### Browsing by Author "Nagi, Rakesh"

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Item Gradient Estimation for Queues with Non-identical Servers(1993) Fu, Michael C.; Hu, Jian-Qiang; Nagi, Rakesh; ISRWe consider a single-queue system with multiple servers that are non-identical. Our interest is in applying the technique of perturbation analysis to estimate derivatives of mean steady- state system time. Because infinitesimal perturbation analysis yields biased estimates for this problem, we apply smoothed perturbation analysis to get unbiased estimators. In the most general cases, the estimators require additional simulation, so we propose an approximation to eliminate this. For two servers, we give an analytical proof of unbiasedness in steady state for the Markovian case. We provide simulation results for both Markovian and non-Markovian examples, and compare the performance with regenerative likelihood ratio estimators.Item Manufacturing Cell Formation by State-Space Search(1993) Ghosh, Subrata; Mahanti, Ambuj; Nagi, Rakesh; Nau, Dana; ISRThis paper addresses the problem of grouping machines in order to design cellular manufacturing cells, with an objective to minimize intercell flow. This problem is replaced to one of the major aims of group technology (GT): to decompose the manufacturing system into manufacturing cells that are as independent as possible.This problem is NP-hard. Thus, nonheuristic methods cannot address problems of typical industrial dimensions because they would require exorbitant amounts of computing time, while fast heuristic methods may suffer from sub-optimality.

We present a branch-and-bound state-space search algorithm that attempts to overcome both these deficiencies. One of the major strengths of this algorithm is its efficient branching and search strategy. In addition, the algorithm employs the efficient Inter-Cell Traffic Minimization Method to provide good upper bounds, and computes lower bounds based on a relaxation of merging.

Item Performance Evaluation of a Hierarchical Production Scheduling Policy for a Single Machine with Earliness and Tardiness(1990) Nagi, Rakesh; Harhalakis, George; Proth, Jean-Marie; ISRThis paper considers the problem of scheduling a given set of jobs on a single machine in order to minimize the total earliness and tardiness costs. The scheduling horizon is divided into elementary periods; jobs have due-dates at the end of these periods. All jobs are assumed initially available. Jobs have unique (weighted) early and tardy penalty functions that are staircase-type. No preemption of jobs is permitted, and idle time may be inserted. This problem is NP-complete. A branch- and-bound scheme that solves the above mentioned problem optimally is presented. We then propose a hierarchical scheduling policy under the assumption that tardiness costs are much greater than earliness costs for all jobs. We also assume that the system if able to meet the production requirements on the average and the scheduling horizon is long enough to absorb cyclicity. The hierarchy is composed of two levels: (i) the high level, and (ii) the low level. The concept of rolling horizon is employed at the high level, which solves the flow control under constraints of no tardiness. The low level, prioritizes jobs resulting from the solution of the high level over a short term horizon. Numerical results relating to the comparison of the performance of this hierarchical policy with the branch-and-bound scheme are presented.