Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts.
Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts.
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter8: Network Models
Section8.5: Minimum-cost Network Flow Problems
Problem 2P
Related questions
Question
6. Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts. Provide a dynamic programming approach to solve this problem given an initial rod of length n with potential cut lengths of 1, 2, 5, and 7 [Adapted from ITA, pg. 370, 15.1-3]
length of cut (i) 1 2 5 7
value (pi) 5 7 30 45
handling cost (ci) 4.5 6 10.5 13.5
Expert Solution
Step 1
Algorithm:
MODIFIED-CUT-ROD(p,n,c)
let r[0..n] be a new array
r[0]=0
for j=1 to n
q=p[j]
for i=1 to j-1
q=max(q,p[i]+r[j-i]-c)
r[j]=q
return r[n]
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Operations Research : Applications and Algorithms
Computer Science
ISBN:
9780534380588
Author:
Wayne L. Winston
Publisher:
Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:
9780534380588
Author:
Wayne L. Winston
Publisher:
Brooks Cole