Search

This paper proposes an uncertain random assignment problem in which random variables coexist with uncertain variables. Critical values of uncertain random variables are used to rank uncertain random variables. An uncertain random simulation algorithm is developed in order to obtain chance distributions and critical values of uncertain random variables. An α -optimistic model is presented. A combined optimization approach is designed to solve the α -optimistic model. This approach incorporates uncertain random simulation into branch and bound algorithm. Finally, an example application of the approach is presented. [ABSTRACT FROM AUTHOR]

This paper discusses a priority based assignment problem related to an industrial project consisting of a total of n jobs. Depending upon its work breakdown structure, the execution of the project is carried out in two stages where the m primary jobs are performed first, in Stage-I whereas the ( n − m ) secondary jobs are performed later in Stage-II (as the secondary jobs cannot be performed until the primary jobs are finished). A number of manufacturing units exactly equal to n , each of them capable of performing all the n jobs involved in the project, are available. A tentative job-performance time taken by each of these manufacturing units for each of the n jobs is available. The purpose of the current study is to assign the jobs to the manufacturing units in such a way that the two-stage execution of the project can be carried out in the minimum possible time. For this, a polynomial time iterative algorithm is proposed, which at each iteration, aims at selecting m manufacturing units to perform primary jobs corresponding to which, the remaining ( n − m ) manufacturing units perform the secondary jobs optimally and from this selection, a pair of times of Stage-I and Stage-II is obtained. The proposed algorithm is such that at each iteration, time of Stage-I decreases strictly and time of Stage-II increases. Out of the pairs so generated, the one with minimum sum of Stage-I and Stage-II times is considered as optimum and the corresponding assignment as the optimal assignment. A numerical illustration is given in the support of the theory. Also, the proposed algorithm is implemented and tested on a variety of test problems and the average run time for each problem is calculated. [ABSTRACT FROM AUTHOR]

Abstract: In view of the simplex-type algorithm, the assignment problem is inherently highly degenerate. It may be the optimal basis has changed, but the optimal assignment is unchanged when parameter variation occurs. Degeneracy then makes sensitivity analysis difficult, as well as makes the classical Type I range, which identifies the range the optimal basis unchanged, impractical. In this paper, a labeling algorithm is proposed to identify two other sensitivity ranges – Type II range and Type III range. The algorithm uses the reduced cost matrix, provided in the final results of most solution algorithms for AP, to determine the Type II range which reflects the stability of the current optimal assignment. Thus, the algorithm generates a streamlined situation from searching the optimal solution until performing the sensitivity analysis of the assignment problem. The Type III range, reflecting the flexibility of optimal decision making, can be obtained immediately after the Type II range is determined. Numerical examples are presented to demonstrate the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, the equilibrium optimization problem is proposed and the assignment problem is extended to the equilibrium multi-job assignment problem, equilibrium multi-job quadratic assignment problem and the minimum cost and equilibrium multi-job assignment problem. Furthermore, the mathematical models of the equilibrium multi-job assignment problem and the equilibrium multi-job quadratic assignment problem with fuzzy parameters are formulated. Finally, a genetic algorithm is designed for solving the proposed programming models and some numerical examples are given to verify the efficiency of the designed algorithm. [Copyright &y& Elsevier]

Abstract: This note shows that the data envelopment analysis (DEA) models formulated by Chen and Lu [L.H. Chen, H.W. Lu, An extended assignment problem considering multiple inputs and outputs, Appl. Math. Modell. 31 (2007) 2239–2248] are not correct. The enveloping form of the Chen and Lu formulation is studied and a simple example is presented to demonstrate the differences between the efficiency scores resulted of the Chen and Lu formulation, and the true ones. [Copyright &y& Elsevier]

Abstract: The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit incurred by each possible assignment. However, in real applications, various inputs and outputs are usually concerned in an assignment problem, such as a general decision-making problem. This paper develops a procedure for resolving assignment problems with multiple incommensurate inputs and outputs for each possible assignment. The concept of the relative efficiency in using various resources, instead of cost or profit, is adopted for each possible assignment of the problem. Data envelopment analysis (DEA) is employed in this paper to measure the efficiency of one assignment relative to that of the others according to a set of decision-making units. A composite efficiency index, consisting of two kinds of relative efficiencies under different comparison bases, is defined to serve as the performance measurement of each possible assignment in the problem formulation. A mathematical programming model for the extended assignment problem is proposed, which is then expressed as a classical integer linear programming model to determine the assignments with the maximum efficiency. A numerical example is used to demonstrate the approach. [Copyright &y& Elsevier]