The shipping cost per unit from each of the factories to each of the regional warehouses is as follows:. Goal is determine the "least cost allocation" that satisfies the regional demands and does not exceed the available factory capacities. Formulate the cost and shipping schedule matrices that needed to solve this transportation problem.

Indicate your decision variablesconstraints and ohjective cell. Find the least cost? At would you change if the unit costs were unit profits and you wanted to make the most profit you could? What is the greatest profit? What if the demand for Region 2 incresed by 10 to 22 units what would you need to do to solve this problem?

### Balanced Transportation Problem in Operational Research - Quantitative Techniques for management

Four subcontractors have submitted bids for three projects. Each contractor can only be awarded at most one project- and each project of course can only be done once. Assign each project to only one contractor so the that the total cost of doing all three projects is a s little as possible. Formulate the cost and project assignment matrices that are needed to solve this.

Indicate your decision variables, constraints and objective cell. If you the contractors could work on no more than 2 projects what would you do to solve?

What is the least expensive way of assigning the project? Why does quantitative analyst have a difficult time in leading and motivating an organization towards its goals? Is the problem balanced or unbalanced What if the demand for Region 2 incresed by 10 to 22 units what would you need to do to solve this problem?

Using What's Best! What is the least cost" Is this a balanced or unbalanced problem?

## Unbalanced Assignment problem with MS Excel solver

Unbalanced Assignment problem with MS Excel solver. Add Solution to Cart Remove from Cart.Whenever the cost matrix of an assignment problem is not a square matrix, that is, whenever the number of sources is not equal to the number of destinations, the assignment problem is called an unbalanced assignment problem. In such problems, dummy rows or columns are added in the matrix so as to complete it to form a square matrix.

The dummy rows or columns will contain all costs elements as zeroes. The Hungarian method may be used to solve the problem. Example : A company has five machines that are used for four jobs.

Each job can be assigned to one and only one machine. The cost of each job on each machine is given in the following Table. Column-wise reduction is not necessary since all columns contain a single zero. Now, draw minimum number of lines to cover all the zeros, as shown in Table. Select the least uncovered element, i.

### Quantitative Techniques: Theory and Problems by P. C. Tulsian, Vishal Pandey

Hence optimality is reached. Now assign the jobs to machines, as shown in Table. Example : In a plant layout, four different machines M1, M2, M3 and M4 are to be erected in a machine shop. The cost of erection of machines is given in the Table. Solution: As the given matrix is not balanced, add a dummy row D5 with zero cost values. While selecting the lowest cost element neglect the high cost assigned H, as shown in Table below. Note: Column-wise reduction is not necessary, as each column has at least one single zero.

**Transportation Problem**

Now, draw minimum number of lines to cover all the zeros, see Table. Hence not Optimal. Select the smallest uncovered element, in this case 1. Subtract 1 from all other uncovered element and add 1 with the elements at the intersection. The element covered by single line remains unchanged.

These changes are shown in Table. Now try to draw minimum number of lines to cover all the zeros. Optimal assignment of machines to areas are shown in Table.

Quantitative Techniques For Management Tutorial. Quantitative Techniques â€” Introduction. Linear Programming: Graphical Method. Linear Programming: Simplex Method. Theoretical Probability Distributions.A transportation problem may have feasible solution only it is a balanced problem. An unbalanced problem can be made balanced by adding dummy supply centre row or dummy demand centre as per the requirement. If in a transportation problem, the sum of supply available from all sources is not equal to the sum of demands of all destinations, i.

But for a feasible solution to exist, total supply must be equal to the total demand thus it is necessary to convert these unbalanced T. Supply is in excess than the demand, we introduce a dummy demand centre additional destination column to the transportation problem to absorb the excess supply. The unit transportation cost for the cells of this dummy destination column are all set equal to zero, because these represents item that are not being made and sent.

Whenever i. The unit transportation cost for the cells of its dummy row are set equal to zero. Solve the transportation problem when the unit transportation costs, demand and supplies are as given below.

We convert this into a balanced T. Hence we have the converted problem as follows.

As this problem is balanced there exists a feasible solution to this problem. Using least cost method we get the following initial solution:. Hence, the solution is a non â€” degenerate one. A product is produced by four factories F 1F 2F 3 and F 4. Their unit production cost are Rs 2, 3, 1 and 5 respectively. Production capacity of the factories are 50, 70, 30 and 50 units resp. The product is supplied to 4 stores S 1S 2S 3and S 4the requirements of which are 25, 35, and 20 resp.

