Question

What is the main goal of the assignment problem?

• A. To minimize the total cost of assigning tasks to agents
• B. To maximize the flow in a network
• C. To schedule project activities
• D. To determine the shortest route for transportation

Hint:

The assignment problem is solved using the Hungarian Method, which is specifically designed to find the cost-minimizing one-to-one allocation of resources to tasks.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the primary optimization objective of the classical assignment problem in operations research.

Step 2: Key Formula or Approach: This is a standard linear programming and operations research concept. The assignment problem is a special case of the transportation problem where the goal is to allocate \(n\) resources (agents) to \(n\) activities (tasks) on a one-to-one basis at minimum total cost.

Step 3: Detailed Explanation:

• In an assignment problem, we are given a cost matrix where the element \(C_{ij}\) represents the cost of assigning agent \(i\) to task \(j\).

• The objective is to find a set of assignments that minimizes the total cost:
\[ \text{Minimize } \sum_{i=1}^{n} \sum_{j=1}^{n} C_{ij} X_{ij} \] subject to the constraints that each agent is assigned to exactly one task, and each task is assigned to exactly one agent (\(X_{ij} \in \{0, 1\}\)).

• Option B describes the maximum flow problem in network optimization.

• Option C describes project management techniques like PERT and CPM.

• Option D describes the shortest path or transportation problem.

Step 4: Final Answer:
The main goal of the assignment problem is to minimize the total cost of assigning tasks to agents.