Mathematic Optimization Application: Southwest Airlines Linear Programming Project - Case Study Example

rces constraining the solution are the number of flights covered, the number of crew members in a flight and the cost of assigning a new crew member to a flight. This type of a problem is a minimization problem since the Southwest Airlines Company seeks to minimize its operational costs by ensuring that it optimally assigns crew members to each of its flights. In solving this problem, I have undertaken to take an approach that allows for the determination of the optimal solution that would minimize the company’s costs (Hooley & Hussey, 2002; Kothari, 2002).

The objective function is to minimize costs and in this case, this is achieved by expressing the variables and the constraints in the format that is indicated above. In this, the case for Southwest Airlines can be argued out to be one in which: The optimal solution is attained through the establishment of the slack variables or the surplus variables. In the case of Southwest Airlines, the objective function’s optimality is attained at the point where there is a resultant surplus variables for variables X1, X5 and X12 (Saltelli, Tarantola & Campolongo, 2004; Le & Laporte, 2002).

In the optimal solution, it these variables that represent positive values indicating that in each, 1 unit of each of the resources were used over and above the expected minimum amount. For the other variables, also referred to as the limiting or binding constraints they were fully used up in the solution to determine the optimality levels for the firm’s objective function (Srivastava et al., 2000; Tulsian & Pandey, 2012). My linear programming model is correctly translated to the Excel in the manner that the rows represent the constraints to each flight, and the columns represent the variables.

The Excel also shows the optimal variables which are X1, X5 and X12 and the costs assigned to each of the variables. Sensitivity analysis for the case is determined in Excel by assigning each of the particular variables to the