Unit cost of transportation are given below. Hence the problem is unbalanced. The initial basic feasible solution is obtained by least cost method, and we have found following initial basic feasible solution. So the solution is non â€” degenerate solution. This solution is not optimum since cell F 4S 4 is having a negative net evaluation value i. Requirement of Linear Programme Problem L. P Operations Research.Use the solver in Excel to find the number of units to ship from each factory to each customer that minimizes the total cost.

To formulate this transportation problemanswer the following three questions. What are the decisions to be made? For this problem, we need Excel to find out how many units to ship from each factory to each customer.

What are the constraints on these decisions? Each factory has a fixed supply and each customer has a fixed demand. What is the overall measure of performance for these decisions? The overall measure of performance is the total cost of the shipments, so the objective is to minimize this quantity. To make the model easier to understand, name the following ranges.

Total Cost equals the sumproduct of UnitCost and Shipments. This solution has a total cost of It is not necessary to use trial and error. We shall describe next how the Excel Solver can be used to quickly find the optimal solution.

Note: can't find the Solver button? Click here to load the Solver add-in. Conclusion: it is optimal to ship units from Factory 1 to Customer 2, units from Factory 2 to Customer 2, units from Factory 2 to Customer 3, units from Factory 3 to Customer 1 and units from Factory 3 to Customer 3.

This solution gives the minimum cost of All constraints are satisfied. Transportation Problem. Formulate the Model Trial and Error Solve the Model Use the solver in Excel to find the number of units to ship from each factory to each customer that minimizes the total cost.

Formulate the Model The model we are going to solve looks as follows in Excel. Download Excel File transportation-problem. Follow Excel Easy. Become an Excel Pro Examples.When the total supplies of all the sources are equal to the total demand of all destinations, the problem is a balanced transportation problem.

Quantitative Techniques For Management Tutorial. Quantitative Techniques â€” Introduction. Linear Programming: Graphical Method. Linear Programming: Simplex Method. Theoretical Probability Distributions.

## Balanced and Unbalanced Transportation Problem | Operations Research

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Top 10 facts why you need a cover letter? Username Password. New to Wisdomjobs?Free Trial. Search form X. Contact Us Login. Live Chat Help Desk. Transportation Problem 1 You are here Home. Minimize the costs of shipping goods from factories to customers, while not exceeding the supply available from each factory and meeting the demand of each customer. Each factory has a limited supply and each customer a certain demand. How should the company distribute the product? Still, this type of model is widely used to save many thousands of dollars each year.

In worksheet Transport2 we will consider a 2-level transportation, and in worksheet Transport3 we expand this to a multi-product, 2-level transportation problem.

Minimize the costs of shipping goods from factories to customers, while not exceeding. Number of products shipped. Total cost of shipping. A company wants to minimize the cost of shipping a product from 2 different factories to 5 different customers. How should the company distribute the. These are given the.

The other two constraints are. This is a transportation problem in its simplest form. Still, this type of model is widely used to save many. In worksheet Transport2 we will consider a 2-level transportation, and in worksheet Transport3 we expand this to.Formulate the given problem and set up in a matrix form. Check whether the problem is a balanced or unbalanced transportation problem. If unbalanced, add dummy source row or dummy destination column as required. Algorithms for all the three methods to find the initial basic feasible solution are given.

Remarks: The initial solution obtained by any of the three methods must satisfy the following conditions:. Quantitative Techniques For Management Tutorial. Quantitative Techniques â€” Introduction. Linear Programming: Graphical Method.

Linear Programming: Simplex Method. Theoretical Probability Distributions. IT Skills. Management Skills. Communication Skills. Business Skills. Digital Marketing Skills.

Human Resources Skills. Health Care Skills. Finance Skills. All Courses. All Practice Tests. Job Recommendation Latest. Jobs in Meghalaya Jobs in Shillong. View All Locations. How to design your resume? Have you ever lie on your resume? Read This Tips for writing resume in slowdown What do employers look for in a resume? Interview Tips 5 ways to be authentic in an interview Tips to help you face your job interview Top 10 commonly asked BPO Interview questions 5 things you should never talk in any job interview Best job interview tips for job seekers 7 Tips to recruit the right candidates in 5 Important interview questions techies fumble most What are avoidable questions in an Interview?

Top 10 facts why you need a cover letter? Username Password. New to Wisdomjobs? Sign up. Balanced Transportation Problem. Solving Transportation Problem Using Computer.

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