Mazoo's Learning Blog: December 2005 Archives

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December 28, 2005

Simplex Algorithm. Example #2

In the previous example we considered the solution of linear programming problem using the simplex method. We modified initial problem into the standard maximization problem with non-negative right-hand side of the constraints equations.

Let us consider more general case of solving standard maximization problem with arbitrary right-hand side of the constraints.

Initial linear programming (LP) problem:

4х1 + 15х2 + 12х3 + 2х4 -> min

2x2 + 3x3 + x4 >= 1
x1 + 3x2 + x3 - x4 >= 0
x1, x2, x3, x4 >=0

Convert initial LP problem to maximization LP problem:

-4х1 - 15х2 - 12х3 - 2х4 -> max

-2x2 - 3x3 - x4 <= -1
-x1 - 3x2 - x3 + x4 <= 0
x1, x2, x3, x4 >=0

Let S1, S2 >= 0 are slack variables.
Rewrite the constraint inequalities as equations by adding these variables:

-4х1 - 15х2 - 12х3 - 2х4 -> max (objective function)

0x1 - 2x2 - 3x3 - x4 + 1s1 + 0s2 = -1 (constraint equations)
-x1 - 3x2 - x3 + x4 + 0s1 + 1s2 = 0
x1, x2, x3, x4, s1, s2 >=0

Set up the initial simplex tableau (Click to see full size image):

Continue reading "Simplex Algorithm. Example #2"

Posted by mazoo at 1:47 PM | Comments (4) | TrackBack

December 18, 2005

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Web visibility is a great advantage for professionals, so you can try your writing skills here. Maybe your articles in this blog will be the first step to your own professional web resource.

Lately I've been very busy at work and I can't pay as much attention to this blog as I'd like to. That's why I want to remind you the following - you can always send me your own articles for publication in this blog.

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It often happens so, that some theoretical fragment doesn't "want" to be learned, but then a kind of insight happens and everything becomes clear. Tell me about issues, which seemed to be very complicated at first and the perfect solutions of such a problem you managed to find.

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Posted by mazoo at 2:48 PM | Comments (3)

December 6, 2005

Quantity variance is the sum of mix and yield variances

The Quantity (Efficiency or Usage) Variance is the difference between the actual material (labor) usage and the standard usage for this level of output, multiplied by standard price.

Quantity Variance = (Standard Quantity for Actual Output - Actual Output) * Standard Price, or

Quantity Variance = (SQ - AQ) * SP

When there is more than one input, we calculate Quantity (Efficiency) Variance for each input individually:

In this situation, the Quantity (Efficiency) Variance may be caused by two different factors:

1. The mix of material (labor) actually used was different from the mix that should have been used, or

2. Total quantity of the inputs actually used to produce the actual output was different from the standard quantity that should have been used to produce actual output.

Therefore, the Quantity (Efficiency) Variance can be broken down into two variances: the Mix Variance and the Yield Variance.

1. Mix Variance: