical model, facilitating a comprehensive evaluation of storage locations that encompasses spatial, demand-related, and physical aspects of inventory. Additionally, our research introduces a versatile decision support system, adaptable to various operational requirements. This system enhances practical decision-making in warehouse management, accommodating scenarios based on single or multiple criteria, including the cube-per-order index (COI). The research results highlight the significant impact of this innovative approach in enhancing warehouse management. By addressing the complexities of storage location assignment and integrating multiple criteria, we achieve more efficient and cost-effective warehouse operations. The approach has been shown to be adaptable and practical, making it a valuable contribution to the field of logistics and warehouse management.

Multiobjective optimization of collaborative robotic task sequence assignment problems under collision-free constraints

This paper proposes a multiobjective optimization approach to address the challenge of collaborative manufacturing with multiple robot arms. Given the necessity for multiple robot arms to work together, the potential for collisions between robotic motions is a significant concern, and the automated task sequence assignment for robots becomes increasingly complex. Previous research has either simplified the collision-free conditions in a limited working area, or employed a master-slave approach to obtain only a local solution. Consequently, we propose a unified global optimization approach for simultaneously addressing various collaborative manufacturing issues, including robotic task sequence assignment (RTSA), multiple inverse kinematics (IK) selection, joint-space collision-free operations and multiple manufacturing objectives. As the optimal collaborative RTSA problem is a combinatorial optimization problem with non-deterministic polynomial-time hard (NP-hard) complexity, this paper presents a hybrid nondominated sorting genetic algorithm III (NSGA-III) method that integrates a Hamming-distance-based method and a greedy strategy within NSGA-III to improve population diversity and solution quality. To validate the efficacy of the proposed approach, simulation experiments were conducted on cooperative manufacturing scenarios, with two objectives: task completion time and task load balancing. The experimental results demonstrate that the proposed approach is effective in obtaining collision-free Pareto solutions. Furthermore, the proposed hybrid NSGA-III method obtains superior solutions compared to the original method in the studied problem, as measured by two performance indices.

Optimized Selective Assembly using Hungarian Algorithm

Assembly of discrete parts guided by hardware design specification constitutes the final phase in product manufacturing. In the course of mass production of components, mating parts with geometric or dimensional deviation from their intended design can be made acceptable by the identification of suitable pairs after analysing design fit and tolerance limits. By transforming this application-specific problem into a unified mathematical model, an optimal solution can be achieved that minimizes the rejection of non-conforming fabricated parts. Regardless of the type and range of a design fit, the problem can be mapped into a matrix using a ranking function defined by the user. The ranking function is modifiable as per the user requirements and may vary based on the selection criteria for an assembly. Based on the type of ranking function used, the tabulated matrix is solved using the Hungarian minimization/maximization algorithm, which is a powerful combinatorial optimization algorithm that solves the classical assignment problem in mathematics. This approach ensures maximum number of suiting pairs as well as nominal suiting of parts with each other resulting in high-quality products and maximum utilization of fabricated resources.

A semi-supervised learning algorithm for multi-label classification and multi-assignment clustering problems based on a Multivariate Data Analysis

Classically, in classification and clustering problems, an individual is exclusively assigned to a class (labeled data) or a cluster (unlabeled data). However, the assignment to a single class or cluster may be too strict in several real-world domains. In many cases, an individual may belong to multiple classes or clusters at the same time. On the other hand, we are starting to see machine learning algorithms that solve the problem of multi-label classification and multiple cluster assignment, but there are no algorithms that solve both problems simultaneously. Classic semi-supervised algorithms can work with labeled and unlabeled data simultaneously, but these types of algorithms assign individuals to a single class or a single cluster. Today, artificial intelligence faces the challenge of developing semi-supervised learning algorithms to work with semi-labeled data that can be assigned to different classes or clusters at the same time. In particular, this paper proposes a semi-supervised learning algorithm to fill this gap, which can solve the problems of multi-label classification and multiple cluster assignment simultaneously, on a semi-labeled dataset. This proposal is based on the LAMDA algorithm (Learning Algorithm for Multivariate Data Analysis), which calculates the degree of membership of a data to a group/class. In this work, a membership threshold is defined, which allows individuals to be assigned to classes or clusters that have a membership greater than this membership threshold. Thus, the main contribution of this work is the development of a semi-supervised algorithm that can process semi-labeled datasets to assign them to multiple classes and/or clusters. Furthermore, the work defines a metric to evaluate its efficiency in a semi-supervised context, called Multi Label-Cluster Index (MULCI). This proposal is tested on several datasets from the domains of multi-label classification or multi-assignment clustering, or a combination of both, showing very encouraging results. Very good quality metrics results are achieved in multiclass and multicluster tasks.

