Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 17, Problem 4RP

Explanation of Solution

a.

New copies of the book sold by the publisher each year:

Let,

NB: New bookB1: Once-used bookB2: Twice-used bookB3: Thrice-used bookNSB: Books not sold back   

The transition probability matrix “P” for the given problem is shown below:

 NBB1B2B3NSB
NB00.9000.1
B1000.800.2
B20000.60.4
B300001

For an organization in which each book is classified into one of “s” groups (here s= 4).

Let,

Pij - Denotes the fraction of books which begin a time period in group i begin the next time periodin group j.Hi - Denotes the number of group i books hired at the beginning of each period.Ni - Denotes the limiting number of group i books.

To determine Ni, use the steady-state condition:

Number of books entering the state i during each period = Number of books leaving the state i during each period

Here,

Amount entering group i= Amount leaving group i

This implies,

Hi+kiNkpki=Ni+kipik(i=1,...,s)

Let steady state census for NB;B1;B2;B3 be N1;N2;N3;N4

Explanation of Solution

b.

Average profit per book:

The bookstore’s profit on each type of book is as given below:

New book: $6Once-used book: $3Twice-used book: $2Thrice-used book: $1

If the steady-state census is the representative of the bookstore’s sales, the total profit on books is as follows:

Total profit =(6×N1)+3×N2'+2×N3+1×N4                   = 6×1

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Chapter 17 Solutions

Operations Research : Applications and Algorithms

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