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Fall 2010
HW 5 Solutions
1. Problem 7, page 419
Let c
ij
= cost incurred if a machine is purchased at beginning of year i and is kept until
beginning of year j. The shortest path problem can be formulated for the network similar to
the one in example 2, page 415 (which was also presented in the lecture slides).
Using the given data, we obtain (in thousands of dollars):
c
12
= 208; c
23
= 258; c
34
= 248; c
45
= 288 c
56
= 388;
c
14
= 355; c
15
= 537; c
16
= 841;
c
24
= 258 c
25
= 375; c
26
= 557;
c
35
= 298; c
36
= 395;
c
46
= 388
Using Dijkstra’s algorithm (or, alternatively, by reformulating the problem as a
transshipment problem) we obtain that the optimal strategy is as follows: we should first
keep the machine for two years and then trade it in, and then we should keep the new
machine for three more years till the end of the planning horizon.
2. Problem 8, page 430
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This note was uploaded on 12/14/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Spring '09 term at University of Florida.
 Spring '09
 VLADIMIRLBOGINSKI
 Operations Research

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