Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

The adaptive approach for storage assignment by mining data of warehouse management system for distribution centres

Abstract: Among distribution centre operations, order picking has been reported to be the most labour-intensive activity. Sophisticated storage assignment policies adopted to reduce the travel distance of order picking have been explored in the literature. Unfortunately, previous research has been devoted to locating entire products from scratch. Instead, this study intends to propose an adaptive approach, a Data Mining-based Storage Assignment approach (DMSA), to find the optimal storage assignment for newly delivered products that need to be put away when there is vacant shelf space in a distribution centre. In the DMSA, a new association index (AIX) is developed to evaluate the fitness between the put away products and the unassigned storage locations by applying association rule mining. With AIX, the storage location assignment problem (SLAP) can be formulated and solved as a binary integer programming. To evaluate the performance of DMSA, a real-world order database of a distribution centre is obtained and used to compare the results from DMSA with a random assignment approach. It turns out that DMSA outperforms random assignment as the number of put away products and the proportion of put away products with high turnover rates increase.

Adaptive and decentralized operator placement for in-network query processing

Abstract: In-network query processing is critical for reducing network traffic when accessing and manipulating sensor data It requires placing a tree of query operators such as filters and aggregations but also correlations onto sensor nodes in order to minimize the amount of data transmitted in the network In this paper, we show that this problem is a variant of the task assignment problem for which polynomial algorithms have been developed These algorithms are however centralized and cannot be used in a sensor network We describe an adaptive and decentralized algorithm that progressively refines the placement of operators by walking through neighbor nodes Simulation results illustrate the potential benefits of our approach They also show that our placement strategy can achieve near optimal placement onto various graph topologies despite the risks of local minima

Evolutionary algorithms and the maximum matching problem

Abstract: Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically well-founded analyses exist. Such an analysis is started in this paper for a fundamental evolutionary algorithm and the well-known maximum matching problem. It is proven that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for this optimization problem, although the algorithm does not employ the idea of augmenting paths. Moreover, for very simple graphs it is proved that the expected optimization time of the algorithm is polynomially bounded and bipartite graphs are constructed where this time grows exponentially.

Stability of the stochastic equilibrium assignment problem: a dynamical systems approach

Abstract: The question of whether plausible dynamical adjustment processes converge to equilibrium was brought to attention by the compelling analysis of Horowitz (1984) . The stability of stochastic equilibrium in a two link transportation network. Transportation Research 18B (1), 13–28. His analysis of discrete time processes, and the question of their convergence to stochastic equilibrium, had the significant restriction of applying only to two-link networks. In spite of a number of significant works on this ‘stability’ issue since, the extension of Horowitz's results to general networks has still not been achieved, and this forms the motivation for the present paper. Previous analyses of traffic assignment stability are first reviewed and classified. The key, and often misunderstood, distinctions are clarified: between stability in discrete time and continuous time, and between stability with respect to deterministic and stochastic processes. It is discussed how analyses since Horowitz's characterise much milder notions of stability. A simple dynamical adjustment process is then proposed for studying the stability of the general asymmetric stochastic equilibrium assignment problem in discrete time. Classical techniques from the dynamical systems literature are then applied in three ways, resulting in: a sufficient condition for stability, applicable to a significant subset of practical problems; a widely-applicable sufficient condition for instability; and a method for estimating domains of attraction for problems with multiple equilibria. The tests are illustrated in relation to a number of simple examples. In principle, they are applicable to networks of an arbitrary size, although further tests would be required to determine the computational feasibility of these techniques in large networks.

An Algorithm for the Quadratic Assignment Problem

Abstract: The paper presents a new approach to solving a class of combinatorial economic allocation problems. One member of this class is known as the quadratic assignment problem. Besides presenting an algorithm to solve this problem, we will discuss in general terms the techniques for treating combinatorial problems. A novel feature of the paper is the development of the statistical properties of the criterion function. These statistical properties are used in conjunction with a general enumerative procedure to form the main parts of the algorithm. Using the idea of confidence level enumeration, an extension of the algorithm is proposed which should allow for the effective treatment of large scale combinatorial problems. Finally we present some computational results in order to illustrate the effectiveness of the general approach.