Showing papers on "Assignment problem published in 2012"

Online task assignment in crowdsourcing markets

Abstract: We explore the problem of assigning heterogeneous tasks to workers with different, unknown skill sets in crowdsourcing markets such as Amazon Mechanical Turk. We first formalize the online task assignment problem, in which a requester has a fixed set of tasks and a budget that specifies how many times he would like each task completed. Workers arrive one at a time (with the same worker potentially arriving multiple times), and must be assigned to a task upon arrival. The goal is to allocate workers to tasks in a way that maximizes the total benefit that the requester obtains from the completed work. Inspired by recent research on the online adwords problem, we present a two-phase exploration-exploitation assignment algorithm and prove that it is competitive with respect to the optimal offline algorithm which has access to the unknown skill levels of each worker. We empirically evaluate this algorithm using data collected on Mechanical Turk and show that it performs better than random assignment or greedy algorithms. To our knowledge, this is the first work to extend the online primal-dual technique used in the online adwords problem to a scenario with unknown parameters, and the first to offer an empirical validation of an online primal-dual algorithm.

Group Role Assignment via a Kuhn–Munkres Algorithm-Based Solution

Abstract: Role assignment is a critical task in role-based collaboration. It has three steps, i.e., agent evaluation, group role assignment, and role transfer, where group role assignment is a time-consuming process. This paper clarifies the group role assignment problem (GRAP), describes a general assignment problem (GAP), converts a GRAP to a GAP, proposes an efficient algorithm based on the Kuhn-Munkres (K-M) algorithm, conducts numerical experiments, and analyzes the solutions' performances. The results show that the proposed algorithm significantly improves the algorithm based on exhaustive search. The major contributions of this paper include formally defining the GRAPs, giving a general efficient solution for them, and expanding the application scope of the K-M algorithm. This paper offers an efficient enough solution based on the K-M algorithm that outperforms significantly the exhaustive search approach.

A Comparison of Greedy and Optimal Assessment of Natural Language Student Input Using Word-to-Word Similarity Metrics

Abstract: We present in this paper a novel, optimal semantic similarity approach based on word-to-word similarity metrics to solve the important task of assessing natural language student input in dialogue-based intelligent tutoring systems. The optimal matching is guaranteed using the sailor assignment problem, also known as the job assignment problem, a well-known combinatorial optimization problem. We compare the optimal matching method with a greedy method as well as with a baseline method on data sets from two intelligent tutoring systems, AutoTutor and iSTART.

Multitarget data association with higher-order motion models

Abstract: We present an iterative approximate solution to the multidimensional assignment problem under general cost functions. The method maintains a feasible solution at every step, and is guaranteed to converge. It is similar to the iterated conditional modes (ICM) algorithm, but applied at each step to a block of variables representing correspondences between two adjacent frames, with the optimal conditional mode being calculated exactly as the solution to a two-frame linear assignment problem. Experiments with ground-truthed trajectory data show that the method outperforms both network-flow data association and greedy recursive filtering using a constant velocity motion model.

Inverse optimization with endogenous arrival time constraints to calibrate the household activity pattern problem

Abstract: A parameter estimation method is proposed for calibrating the household activity pattern problem so that it can be used as a disaggregate, activity-based analog of the traffic assignment problem for activity-based travel forecasting. Inverse optimization is proposed for estimating parameters of the household activity pattern problem such that the observed behavior is optimal, the patterns can be replicated, and the distribution of the parameters is consistent. In order to fit the model to both the sequencing of activities and the arrival times to those activities, an inverse problem is formulated as a mixed integer linear programming problem such that coefficients of the objectives are jointly estimated along with the goal arrival times to the activities. The formulation is designed to be structurally similar to the equivalent problems defined by Ahuja and Orlin and can be solved exactly with a cutting plane algorithm. The concept of a unique invariant common prior is used to regularize the estimation method, and proven to converge using the Method of Successive Averages. The inverse model is tested on sample households from the 2001 California Household Travel Survey and results indicate a significant improvement over the standard inverse problem in the literature as well as baseline prescriptive models that do not make use of sample data for calibration. Although, not unexpectedly, the estimated optimization model by itself is a relatively poor forecasting model, it may be used in determining responses of a population to spatio-temporal scenarios where revealed preference data is absent.

