Two-stage time minimizing assignment problem |
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Authors: | Sonia MC Puri |
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Institution: | 1. Decision Sciences Group, Indian Institute of Management, Off Sitapur Road, Lucknow 226013, India;2. Department of Mathematics, Indian Institute of Technology, New Delhi 110016, India |
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Abstract: | This paper deals with the optimal selection of m out of n facilities to first perform m given primary jobs in Stage-I followed by the remaining (n-m) facilities performing optimally the (n-m) secondary jobs in Stage-II. It is assumed that in both the stages facilities perform in parallel. The aim of the proposed study is to find that set of m facilities performing the primary jobs in Stage-I for which the sum of the overall completion times of jobs in Stage-I and the corresponding optimal completion time of the secondary jobs in Stage-II by the remaining (n-m) facilities is the minimum. The developed solution methodology involves solving the standard time minimizing and cost minimizing assignment problems alternately after forbidding some facility-job pairings and suggests a polynomially bound algorithm. This proposed algorithm has been implemented and tested on a variety of test problems and its performance is found to be quite satisfactory. |
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Keywords: | Combinatorial analysis Mathematical programming Non-linear programming Allocation |
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