Formulation problems
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(Transportation) Bayville has built a new elementary school so that the town now has a total of four schools- Addison, Beeks, Canfield and Daley. They have capacities (the maximum number of students that can be registered) of 300, 300, 600 and 500 respectively. The school wants to assign children to schools so that their travel time by bus is as short as possible. The school has partitioned the town into three districts conforming to population density- north, south and east. The average bus travel time from each district to each school (from a source to a destination) is shown as follows. Travel time (cost) matrix
The numbers in the table show the average bus travel time from each district to each school The numbers in the last column show the number of students in each district The numbers in the last row show the maximum number o students that can be registered to each school. Formulate the problem Assume the solution values in bold. What would you do if students from East are not accepted at Daley What would you do if the student population exceed the school capacities? (Transshipment) Ryan Electronics has production facilities in Denver and Atlanta. Components produced at either facility may be shipped to either of the firm’s regional warehouse, which are located in Kansas City and Louisville. From the regional warehouses, the firm supplies retail outlets in Detroit, Maimi, Dallas and New Orleans. Warehouses do not have any long-term stocking facilities Transportation costs per unit for the Ryan Electronics are given below:
* The capacities of plants are 600 units at Denver and 400 units in Atlanta. * The demands at retail outlets are estimated to be 200 units at Detroit, 150 units at Miami, 350 units at Dallas and 250 units at New Orleans. Draw the network, define the decision variables and formulate this transshipment problem assuming that Ryan does not want to ship any items From Kansas City to Miami. (Course Assignment) A university department head has five instructors to be assigned to four different courses all the instructors have thaught the courses in the past and have been evaluated by the students. The rating for each instructor for each course is given in the following table (a perfect sore is 100) Course
The department head wants to know the optimal assignment of instructors to courses to maximize the overall average evaluation. The instructor who is not assigned to teach a course will be assigned to grade exams. Formulate the problem. (Assignment) . There are five professors and four sections of finance. Professors are paid differing rates according to the time periods. The costs of each assignment is as shown on the Table below. Because of personal reasons Professor 4 should not be assigned to the section whose class start time is 1 p.m. The professor who is not assigned to teach a course will be assigned to grade exams. Formulate the problem so as to assign professors to sections that will minimize the costs. What will be the impact of the imbalance of the problem on the optimal solution. (10 points)
(Assignment). Three professors must be assigned to teach six sections of finance. Each professor must teach two sections of finance, and each has ranked the six time periods during which finance is taught. Professors are paid differing rates according to the time periods. The costs of each assignment is as shown on the Table below. Formulate the problem so as to assign professors to sections that will minimize the costs by assuming that it is impossible to assign Professor 1 to the courses that begin at 9 a.m. State the impact of the imbalance of the problem on the course Schedule. What do you recommend to the department head.
(Assignment). A dispatcher for the Citywide Taxi Company has six taxicabs at different locations and five customers who have called for service. The mileage from each taxi’s present location to each customer is shown in the following table. Determine the optimal assignment(s) that will minimize the total mileage traveled.
(Assignment) Given the following cost table for an assignment problem. Determine the optimal assignment and compute the minimum cost. Identify all alternative solutions if there are multiple optimal solutions. (8) Machine
(Assignment) Prentice-Hall wants to assign recently hired colloge graduates: Jones, Smith, Andy and Wilson to regional sales districts in Omaha, Dallas and Miami. But the firm also has an opening in New York and would send one of the three there if it were more economical than a move to Omaha, Miami, or Dallas. It will cost $10 to relocate Jones to New York, $8 to relocate Smith there and $15 to move Wilson.What is the optimal assignment of personel to offices?
(Integer Programming) Consider a minimization Integer Linear Programming problem. Does the optimal value for the LP relaxation provide an upper or a lower bound for the optimal value of the ILP? Explain your answer (Binary Programming) Melissa Jacobson, an undergraduate business major at State University, is attempting to determine her course schedule for the fall semester. She is considering nine 3-credit-hour courses, which are shown in the following table. Of these courses Production Management, Organizational Theory, Corporate Finance and Marketing Management are must courses. Also included are the average number of hours she expects to have to devote to each course each week (based on information from other students) and her minimum expected grade in each course based on an analysis of the grading records of the teachers in each course.
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