Question

Assignment 5 Mixed-Integer Programming Due: 9 am on January 17 Problem 1 five operations do not need to be performed in a particular order, and the two in parallel. The time taken for each operation on each of the given machines is given in the operations, A, B, C D, and E, each of which can be done on either machine 1 or machines A job requires five machine 2. The can run folmowing table Machine 1 5 9 2 3 4 Machine 2 34 7 5 4 Formulate an Integer Linear Programming (LP) model to assign the jobs to the machines to minimize the total operation time for the five operations. (Hints: if T1 is the total time taken on machine 1 and T2 is the time taken on machine 2, then Max (T1, T2) is to be minimized.) Problem 2 A model faced by an electrical utility each day is that of deciding which generators to start up. The utility in question has three generators with the characteristics shown in the following table. There are two periods in a day, and the number of megawatts needed in the first period is 2,900. The second period requires 3,900 megawatts. A generator started in the first period may be used in the second period without incurring an additional startup cost. All major generators (e.g., A, B, and C) are turned off at the end of each day. The electrical utility company wishes to minimize the total cost. Formulate this problem as a Mixed Integer Programming. GeneratorFixed Setup Cost (S) Cost Per Period Maximum Capacity Per Megawatt Used (S) in Each period (MW) 2000 1000 2100 1800 3000

Answer 1