Body: <p>I am working on an assignment problem. </p>
  
  <p>Consider <span class="math-container">$K$</span> agents <span class="math-container">$A_1, \dots A_K$</span> and <span class="math-container">$N$</span> tasks <span class="math-container">$T_1, \dots T_N$</span>. Each task has a certain time <span class="math-container">$t(T_i)$</span> to be completed and each agent has a matching (or affinity) value associated with each task <span class="math-container">$M_{A_j}(T_i), \forall i, j$</span>. The goal is to assign agents to tasks, such that the matching value is maximized and the overall time to complete the tasks is minimized. Moreover, an agent can be assigned to multiple tasks. However, an agent cannot start a new task before finishing the previous one.I want to solve it with GA+MOA*algorithm What would be an admissible heuristic function?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-14T02:59:09.677Z
Comments.Text: See also [https://en.wikipedia.org/wiki/Interval_scheduling](https://en.wikipedia.org/wiki/Interval_scheduling), but this is not exactly your problem too, I am afraid.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-11-14T06:11:50.023Z
Comments.Text: No this not same with my problem,tasks in interval have fixed execution start and finish time
Comments.UserDisplayName: Tariq Kavish Arain
Tags: <ai-design><optimization><a-star><constraint-satisfaction-problems>
Title: How can I assign agents to tasks based on time and affinity?
UserDisplayName: Tariq Kavish Arain
ThreadText: # How can I assign agents to tasks based on time and affinity?
  
  (Asked by: username_0 on 2019-11-14)
  
  I am working on an assignment problem.
  
  Consider $K$ agents $A\_1, \dots A\_K$ and $N$ tasks $T\_1, \dots T\_N$. Each task has a certain time $t(T\_i)$ to be completed and each agent has a matching (or affinity) value associated with each task $M\_{A\_j}(T\_i), \forall i, j$. The goal is to assign agents to tasks, such that the matching value is maximized and the overall time to complete the tasks is minimized. Moreover, an agent can be assigned to multiple tasks. However, an agent cannot start a new task before finishing the previous one.I want to solve it with GA+MOA\*algorithm What would be an admissible heuristic function?
  
  **Tags:** ai-design, optimization, a-star, constraint-satisfaction-problems
  
  > **Comments:**
  > **username_1**: See also [https://en.wikipedia.org/wiki/Interval_scheduling](https://en.wikipedia.org/wiki/Interval_scheduling), but this is not exactly your problem too, I am afraid.  
  > **username_0**: No this not same with my problem,tasks in interval have fixed execution start and finish time  
  
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  ## 0 answers
  
  