This is for my Management Science class. In the Par Inc. example from chapter 2,
ID: 409270 • Letter: T
Question
This is for my Management Science class.
In the Par Inc. example from chapter 2, the solutions were not integer values. Does this make sense for this application? Is this a general property of Linear Programming problems? Explain why rounding or truncating non-integer values for the solutions is not an appropriate method for obtaining integer solutions. After posting your response, please comment on the response of at least two other classmates.
135
I think the question is pertaining to what we were working on in week 2 vs week 4. This week its Integer Linear Programming is an important extension of linear programming. This is critical for two reasons:
Integer linear programming can be helpful when factional values for the variables are not permitted. Remember, we are looking for the optimal integer solution. Rounding a linear programming solution may not provide us the "best" or optimal solution or may result in an infeasible solution.
Integer linear programming also allows increased modeling flexibility.
A special case of an Integer Linear Programming model is one where the variables are either 0 or 1, these are called Binary Variables. These types of models can be used to determine whether to choose an option or not.
Par, Inc. Production Time Operation Standard Deluxe Time Available Cutting and Dyeing 0.7 1 630 Sewing 0.5 0.83333 600 Finishing 1 0.66667 708 Inspection and Packaging 0.1 0.25 135 Profit Per Bag 10 9 Model Decision Variables Standard Deluxe Bags Produced 539.99842 252.00110 Maximize Total Profit 7668 Constraints Hours Used (LHS) Hours Available (RHS) Cutting and Dyeing 630 <= 630 Sewing 479.99929 <= 600 Finishing 708 <= 708 Inspection and Packaging 117.00012 <=135
Explanation / Answer
The answer which you got is not lNTEGER SOLUTION, Because in you final answer number of bags to be produced in standard is 539.99 and deluxe is 252.00113. In integer program, the answer will be a specific whole digit number like 538, 252.
In order to get the answer is whole number (integer ), you can add constrain x1, x2 (May be cell B23, and B24 ) as integer
How to put
After assigning constrains , you can add
b23 (In the column consist of <=, >=, select INTEGER). tHEN B24 integer. You can see that in excel.
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