The Analysis of Solution Efficiency under Different Constraint Tightness for GAP
碩士 === 國立臺北科技大學 === 商業自動化與管理研究所 === 97 === In the real world, many decision-making problems are related to the Generalized Assignment Problem（GAP）. GAP is a combinatorial problem that belongs to NP-hard. In addition to problem scale, constraint tightness is also a significant factor that affects pro...
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| Format: | Others |
| Language: | zh-TW |
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2009
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| Online Access: | http://ndltd.ncl.edu.tw/handle/835874 |
| Summary: | 碩士 === 國立臺北科技大學 === 商業自動化與管理研究所 === 97 === In the real world, many decision-making problems are related to the Generalized Assignment Problem（GAP）. GAP is a combinatorial problem that belongs to NP-hard. In addition to problem scale, constraint tightness is also a significant factor that affects problem complexity.
This research constructs GAP model for a large project where there are some critical jobs to be executed. These jobs are to be assigned to the available agents to complete with minimum cost objectivity.
In the experimental evaluation analysis, this research designs five ranges with different proportion between lower and upper limits. A total of 17 different tightness levels ranging from 30% to 70% are designed at each range to generate 10 instances (A total of 850 test problem are generated).These test problems are solved using LINGO software by recording the number of iterations needed during the branch and bound procedure before reaching the optimal solution.
The results of this computational experiment reveal the followings.
（1）It needs less iterations to find global optimum when tightness close to 50%.
（2）With the increase of large proportion range, more solution efficiency is needed when the tightness is in between medium to tight or the tightness is too loose. Second order polynomial regression model can be used to predict the relationship between constraint tightness and solution efficiency.
（3）With the decrease of proportion range, solution efficiency becomes less significant under various tightness.
The findings of this research can provide adequate suggestions to business and research field.
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