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.

Finite spectrum assignment problem of systems with multiple commensurate delays in states and control

Abstract: This paper presents a necessary and sufficient condition for finite spectrum assignability of systems with multiple commensurate delays in both states and control. A systematic design procedure of the control law is presented. The important point of the proposed method is that finite spectrum assignment can be accomplished without any extra integrators, in contrast to the suggestion given by Manitius and Olbrot (1979).

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.

Scheduling identical jobs on uniform parallel machines

Abstract: textWe address the problem of scheduling n identical jobs on m uniform parallel machines to optimize scheduling criteria that are nondecreasing in the job completion times. It is well known that this can be formulated as a linear assignment problem, and subsequently solved in O(n3) time. We give a more concise formulation for minsum criteria, and show that general minmax criteria can be minimized in O(n2) time. We present faster algorithms, requiring only O(n+mlog m) time for minimizing makespan and total completion time, O(nlogn) time for minimizing total weighted completion time, maximum lateness, total tardiness and the weighted number of tardy jobs, and O(nlog2n) time for maximum weighted tardiness. In the case of release dates, we propose an O(nlogn) algorithm for minimizing makespan, and an O(mn2m+1) time dynamic programming algorithm for minimizing total completion time.

Almost-optimum speed-ups of algorithms for bipartite matching and related problems

Abstract: We present algorithms for matching and related problems that run on an EREW PRAM with p processors. Given is a bipartite graph G with n vertices, m edges, and integral edge costs at most N in magnitude. We give an algorithm for the assignment problem (minimum cost perfect bipartite matching) that runs in O(√nm log (nN)(log(2p))/p) time and O(m) space, for p ≤ m/(√nlog2n). For p = 1 this improves the best known sequential algorithm, and is within a factor of log (nN) of the best known bound for the problem without costs (maximum cardinality matching). For p > 1 the time is within a factor of log p of optimum speed-up. Extensions include an algorithm for maximum cardinality bipartite matching with slightly better processor bounds, and similar results for bipartite degree-constrained subgraph problems (with and without costs). Our ideas also extend to general graph matching problems.

Analytical models of the dynamic traffic assignment problem

Abstract: A review of analytical formulations of the dynamic traffic assignment problem is presented, focusing on the authors' experience with variational inequality approaches. Solution algorithms and computational issues requiring additional study are discussed.