Technician assignment in multi-shift maintenance schedules in an offshore wind farm

Offshore wind farms are becoming more and more important to sustainable energy strategies, yet their maintenance presents unique logistical challenges. The focus of this research is the Technician Assignment Problem (TAP) which involves a complicated and fluctuating scheduling problem. The key objective is to determine the most effective assignment of technicians to maintenance tasks to maximize operational efficiency and ensure reliable service. This study introduces a mathematical optimization model that processes numerous variables—technician availability, skill sets, and temporal constraints—to minimize unmet maintenance needs and ensure equitable workload distribution. The model is based on assumptions derived from actual operational conditions and human resource practices, guaranteeing that its results are not only theoretically valid but also practically feasible. TAP adheres to labor regulations, employs human resource capabilities, and aims for a smart assignment of workforce. It complies with restrictions that prevent excessive work, require breaks, and ensure that technicians are assigned tasks that match their skills, thus promoting the well-being of the workforce and the efficiency of operations. The computational investigation of the model shows that it has a remarkable ability to improve scheduling decisions which effectively reduce unassigned positions and uniformly distribute work hours. In essence, this research contributes a methodologically robust framework to the field of workforce scheduling, with the potential to inform the maintenance strategies of offshore wind farms and similar complex service systems.

The assignment problem as a cooperative game

The assignment problem as a cooperative game

Optimization techniques of Assignment Problem using Trapezoidal Intuitionistic Fuzzy Numbers and Interval Arithmetic

This paper discusses the Assignment problem to optimize the assigning of jobs to workers based on their talents and efficiency. In general, scheduling jobs plays a significant role in manufacturing and is advantageous in real world applications as we face more uncertainty and ambiguity in assigning jobs. The Intuitionistic Fuzzy Assignment problem (IFAP) is employed in circumstances when decision-makers have to deal with uncertainty. The domains are Trapezoidal Intuitionistic Fuzzy Numbers (TrIFNs) and the techniques used are Hungarian Method (HM), Brute Force Method (BFM), and Greedy Method (GM). The suggested model's performance is compared with the existing approach with the help of interval arithmetic operations. Allocating work to the individual is illustrated numerically, the optimal solution of minimizing cost is obtained using R programming and the results of comparative analysis are shown diagrammatically that help viewers to easily understand and generate results from comparisons.

Routing and scheduling of trains and engines in a railway marshalling station yard

In a busy railway marshalling station, train and engine traffic management in the receiving/departure yard plays a crucial role in efficient and stable operations. Traditionally, a track assignment problem (TAP) is solved to assign tracks to trains for berthing at a receiving/departure yard. However, the TAP does not encompass shunting operations in the yard (e.g., engine replacement and train disassembly), which can result in additional scheduling challenges for dispatchers and route conflicts between operations. This paper investigates a train and engine routing and scheduling problem (TERSP) in a receiving/departure yard of railway marshalling stations, which involves simultaneously assigning routes and scheduling route-setting start times for both train and shunting operations to be conducted in the yard. By introducing the concepts of task, activity, and pattern, we transform the original problem into assigning pre-generated patterns incorporating both route and route-setting start time alternatives to activities. The transformed problem is formulated into a compact binary integer linear programming model with a linear number of constraints and the objective of minimizing the total time deviation of all involved tasks. An improved technique that relies on listing all maximal (bi)cliques in a constructed graph is designed to effectively model the time coherence and track section occupation constraints. A heuristic that gradually expands the patterns for the identified key activities by adding more start time alternatives is applied to remedy an infeasible model caused by potential route conflicts. In addition, a rolling horizon algorithm that decomposes the original problem into consecutive smaller stages using either a time-rolling or a train-rolling rule is developed to efficiently solve instances. Finally, numerical experiments based on the physical layouts and real timetables of a receiving yard and a departure yard of a large marshalling station in China are conducted to assess the performance and applicability of our proposed approaches. The results demonstrate that our approaches typically find (near-)optimal solutions within several minutes for the investigated instances by simultaneously addressing different classes of yard operations and resources.

