Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 17.6, Problem 11P
Explanation of Solution
a.
The fraction of all refrigerators we have to replace is obtained using [(l – Q)-1 * R] matrix...
Explanation of Solution
b.
If company continues with the current policy Freezco's annual sale is 10000 refrigerators. Thus, fraction of refrigerators to be replaced is shown below:
0.143 x 10000 = 1430 refrigerators
Cost to replace 1 refrigerator is $500. Thus, cost to replace 1430 refrigerators annually is as follows:
Cost1 = 1430 x 500
= $715000 …(1)
On suggestion to change the replacement policy from 3 to 2 years, his markov chain transition probability matrix is modified accordingly. The changed matrix is given below.
Other matrices also get updated accordingly. Here he states 1, 2, are the transient states and >2, fail are absorbing states. The matrix Q consists of all transient states and R consists of transient to absorbing states. The probability matrix Q comprising of all the transient states is given below.
Here, l is 2 x 2 identity matrix.
The matrix (l – Q) is given below:
Using the excel function MINVERSE (), we can obtain (l – Q)-1 matrix. The function returns the inverse matrix for the matrix stored in an array. Note that the MINVERSE function must be entered with CONTROL + SHIFT + ENTER because it is an array function. The matrix (l – Q)-1 is given below.
The R matrix consists of transient to absorbing states. The Matrix R is given below...
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Operations Research : Applications and Algorithms
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