On very large scale assignment problems

"May 1993."Includes bibliographical references (p. 24-25).Yusin Lee [and] James B. Orlin

QuickMatch--a very fast algorithm for the assignment problem

Includes bibliographical references (p. 25-27).James B. Orlin, Yusin Lee

A new solution approach for assignment problem

Bu çalışmanın amacı klasik atama problemi için özgün bir çözüm yöntemini tanıtmaktır. Atama probleminin çözümünde en çok bilinen yöntem  Macar yöntemidir. Bu yöntemde maliyet  matrisi her seferinde sistematik bir şekilde yeni bir indirgenmiş matrise dönüştürülerek çözüme gidilmektedir. Yöntem gereği indirgenmiş maliyet matrisindeki sıfır elemanlar en az sayıda çizgi ile kapatılmakta ve buna göre matris üzerinde işlem yapılmaktadır. Ancak problemin büyüklüğü arttıkça ve indirgenmiş maliyet matrisinde sıfır eleman sayısı çoğaldıkça, matristeki sıfır elemanlarını kapatmak üzere gereken en az sayıda çizgi sayısı ve bu çizgilerin nasıl çizilmesi gerektiği sorunu ortaya çıkar. Bu çalışmada Macar yöntemindeki bu boşluğu doldurmak üzere özgün bir yöntem tanıtılmaktadır.Anahtar Kelimeler: Atama problemi, Macar yöntemi.The purpose of this study is to present a new solution approach  for the assignment problem. In assignment problem, there are (m) individuals are to be assigned to (m) jobs. If the individual (i) assigned to job (j), the cost incurred will be (cij), and accordingly the cost matrix is denoted by C. It is desired to find the minimal cost assignment or a one-to-one matching of individuals to jobs. There are many solution methods for this problem, but the simplicity and robutsness of the Hungarian method makes it the best known method among all others. The Hungarian method solves the problem by converting the cost matrix into a reduced matrix systematically at each iteration. A part of this process is finding fewest number of lines to cover all zero elements in the reduced matrix. When the size of the problem increases and reduced matrix contains many zeros, it is a tedious task to find minimum number of lines and the way of drawing them. The Hungarian method has an ambiguity at this point. A solution method is presented in this study to eliminate this ambiguity. A systematic and simple procedure is defined to find the fewest number of lines to cover all zero elements in the reduced matrix. Keywords: Assignment problem, Hungarian method

On Solving Bi-objective Interval Valued Neutrosophic Assignment Problem

The assignment problem (AP) is a well-researched combinatorial optimization problem in which the overall assignment cost or time is minimized by assigning multiple items (tasks) to several entities (workers). Today's optimization challenges cannot be adequately addressed by a single-objective AP, hence the bi-objective AP (BOAP) is taken into consideration. This problem frequently occurs in practical applications with ambiguous parameters in real life. Henceforth, in this article the uncertain parameters are presented as interval valued neutrosophic numbers. In the present study, we formulate bi-objectives assignment problem (BOAP) having cost and time parameters as an interval valued neutrosophic numbers. We proposed interactive left-width method to solve the interval valued neutrosophic BOAP (IVNBOAP). In this method interval valued neutrosophic numbers is reduced to interval numbers using score function. Then, the bi-objective interval assignment problem (BOIAP) is reduced to a deterministic BOAP using the left-width attributes on each objective function. The reduced deterministic objective function is separated and constructed as a multi-objective AP. In the solution procedure, the global weighted sum method is adopted to convert the multi-objective AP into a single objective problem (SOP) and solved using Lingo 18.0 software. Finally, numerical examples are illustrated to clarify the steps involved in the proposed method and results are compared with the other existing methods