Reducing Multivalued Discrete Variables in Solving Separable Task Assignment Problems

In this paper, we introduce the separable task assignment problem (STAP) in which n separable tasks are assigned to m agents subject to agents’ capacity constraints. The objective is to minimize the costs that occur during the manufacturing and the communication between agents. A task is separable i...

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Bibliographic Details
Published in:Journal of the Operations Research Society of China (Internet) Vol. 4; no. 1; pp. 97 - 110
Main Authors: Gai, Ling, Jin, Qing-Wei, Tian, Yuan, Huang, Yao-Huei
Format: Journal Article
Language:English
Published: Beijing Operations Research Society of China 01.03.2016
Springer Nature B.V
Subjects:
Algorithms
Assignment problem
Communication
Continuity (mathematics)
Costs
Management Science
Manufacturing
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research
Variables
Task-assignment problem
90C10
90B80
Ternary variables
Binary variables
Mixed integer programming problem
ISSN:2194-668X, 2194-6698
Online Access:Get full text
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Summary:In this paper, we introduce the separable task assignment problem (STAP) in which n separable tasks are assigned to m agents subject to agents’ capacity constraints. The objective is to minimize the costs that occur during the manufacturing and the communication between agents. A task is separable if it can be divided into two pieces, and both of them can be assigned individually or together to any agents. A separable task is considered as being assigned if and only if its two pieces are both assigned. Since several discrete (ternary) variables may be involved in STAP modeling, computing the problem in a reasonable time period is not an easy work. We replace the ternary variables by binary and continuous variables through extending the logarithmic method introduced by Li et al. (INFORMS J Comput 25(4): 643–653, 2012 ) and Vielma et al. (Oper Res 58(2): 303–315, 2010 ). Our numerical experiments demonstrate that the newly generated model performs well in solving difficult separable task-assignment problems for pretty large scale of instance sizes.
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ISSN:2194-668X
2194-6698
DOI:10.1007/s40305-015-0087-x