Santa Claus Schedules Jobs On Unrelated Machines

Abstract: One of the classic results in scheduling theory is the $2$-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines; ie, job $j$ requires time $p_{ij}$ if processed on machine $i$ More than two decades after its introduction it is still the algorithm of choice even in the restricted model where processing times are of the form $p_{ij} \in \{p_j, \infty\}$ This problem, also known as the restricted assignment problem, is NP-hard to approximate within a factor less than $15$, which is also the best known lower bound for the general version Our main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor $33/17 + \epsilon \approx 19412 + \epsilon$, where $\epsilon > 0$ is an arbitrarily small constant The result is obtained by upper bounding the integrality gap of a certain strong linear program, known as the configuration LP, that was previously successfu

Path-Constrained Traffic Assignment

Abstract: This paper presents a mathematical programming model and solution method for the path-constrained traffic assignment problem, in which route choices simultaneously follow the Wardropian equilibrium principle and yield the distance constraint imposed on the path. This problem is motivated by the need for modeling distance-restrained electric vehicles in congested networks, but the resulting model and solution method can be applied to various conditions with similar path-based constraints. The equilibrium conditions of the problem reveal that any path cost in the network is the sum of corresponding link costs and a path-specific out-of-range penalty term. The suggested method, based on the classic Frank-Wolfe algorithm, incorporates an efficient constrained shortest-path algorithm as its subroutine. This algorithm fully exploits the underlying network structure of the problem and is relatively easy to implement. Numerical results from the examples of problems provided show how the equilibrium conditions are...

Stochastic optimization models for the airport gate assignment problem

Abstract: Uncertainties inherent in the airport traffic may lead to the unavailability of gates for accommodating scheduled flights. Incorporating random disruptions is crucial in constructing effective flight-gate assignments. We consider the gate assignment problem under uncertainty in flight arrival and departure times and develop stochastic programming models incorporating robustness measures based on the number of conflicting flights, idle and buffer times. The proposed models are formulated as large-scale mixed-integer programming problems and tabu search algorithms are implemented to obtain assignments of reasonable quality. We conduct a computational study to analyze the proposed alternate models and show the effectiveness of the solution methods.

Branch-and-price global optimization for multi-view multi-target tracking

Abstract: We present a new algorithm to jointly track multiple objects in multi-view images While this has been typically addressed separately in the past, we tackle the problem as a single global optimization We formulate this assignment problem as a min-cost problem by defining a graph structure that captures both temporal correlations between objects as well as spatial correlations enforced by the configuration of the cameras This leads to a complex combinatorial optimization problem that we solve using Dantzig-Wolfe decomposition and branching Our formulation allows us to solve the problem of reconstruction and tracking in a single step by taking all available evidence into account In several experiments on multiple people tracking and 3D human pose tracking, we show our method outperforms state-of-the-art approaches

The use of meta-heuristics for airport gate assignment

Abstract: Improper assignment of gates may result in flight delays, inefficient use of the resource, customer's dissatisfaction. A typical metropolitan airport handles hundreds of flights a day. Solving the gate assignment problem (GAP) to optimality is often impractical. Meta-heuristics have recently been proposed to generate good solutions within a reasonable timeframe. In this work, we attempt to assess the performance of three meta-heuristics, namely, genetic algorithm (GA), tabu search (TS), simulated annealing (SA) and a hybrid approach based on SA and TS. Flight data from Incheon International Airport are collected to carry out the computational comparison. Although the literature has documented these algorithms, this work may be a first attempt to evaluate their performance using a set of realistic flight data.

Goal assignment using distance cost in multi-robot exploration

Abstract: In this paper, we discuss the problem of goal assignment in the multi-robot exploration task. The presented work is focused on the underlying optimal assignment problem of the multi-robot task allocation that is addressed by three state-of-the art approaches. In addition, we propose a novel exploration strategy considering allocation of all current goals (not only immediate goal) for each robot, which leads to the multiple traveling salesman problem formulation. Although the problem is strongly NP-hard, we show its approximate solution is computationally feasible and its overall requirements are competitive to the previous approaches. The proposed approach and three well-known approaches are compared in series of problems considering various numbers of robots and sensor ranges. Based on the evaluation of the results the proposed exploration strategy provides shorter exploration times than the former approaches.