FairColor: An efficient algorithm for the Balanced and Fair Reviewer Assignment Problem

As the volume of submitted papers continues to rise, ensuring a fair and accurate assignment of manuscripts to reviewers has become increasingly critical for academic conference organizers. Given the paper-reviewer similarity scores, this study introduces the Balanced and Fair Reviewer Assignment Problem (BFRAP), which aims to maximize the overall similarity score (efficiency) and the minimum paper score (fairness) subject to coverage, load balance, and fairness constraints. Addressing the challenges posed by these constraints, we conduct a theoretical investigation into the threshold conditions for the problem’s feasibility and optimality. To facilitate this investigation, we establish a connection between BFRAP, defined over m reviewers, and the Equitable m-Coloring Problem. Building on this theoretical foundation, we propose FairColor, an algorithm designed to retrieve fair and efficient assignments. We compare FairColor to Fairflow and FairIR, two state-of-the-art algorithms designed to find fair assignments under similar constraints. Empirical experiments were conducted on four real and two synthetic datasets involving (paper, reviewer) matching scores ranging from (100,100) to (10124,5880). Results demonstrate that FairColor is able to find efficient and fair assignments quickly compared to Fairflow and FairIR. Notably, in the largest instance involving 10,124 manuscripts and 5680 reviewers, FairColor retrieves fair and efficient assignments in just 67.64 s. This starkly contrasts both other methods, which require significantly longer computation times (45 min for Fairflow and 3 h 24 min for FairIR), even on more powerful machines. These results underscore FairColor as a promising alternative to current state-of-the-art assignment techniques.

Reactive tabu search and mixed-integer linear programming for multi-day assignment, scheduling, and routing problems of specialised education and home-care services

In this paper, we address the Multi-Day Assignment, Scheduling, and Routing Problem for Specialized Education and Home Care Services (SEHCS-MASRP), which involves heterogeneous employees and missions, posing a complex optimisation challenge. To tackle this, we propose a novel Mixed-Integer Linear Programming (MILP) model that considers employee qualifications, service requirements, scheduling constraints, routing decisions, and multiple objectives across the planning horizon. Additionally, we develop two metaheuristic approaches: a Reactive Tabu Search (RTS) algorithm incorporating either a Probabilistic Greedy Heuristic (PGH) or a Greedy Randomized Adaptive Search Procedure (GRASP) for initial solutions and a tailored genetic algorithm (GA). The three approaches aim to minimise wasted and overtime hours, total travel distances, and the number of assignments with an unsatisfied specialty while balancing wasted hours, overtime hours, and travel distances among the employees. Gurobi uses the proposed MILP model to find the optimal solutions, which are then compared with RTS and GA results across various instance sizes based on real-life SEHCS scenarios. Experimental results demonstrate the efficiency of MILP, RTS, and GA. MILP achieves proven optimal solutions for smaller to large instances. For huge instances, RTS generates high-quality solutions within reasonable computing times, outperforming GA performance. Notably, RTS consistently finds solutions within 5% of optimality for most instances.

Analysis of lithium trade patterns and influencing factors in the regions along the "Belt and Road".

Lithium has broad applications in several emerging industries and fields, including high energy batteries, energy storage, aerospace, and controlled nuclear reactions. Currently, the discrepancy between the supply and demand for lithium resources increases, and its distribution is uneven. Within the framework of the "Belt and Road" Initiative, the lithium trade pattern evolves constantly. However, the trade pattern of lithium in the nations along the "Belt and Road" is likely to face substantial repercussions in modern world of unilateral protectionism and geopolitical conflicts. Taking the social network analysis approach as a tool, this study first examines the characteristics of the lithium trade network structure as it has evolved over the years in the Belt and Road countries, from 2000 to 2022. Additionally, this study uses the quadratic assignment problem approach to analyze the factors influencing the evolution of the lithium trade network. The study shows that: (1) The spatial patterns of import and export trade network of lithium in countries along the route has a certain path dependence. And the market is mainly concentrated in East Asia, Central and Eastern Europe, South America and Southeast Asia. (2) The network density of the countries along the route has increased year after year, but it remains low. And the fluctuation of the network's reciprocity has increased, with a huge magnitude of variation. The number of core countries in the network has decreased over time, but the core-periphery structure has stayed largely steady. China, Chile, and South Korea are the network's main node countries. (3) Regarding the influencing factors, the differences in economic and technological development between these countries have a beneficial impact on the formation of lithium trade; whether or not regional trade agreements have been signed, the differences about average tax rates for mineral products, bordering countries, and similar languages and cultures are all conducive to the establishment of close trade links. The contribution of this essay is of paramount importance for understanding different countries' role along the Belt and Road in the lithium trade network pattern, and promoting regional trade cooperation.

