# Operation research assignment

### Assignment method

In standard form when maximizing , if there is slack in a constrained primal resource i. Step 3: Make Assignment in the Opportunity Cost Matrix: The procedure of making assignment is as follows: a Examine rows successively until a row with exactly one unmarked zero is obtained. Example 3: There are four jobs to be assigned to the machines. All zeros in the assigned columns are now crossed off as shown in table 2. Examples- Covering and packing LPs commonly arise as a linear programming relaxation of a combinatorial problem and are important in the study of approximation algorithms. Rather than determining a first approximation by a direct application of the simplex method it is more efficient to work with the table given below called the transportation table. What is the basic assumption behind the transportation problem? In this case, there is one constraint for each vertex of the graph and one variable for each independent set of the graph. It is assumed that the total supply and the total demand are equal i. This holds more generally for convex programs: see the KKT theorem. Assign this cell as shown in table 4. The supply at each source and the demand at each destination are known.

All zeros in the assigned column are crossed off as shown in table 3. We form the 2nd modified matrix by subtracting the smallest uncovered element i from the remaining uncovered elements and add to the element at the point of intersection of lines.

It is assumed that the total supply and the total demand are equal i. The new assignment is shown in Table 5. Here a i and bj are positive integers. This also means that a feasible solution to a T.

### Assignment problem in operational research ppt

All zeros in the assigned columns are now crossed off as shown in table 2. Then the objective function is taken without the artificial variables and is solved by simplex method. The problem of assignment arises because available resources such as men, machines etc. Step 3 a : We examine all the row starting from A one-by-one until a row containing only single zero element is located. Then we proceed to phase II. For any given pairing the crew will 1 be based at the city that results in the smaller layover. This necessary condition for optimality conveys a fairly simple economic principle. They are- Formulate the new problem by eliminating the original objective function by the sum of the artificial variables for a minimization problem and the negative of the sum of the artificial variables for a maximization problem. To make it balanced we add a dummy row or dummy column with all the entries is zero. So if the ith slack variable of the primal is not zero, then the ith variable of the dual is equal zero. Let d denote the dimension, i. Opportunity cost show the relative penalties associated with assigning resources to an activity as opposed to making the best or least cost assignment. To overcome this difficulty, a new method is considered, where the use of M is eliminated by solving the problem in two phases. The LP relaxation of set cover problem, vertex cover problem, or dominating set problem is a covering LP. Example 2: A department has five employees with five jobs to be performed.

The cost of transportation from the fictitious destination to all sources and from all destinations to the fictitious sources are assumed to be zero so that total cost of transportation will remain the same.

To overcome this difficulty, a new method is considered, where the use of M is eliminated by solving the problem in two phases. Definition of Assignment Problem 3.

## Assignment problem maximization

We begin by imagining that the transportation table is blank i. Modified matrix. The figures circled indicate layover for crew based at Calcutta, whereas not circled figures are for Delhi based crew. The supply at each source and the demand at each destination are known. Solution: Let us first construct the table for the possible layovers between flights, when crews are based at Delhi. Describe the MODI method of solving transportation problem. Make an assignment single zero by making a square around it. As per the given constraint, minimum layover time is now given in the table below. Only one job could be assigned to one machine are given in following matrix. Step 3: Make Assignment in the Opportunity Cost Matrix: The procedure of making assignment is as follows: a Examine rows successively until a row with exactly one unmarked zero is obtained.

The assignment cost for dummy cells are always zero. The solution is not optimal because only four assignments are made.

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