如何优化具有这些约束的任务分配给座席？ [英] How to optimize assignment of tasks to agents with these constraints?

问题描述

我的硕士论文中有一个作业问题，我正在寻找解决这个问题的一般方向。

I have an assignment problem as a part of my Master's Thesis, and I am looking for general direction in solving the same.

因此，这里有一个清单代理，以及任务列表，任务数量大于代理数量。

So, there is a list of agents, and a list of tasks, with number of tasks being greater than the number of agents.

代理提交他们可以/想要执行的任务的优先顺序列表。 。列表的长度固定为比任务总数小得多的数量。

The agents submit a prioritized ordered list of tasks they can/want to do. The length of the list is fixed to a number much smaller than the total number of tasks.

必须为每个座席分配一个任务。一旦分配了任务，则无法将其分配给其他座席。

Every agent must be assigned a task. A task once assigned cannot be assigned to another agent.

目标是找到一个分配，以使分配的任务的平均优先级/优先级最低。此外，如果这是一个完整的解决方案，即为每个座席分配一个任务，那就更好了。

The objective is to find an assignment such that the average priority/preference of the assigned tasks is the lowest. Additionally, if it is complete solution i.e. every agent is assigned a task, it is even better.

我研究了广义分配问题和匈牙利算法，但是这些不能满足特定情况的需要，在某些情况下一项任务会增加成本，而且代理人也无法执行某些任务。

I have looked at the generalized assignment problems, and the Hungarian algorithm, but these do not cater to the specific situation where there is a cost to a task and also the possibility of the agent being unable to do some of the tasks.

请帮助。谢谢。

推荐答案

如果需要通用方法，则可以将问题建模为混合整数程序，为程序引入二进制变量。将任务分配给代理，并将优先级成本和（非常高的）非分配成本纳入目标功能。混合整数程序可以使用各种求解程序来求解，包括CPLEX或Gurobi，这些程序免费用于学术目的。

If you want a general approach, you can model the problem as Mixed Integer Program, introducing binary variables for the assignment of tasks to agents and putting the priority costs and (very high) non-assignment costs into the objective function. Mixed Integer Programs can be solved using a variety of solver programs, including CPLEX or Gurobi which are free for academic purposes.

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