Regularities and Anomalies in Neon Matrix Shifts of Hydrogen-Bonded O-H Stretching Fundamentals.

O-H bond stretching vibrations in hydrogen-bonded complexes embedded into cryogenic neon matrices are subtly downshifted from cold gas phase reference wavenumbers. To the extent that this shift is systematic, it enables neon matrices as more universally applicable spectroscopic benchmark environments for quantum chemical predictions. Outliers are indicative of either an assignment problem in one of the two cryogenic experiments or they reveal interesting dynamics or structural effects on the complexes as a function of the environment. We compile 6 literature-known pairs of experimental data in jet and neon matrix expansions and realize a 6-fold expansion of that number through targeted matrix isolation and/or slit jet expansion spectroscopy presented in this work. In many cases, the neon matrix shift is less than the uncertainty of the currently best-performing blind quantum chemical predictions for the gas phase, but in specific cases, it may exceed the currently achievable theoretical accuracy. Some evidence for a positive correlation of the matrix shift with the hydrogen bond shift is found, similar to observations for helium nanodroplets. Outliers in particular for water acting as a donor are discussed, and in a few cases they call for a future reinvestigation. Substantial improvement in the correlation of the matrix shift with the hydrogen bond shift is achieved for ketone monohydrates by removing a vibrational resonance. New insights into nitrile hydration isomerism are obtained, and the linear OH stretching spectrum of the jet-cooled ammonia-water complex is presented for the first time. Vibrational spectroscopy in weakly perturbing solid rare gas quantum matrices for the benchmarking of gas phase theory and future explicit theoretical treatments of the quantum matrix environment to better understand the outliers are both encouraged.

Dynamic Target Assignment by Unmanned Surface Vehicles Based on Reinforcement Learning

Due to the dynamic complexities of the multi-unmanned vessel target assignment problem at sea, especially when addressing moving targets, traditional optimization algorithms often fail to quickly find an adequate solution. To overcome this, we have developed a multi-agent reinforcement learning algorithm. This approach involves defining a state space, employing preferential experience replay, and integrating self-attention mechanisms, which are applied to a novel offshore unmanned vessel model designed for dynamic target allocation. We have conducted a thorough analysis of strike positions and times, establishing robust mathematical models. Additionally, we designed several experiments to test the effectiveness of the algorithm. The proposed algorithm improves the quality of the solution by at least 30% in larger scale scenarios compared to the genetic algorithm (GA), and the average solution speed is less than 10% of the GA, demonstrating the feasibility of the algorithm in solving the problem.

A Vehicle-to-Grid planning framework incorporating electric vehicle user equilibrium and distribution network flexibility enhancement

The rapid surge in electric vehicle (EV) adoption, coupled with advancements in charging technologies, emphasizes the critical necessity for expanding EV recharging infrastructure. Simultaneously, the Distribution Network (DN) encounters escalating challenges in meeting charging demand during peak traffic periods. Consequently, there is a mounting demand for the deployment of innovative Vehicle-to-Grid (V2G) technologies to augment the DN’s flexibility in power dispatch and alleviate travel costs for EV users. Hence, this paper proposes an EV-user-equilibrium-(UE)-constrained V2G planning framework that enhances flexibility in the DN. The framework aims to ascertain the optimal placement and capacity of EV charging stations (EVCSs) and V2G charging piles within the Transportation Network (TN). It takes into account the equilibrium condition stemming from competitive EV charging and routing behaviors alongside the optimal expansion of DN energy resources to accommodate the electricity supplied by the V2G piles. This study commences by analyzing EV drivers’ travel decisions, considering the influence of charging and V2G pile locations and sizes. Subsequently, we tackle the Traffic Assignment Problem with User Equilibrium (TAP-UE) model to characterize the steady-state traffic flow distribution of EVs. Following this, we formulate the optimization model for the Coordinated Power and Transportation Network (CPTN), which encompasses the optimal expansion of DN facilities and traffic flow regulation under UE conditions. To mitigate the computational complexity associated with the V2G planning model, we introduce a series of linearization methods to obtain a manageable Mixed-Integer Linear Programming (MILP) solution. Finally, to validate the efficacy of our proposed planning framework, we apply it to two test systems, including a real-world case study. Through these case studies, we explore the necessity and potential benefits of V2G technologies.

