1) Objectives Solving Assignment problem: - Using Least-Cost Branch and Bound - Using the Hungarian Method - Using Branch and Bound for ILP and comparing results with others algorithms 2) The problem data 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 incured is minimized. The element Cij represents the cost of assigning worker i to jobj Ij=1.2----1). 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. Job 1 Job 2 Job 3 Job 4 Machine 1 18 26 11 13 28 14 26 Machine 2 Machine 3 Machine 4 38 19 18 15 19 26 24 10 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 the obtained results