The assignment problem is a special case of transportation problem in which the objective is to...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The assignment problem is a special case of transportation problem in which the objective is to assign 'm' jobs or workers to 'n' machines such that the cost incurred is minimized. The element Cij represents the cost of assigning worker i to job j (1.j- 1,2,---n). There is no loss in generality in assuming that the number of workers always equals the number of jobs because we can always add fictitious (untrue or fabricated) workers or fictitious jobs to affect this result. Four jobs are to be assigned to Four machines. The processing costs are as given in the matrix shown below. Find the allocation which will minimize the overall processing cost. Machine 1 Machine 2 Machine 3 Machine 4 Job 1 18 13 38 19 Job 2 26 28 19 26 Job 3 17 14 18 24 Solve this balanced assignment problem using 1) ILP formulation and Branch and Bound for ILP (Lingo Software) 2) Least-Cost Branch and Bound 3) Using the Hungarian Method Comparing results Job 4 11 26 15 10 The assignment problem is a special case of transportation problem in which the objective is to assign 'm' jobs or workers to 'n' machines such that the cost incurred is minimized. The element Cij represents the cost of assigning worker i to job j (1.j- 1,2,---n). There is no loss in generality in assuming that the number of workers always equals the number of jobs because we can always add fictitious (untrue or fabricated) workers or fictitious jobs to affect this result. Four jobs are to be assigned to Four machines. The processing costs are as given in the matrix shown below. Find the allocation which will minimize the overall processing cost. Machine 1 Machine 2 Machine 3 Machine 4 Job 1 18 13 38 19 Job 2 26 28 19 26 Job 3 17 14 18 24 Solve this balanced assignment problem using 1) ILP formulation and Branch and Bound for ILP (Lingo Software) 2) Least-Cost Branch and Bound 3) Using the Hungarian Method Comparing results Job 4 11 26 15 10
Expert Answer:
Answer rating: 100% (QA)
Here are the stepbystep calculations for each method 1 ILP formulation solved using Lingo The ILP mo... View the full answer
Related Book For
Quantitative Methods for Business
ISBN: 978-0324651751
11th Edition
Authors: David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey cam
Posted Date:
Students also viewed these general management questions
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
This exercise outlines a proof of the Birkhoff-von Neumann Theorem. (a) For n Z+, an n n matrix is called a permutation matrix if there is exactly one 1 in each row and column, and all other...
-
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). n = 10 x = 55 y = 55 x2 = 385 y2 = 385 xy = 220 Refer to Exhibit. The...
-
Tell the number of hydrogens bonded to each carbon atom in the following substances, and give the molecular formula ofeach: (c) (b) (a) Br. CEN
-
A glass manufacturer claims that the mean number of glasses that break is no more than 3 glasses per production run. State H 0 and H a in words and in symbols. Then determine whether the hypothesis...
-
Deanna Golds started an interior design company called Interiors by Deanna, Inc., on November 1,2010. The following amounts summarize the financial position of her business on November 14, 2010,...
-
Consider the following problem. Maximize Z = 8x1 + 4x2 + 6x3 + 3x4 + 9x5, Subject to And x1 0, j = 1,.,5. You are given the facts that the basic variables in the optimal solution are x 3 , x 1 , and...
-
How is shared governance at work sites impacted by institution type such as public, private, or for-profit?
-
Cherry Hill Glass Company employs a normal-costing system. The following information pertains to the year just ended. Total manufacturing costs were $1,250,000. Cost of goods manufactured was...
-
Create a complete analysis table for the circuit of Figure 3-15 (a) by finding the logic levels present at each gate output for each of the 32 possible input combinations. (b) Change each OR to an...
-
The responsibilities of Operations Management include obtaining all necessary inputs and drawing up a production plan that effectively uses the materials, capacity and knowledge available at the...
-
long, thin wire carrying 6.0 nC/m runs down the center of a long, thin-walled pipe with radius 1.8 cm carrying -4.2 nC/m spread uniformly over its surface. Part A Find the electric field 0.90 cm from...
-
On May 1, 2023 our client, Penny Smith was driving north on Main Street. She came to the intersection of Hail Street and Main Street, saw that the light was a green left, and proceeded to make a...
-
13. An investor is in a 30% combined federal plus state tax bracket. If corporate bonds offer 6% yields, what yield must municipals offer for the investor to prefer them to corporate bonds? 14. Find...
-
What is the net present value of the following project cash flows at a discount rate of 7 percent? At 20 percent? Year 0 $ Cash Flow -$17,000 1 $4,500 2 $8,700 3 $11,900
-
For the presidential election, votes are recorded electronically using the following ER model. Write down the tables for the ER model. Identify foreign keys and write down the necessary CREATE TABLE...
-
Sportique Boutique reported the following financial data for 2012 and 2011. Instructions(a) Calculate the current ratio for Sportique Boutique for 2012 and 2011.(b) Suppose that at the end of 2012,...
-
Refer to Problem 21. Assume that management desires a 12-day project completion time. a. Formulate a linear programming model that can be used to assist with the crashing decisions. b. What...
-
A study examined waiting times in the X-ray department for a hospital in Jacksonville, Florida. A clerk recorded the number of patients waiting for service at 9:00 A.M. on 20 consecutive days and...
-
Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7200 copies. The cost of one copy of the book is $14.50....
-
The two rectangular smooth flat plates are to have the same drag in the same fluid stream. Calculate the required value of \(x\). If the two plates are combined into the \(\mathrm{T}\)-shape...
-
A uniform flow of standard air at \(60 \mathrm{~m} / \mathrm{s}\) enters a plane-wall diffuser with negligible boundary-layer thickness. The inlet width is \(75 \mathrm{~mm}\). The diffuser walls...
-
For flow over a flat plate with zero pressure gradient, will the shear stress increase, decrease, or remain constant along the plate? Justify your answer. Does the momentum flux increase, decrease,...
Study smarter with the SolutionInn App