A cost assignment policy for home care patients

Abstract: The patient assignment problem in Home care (HC) consists of allocating each newly admitted patient to his/her reference operator, chosen among a set of possible operators. The continuity of care, where pursued, imposes that the assignment is not changed for a long period. The main goal of the assignment is to balance the workload among the operators. In the literature, the problem is usually solved with numerical approaches based on mathematical programming that do not consider the stochastic aspects of the problem. We derive a structural policy to assign a newly admitted patient while balancing the workload among the operators, by minimizing the expected value of a cost function that penalizes the overtime of operators. The workloads already loaded to the operators are assumed to be random variables as they are in the practice, while the demand related to the new patient is considered both deterministic and stochastic. Results show that the variability of the new patient’s demand is negligible with respect to the variability of the already assigned workloads and that similar assignments are obtained both in the presence or in the absence of this demand variability. A numerical comparison with the current practice of assigning the new patient to the operator with the highest expected available capacity shows that better balancings and cost savings can be reached by implementing the proposed policy.

Storage location assignment and order picking optimization in the automotive industry

Abstract: The objective of this study is to design storage assignment and order picking system using a developed mathematical model and stochastic evolutionary optimization approach in the automotive industry. It is performed in two stages. At the first stage, storage location assignment problem is solved with a class-based storage policy with the aim of minimizing warehouse transmissions by using integer programming. At the second stage, batching and routing problems are considered together to minimize travel cost in warehouse operations. A warehouse in the automotive industry is analyzed, and an optimum solution is obtained from an integer programming model. Due to the computational time required for solving the integer programming problem, a faster genetic algorithm is also developed to form optimal batches and optimal routes for the order picker. The main advantage of the algorithm is the quick response to production orders in real-time applications. The solutions showed that the proposed approach based on genetic algorithms can be applied and integrated to any kind of warehouse layout in automotive industry.

A stochastic neighborhood search approach for airport gate assignment problem

Abstract: An appropriate and efficient gate assignment is of great importance in airports since it plays a major role in the revenue obtained from the airport operations. In this study, we have focused mainly on maximum gate employment, or in other words minimize the total duration of un-gated flights. Here, we propose a method that combines the benefits of heuristic approaches with some stochastic approach instead of using a purely probabilistic approach to top-down solution of the problem. The heuristic approaches are usually used in order to provide a fast solution of the problem and later stochastic searches are used in order to ameliorate the previous results of the heuristic approach whenever possible. The proposed method generates an assignment order for the whole planes that corresponds to assignment priority. The ordering process is followed by the allocation step. Since, in practice, each airport has its own physical architecture, there have been arisen many constraints mainly concerning airplane types and parking lots in this step. Sequentially handling the plane ordering and allocation phases provides us great modularity in handling the constraints. The effectiveness of the proposed methodology has been tried to be illustrated firstly on fictively generated flight schedule data and secondly on the real world data obtained from a real world application developed for Istanbul Ataturk Airport.

A hierarchical procedure for storage allocation and assignment within an order-picking system. A case study

Abstract: Advanced approaches to improve order-picking efficiency can significantly reduce customer response time in a supply chain system, decrease the overall logistic costs, and improve the customer service level. This paper focuses on storage allocation to properly define the right inventory level for each stock-keeping unit (SKU) and on the storage assignment problem to properly locate the SKU to the most convenient positions. The aim of this paper is to present a systematic hierarchical top-down procedure that allows the combining of sequential decision steps concerned with allocation and assignment issues. The proposed procedure is applied to a case study, and the results obtained from a what-if analysis are presented.

Models and algorithms for shuffling problems in steel plants

Abstract: In this article, we study item shuffling (IS) problems arising in the logistics system of steel production. An IS problem here is to optimize shuffling operations needed in retrieving a sequence of steel items from a warehouse served by a crane. There are two types of such problems, plate shuffling problems (PSP) and coil shuffling problems (CSP), considering the item shapes. The PSP is modeled as a container storage location assignment problem. For CSP, a novel linear integer programming model is formulated considering the practical stacking and shuffling features. Several valid inequalities are constructed to accelerate the solving of the models. Some properties of optimal solutions of PSP and CSP are also derived. Because of the strong NP-hardness of the problems, we consider some special cases of them and propose polynomial time algorithms to obtain optimal solutions for these cases. A greedy heuristic is proposed to solve the general problems and its worst-case performances on both PSP and CSP are analyzed. A tabu search (TS) method with a tabu list of variable length is proposed to further improve the heuristic solutions. Without considering the crane traveling distance, we then construct a rolling variable horizon heuristic for the problems. Numerical experiments show that the proposed heuristic algorithms and the TS method are effective. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Assignment problem in content distribution networks: Unsplittable hard-capacitated facility location

