In an organization, A 1 prefers three (3) tasks T 3 , T 2 , and T 1 in order of
ID: 347889 • Letter: I
Question
In an organization, A1 prefers three (3) tasks T3, T2, and T1 in order of preference. A2 prefers the three (3) tasks as follows T2, T3, and T1. A3 prefers the three (3) tasks as follows T2, T3, and T1, the same as A2. The owner P has assessed the competency of each agent to do each task in order of ability as follows. For T1, the best agents in order are A1, A2, and A3. For T2, the best agents in order are A1, A2, and A3, the same as T1. For T3, the best agents in order are A2, A1, and A3. Each Agent can only do one task.
(a) How could P match each agent to each task optimally?
(b) Why can this algorithm be said to be efficient as well as satisfying the total value maximization principle?
(c) What happens if A2 misrepresents its preferences as T2, T1, and T3, instead of T2, T3, and T1?
Explanation / Answer
Agent
Task Preference 1
Task Preference 2
Task Preference 3
A1
T3
T2
T1
A2
T2
T3
T1
A3
T2
T3
T1
Task
Agent Preference 1
Agent Preference 2
Agent Preference 3
T1
A1
A2
A3
T2
A1
A2
A3
T3
A2
A1
A3
As P had assessed the competency of each agent for each task, this will be given preference to over the task preference of agents. This is so because, competency for a task is more important than the liking to do a particular task.
No agent has given first preference to Task T1, may be because it is a difficult task. T1 can be the most critical task of the project as well, so based on competency assessment; it must be given to A1.
Task T1-> A1
As agent A2 and A3 had both preferred task T2 as first preference, but as per competency, since agent A1 is not available, T2 must be allotted to A2
Task T2-> A2
Therefore, Task T3-> A3
2. As per the principle of value maximization, a manager must aim all his decisions towards increasing the market value of the business. Market value of business can be increased if the products and tasks are done with 100% efficiency. So the competency matrix mapped by P is efficient in aiming at total value maximization.
3.
Agent
Task Preference 1
Task Preference 2
Task Preference 3
A1
T3
T2
T1
A2
T2
T1
T3
A3
T2
T3
T1
Task
Agent Preference 1
Agent Preference 2
Agent Preference 3
T1
A1
A2
A3
T2
A1
A2
A3
T3
A2
A1
A3
In this case, task T1 will be assigned to A2 as both efficiency and competency are matching in the second quadrant.
Task T1-> A2
Correspondingly, Task T2-> A1
Task T3-> A3
Agent
Task Preference 1
Task Preference 2
Task Preference 3
A1
T3
T2
T1
A2
T2
T3
T1
A3
T2
T3
T1
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