Integer Programming Problem and Project Management Problem

Production Operation Management Home work 3 Due: August 16 th Question 1: Integer Programming (50 Points) Grading breakdown for this question: Model Formulation ( 50 points) Def inition of Decision variables: 3 0 points Deve lopment of Objective Function: 10 points Development of constraints: Formulas 10 points Problem Statement A workshop has 6 machines that can perform any job assigned to them. The workshop has 10 jobs that it needs to complete over two days. Jobs 1 to 5 mu st be finished on the first day and jobs 6 to 10 must be finished on the second day. Any of the machines will take a complete day to finish any of the jobs. The workshop manager requires that none of the machines stay idle for the two days. Write an intege r programming model that would minimize the total costs of running the 10 jobs. The cost per job per machine is given in the Table below . Question 2: (Project Management Problem ) (50 Points) Grading breakdown for this question: Model Formulation ( 50 points) Project Schedule Network: 10 Points Def inition of Decision variables: 10 points Development of Objective Function: 10 points Develop ment of constraints: 10 points Computer Solution: 10 points Problem Statement A company hired a contractor to perform the following project. The project consists of 8 activities, A – H. The table below lists the activities, their prerequisites, the normal duration of each activity , the fixed and variable costs of reducing that duration, and the maxim um days that can be crashed. a. Create the project schedule network b. Develop the complete optimization model to minimize the total cost (fixed cost+variable cost) of finishing the project in 31 days. c. Solve this model using Solver