Abstract: In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to minimize the total cost of these assignments—cost of each is proportional to the distance between the client and the server as well as the request size—while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hard-capacitated facility location problem. As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NP-hard to approximate the cost to within any bounded factor in this case. Thus, for an arbitrary constant e>0, we relax the capacities to a 1+e factor. For the case where capacities are almost uniform, we give a bicriteria O(log n, 1+e)-approximation algorithm for general metrics and a (1+e, 1+e)-approximation algorithm for tree metrics. A bicriteria (α,β)-approximation algorithm produces a solution of cost at most α times the optimum, while violating the capacities by no more than a β factor. We can get the same guarantees for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation.It is worth noting that our results generalize bin packing (zero connection costs and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all connection costs being zero), and some facility location problems.

A Note on Bar-Gera's Algorithm for the Origin-Based Traffic Assignment Problem

Abstract: Recently, Bar-Gera (Bar-Gera, H. 2002. Origin-based algorithm for the traffic assignment problem. Transportation Sci.36(4) 398--417) proposed a quasi-Newton method for the origin-based formulation of the user equilibrium traffic assignment problem. This note shows that Bar-Gera's algorithm may generate negative second-order derivative, leading to a “wrong search direction,” which compromises the overall convergence performance. We prove that this shortcoming can be overcome by approximating the second-order derivative with an upper bound. The revised algorithm not only fixes a theoretical flaw but indeed demonstrates more satisfying computational performance in numerical experiments. This note also offers a rigorous derivation of optimality conditions that synthesizes the results of the literature.

Improved Approximation Algorithms for Bipartite Correlation Clustering

Abstract: In this work we study the problem of bipartite correlation clustering (BCC), a natural bipartite counterpart of the well-studied correlation clustering (CC) problem [N. Bansal, A. Blum, and S. Chawla, Machine Learning, 56 (2004), pp. 89--113], also referred to as graph editing [R. Shamir, R. Sharan, and D. Tsur, Discrete Appl. Math., 144 (2004), pp. 173--182]. Given a bipartite graph, the objective of BCC is to generate a set of vertex disjoint bicliques (clusters) that minimizes the symmetric difference to the original graph. The best-known approximation algorithm for BCC due to Amit [N. Amit, The Bicluster Graph Editing Problem, Master's Thesis, Tel Aviv University, Tel Aviv, Israel, 2004] guarantees an $11$-approximation ratio. In this paper we present two algorithms. The first is a linear program based $4$-approximation algorithm. Like the previous approximation algorithm, it requires solving a large convex problem, which becomes prohibitive even for modestly sized tasks. The second algorithm, and our...

Finding a robust assignment of flights to gates at Amsterdam Airport Schiphol

Abstract: In this paper we investigate the gate assignment problem as it appears at Amsterdam Airport Schiphol (AAS). Currently, the gate planners spend many hours on adjusting the automatically generated planning during the day of operation to make it proof against small deviations from the schedule. To alleviate this problem, we aim at finding a robust solution, given the planned arrivals and departures for the next day. We present a completely new integer linear programming formulation that is based on so-called gate plans. Each gate plan consists of a subset of the flights that can be assigned to a single gate of the corresponding type; gates with identical characteristics are aggregated in gate types. The gate assignment problem then boils down to selecting the best subset of gate plans such that each flight belongs to one selected gate plan, and such that the number of selected gate plans for a certain type of gate is equal to the number of gates of this type. In the first phase, we solve the LP-relaxation through column generation, and we describe specific features to find a very good solution to the ILP quickly. This solution is then handed to the planners at AAS in order to assign gate plans to physical gates. This consists of a number of relatively small problems that can be solved by hand and in which additional operational constraints can be incorporated. We also present the possibility of directly assigning flights to physical gates using the column generation formulation, where we then take into account other criteria as well. Computational results with real-life data provided by AAS are promising and indicate that the algorithm is able to solve real-life instances within rather small running times.