Efficient routing in robotic movable fulfillment systems with integer programming: A rolling horizon and heuristic approach

This paper addresses an integrated rack assignment and robot routing problem arising in robotic movable fulfillment systems (RMFS). This NP-hard planning task goes beyond current literature by simultaneously optimizing movable rack selection and multi-agent collision-free path finding, rather than decomposing them. A mixed integer programming (MIP) model with a new level-space-time network representation is proposed, jointly considering reusable racks, robot-rack pairings, storage repositioning, and collision avoidance. To improve computational efficiency, a fast rolling horizon heuristic and greedy algorithm are developed. Extensive experiments demonstrate that the integrated method's solutions can improve by 30 % upon conventional decomposed approaches. Intriguing test cases reveal the model, suggesting non-intuitive robot carryover policies that are unfound by separate selection and routing methods. This indicates potential optimization benefits from explicitly coordinating task assignment, scheduling, and routing decisions in complex automated warehousing systems. The rolling horizon heuristic solutions approach optimality with much greater efficiency than directly solving one large MIP, validating its practical value. This research provides useful integrated modeling insights, efficient solution algorithms, and decision support for efficiently controlling next-generation robotic movable fulfillment systems.

On non-superperfection of edge intersection graphs of paths

The routing and spectrum assignment problem in modern flexgrid elastic optical networks asks for assigning to given demands a route in an optical network and a channel within an optical frequency spectrum so that the channels of two demands are disjoint whenever their routes share a link in the optical network. This problem can be modeled in two phases: firstly, a selection of paths in the network and, secondly, an interval coloring problem in the edge intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the weighted clique number is a natural lower bound. Graphs where both parameters coincide for all possible non-negative integral weights are called superperfect. Therefore, the occurrence of non-superperfect edge intersection graphs of routing paths can provoke the need of larger spectral resources. In this work, we examine the question which minimal non-superperfect graphs can occur in the edge intersection graphs of routing paths in different underlying networks: when the network is a path, a tree, a cycle, or a sparse planar graph with small maximum degree. We show that for any possible network (even if it is restricted to a path) the resulting edge intersection graphs are not necessarily superperfect. We close with a discussion of possible consequences and of some lines of future research.

Symmetry-free routing and spectrum assignment: a universal algorithm based on first-fit

First-fit (FF) is a well-known and widely deployed algorithm for spectrum assignment (SA), but until our recent study [J. Opt. Commun. Netw. 14, 165 (2022)JOCNBB1943-062010.1364/JOCN.445492], investigations of the algorithm had been experimental in nature and no formal properties of the algorithm with respect to SA were known. In this work, we make two contributions. First, we show that FF is a universal algorithm for the SA problem in the sense that, for any variant, 1) it can be used to construct solutions equivalent to, or better than, any solution obtained by any other algorithm, and 2) it can construct an optimal solution. This universality property applies to both the min-max and min-frag objectives and to variants of the SA problem with or without guard band constraints. Consequently, the spectrum symmetry-free model of our recent study [J. Opt. Commun. Netw. 14, 165 (2022)JOCNBB1943-062010.1364/JOCN.445492] extends to all known SA variants, which therefore reduce to permutation problems. Second, we extend the spectrum symmetry-free model to the routing and spectrum assignment (RSA) problem in general topologies. This model allows for the design of more efficient algorithms as it eliminates from consideration an exponential number of equivalent symmetric solutions. By sidestepping symmetry, the RSA solution space is naturally and optimally decomposed into a routing space and a connection permutation space. Building upon this property, we introduce a two-parameter, symmetry-free universal algorithm that can be used to tackle any RSA variant in a uniform manner. The algorithm is amenable to multi-threaded execution to speed up the search process, and the value of the parameters can be adjusted to strike a balance between running time and solution quality. Our evaluation provides insight into the relative benefits of path diversity (which determines the size of the routing space) and connection diversity (which determines the size of the permutation space).

Deterministic Impartial Selection with Weights

In the impartial selection problem, a subset of agents up to a fixed size k among a group of n is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is α -optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of α of the votes received by the subset of size k with the highest number of votes. We study deterministic impartial mechanisms in a more general setting with arbitrarily weighted votes and provide the first approximation guarantee, roughly 1/⌈2 n / k ⌉. When the number of agents to select is large enough compared to the total number of agents, this yields an improvement on the previously best known approximation ratio of 1/ k for the unweighted setting. We further show that our mechanism can be adapted to the impartial assignment problem, in which multiple sets of up to k agents are to be selected, with a loss in the approximation ratio of 1/2.