Consider the 0/1/2/3 Knapsack Problem. Unlike 0/1 Knapsack problem which restricts xi to be either O or 1, 0/1/2/3 Knapsack Problem allows xi to be either O or 1 or 2 or 3 (that is, we assume that 3 copies of each object i are available, for all i). (a) Obtain the dynamic programming functional equation to solve (find optimal profit) the 0/1/2/3 Knapsack Problem. (b) Give an algorithm to implement your functional equation. (c) What is the complexity of your algorithm?

Consider the 0/1/2/3 Knapsack Problem. Unlike 0/1 Knapsack problem which restricts xi to be either O or 1, 0/1/2/3 Knapsack Problem allows xi to be either O or 1 or 2 or 3 (that is, we assume that 3 copies of each object i are available, for all i). (a) Obtain the dynamic programming functional equation to solve (find optimal profit) the 0/1/2/3 Knapsack Problem. (b) Give an algorithm to implement your functional equation. (c) What is the complexity of your algorithm?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter4: The Simplex Algorithm And Goal Programming

Section: Chapter Questions

Problem 16RP

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