Class 8 IAshhjjj3hwjkwkwmmdjjsignment Problem.pptx

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1. What is the Assignment Problem? The assignment problem is a fundamental concept in scheduling. Imagine you have a team of workers and a set of tasks that need to be completed. Each worker has varying skillsets and efficiencies when it comes to each task. The assignment problem helps us determine the optimal way to assign these tasks to workers, ensuring that the total cost (time, money, etc.) of completing all tasks is minimized. Here, we have two key constraints: each worker can only handle one task at a time, and each task can only be assigned to one worker . The cells in the table contain numbers, representing the cost of each worker completing each job] * An optimization problem in scheduling. * Involves assigning resources (people, machines) to tasks. * Goal: Minimize total cost (or maximize total profit) of assignments. * Each resource can only be assigned one task. * Each task can only be assigned to one resource.

2. Understanding the Assignment Problem The assignment problem arises in various business scenarios. Imagine a team of workers and a set of projects. Each worker has different skillsets and experience levels, impacting the cost (time, money) of completing each project. The assignment problem helps us determine the optimal assignment of workers to projects, ensuring the total cost of completing all projects is minimized. * The assignment problem involves allocating a fixed number of resources to a similar number of tasks. * Each resource can only be assigned one task, and each task can be assigned to only one resource. * The objective is to minimize the total cost associated with these assignments.

3. Application Areas of Assignment Problem hough assignment problem finds applicability in various diverse business situations, we discuss some of its main application areas: ( i ) In assigning machines to factory orders. (ii) In assigning sales/marketing people to sales territories. (iii) In assigning contracts to bidders by systematic bid- evaluation. (iv) In assigning teachers to classes. (v) In assigning accountants to accounts of the clients

4. Steps of the Hungarian Method A flowchart with a start box labeled " Step 1: Reduce the Cost Matrix" and an end box labeled "Optimal Assignment Found." In between, there are several diamond-shaped decision boxes and rectangular boxes with instructions. The instructions include subtracting minimum values from rows and columns, drawing lines to cover zeros, checking for optimality, and adjusting the matrix] * The Hungarian Method is a systematic algorithm for solving the assignment problem. * It works by iteratively reducing a cost matrix that represents the cost of assigning each resource to each task. * Here's a simplified overview of the steps: * Step 1: Reduce the Matrix: Subtract the minimum value in each row from all elements in that row. Repeat for each column. * Step 2: Identify Minimum Number of Lines: Draw horizontal and vertical lines to cover all zeros in the matrix using the minimum number of lines.

5. Steps of the Hungarian Method * Step 3: Identify the Number of Lines: If the number of lines equals the matrix dimension (number of rows/columns), an optimal solution is found. * Step 4: Create Zeroes Covering Lines: If not, adjust the matrix by subtracting the minimum uncovered value from uncovered elements and adding it to elements covered by exactly two lines. * Step 5: Test for Optimality and Adjust: Repeat steps 2-4 until an optimal solution is found, which identifies the minimum cost assignments for all resources.

6. Application of the Hungarian Method The assignment problem can be applied to various real-world scenarios. Here, a delivery company wants to optimize their delivery schedule. Each driver's experience in a zone translates to a different delivery time (cost). The Hungarian Method can help assign drivers to zones, minimizing the total delivery time across all zones A delivery truck with a company logo parked on a residential street. A delivery driver in a uniform is walking towards a house carrying a package] company has 4 delivery drivers and 4 delivery zones. * Each driver has varying experience levels in each zone, affecting delivery time (cost). * The company wants to assign drivers to zones to minimize total delivery time.