348 CHAPTER 8 THE TRANSPORTATION AND ASSIGNMENT PROBLEMS
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EXAMPLE: SOLVING KNAPSACK PROBLEM WITH DYNAMIC PROGRAMMING
Selection of n=4 items, capacity of knapsack M=8
Item i
1
2
3
4
Value vi
15
10
9
5
Weight wi
1
5
3
4
f(0,g) = 0, f(k,0) = 0
Recursion formula:
f(k,g) =
f(k-1,g)
if wk > g
9 max cfw_vk + f(k-1,g-wk

The Equipment-Replacement Problem
Consider a piece of equipment, say a car, that has to be operated throughout a planning horizon of N periods. Suppose that each period corresponds to one year; and that we are required to make a decision as to whether or

ASSIGNMENT
Transportation Problem
1) Suppose that England, France, and Spain produce all the wheat, barley, and oats in the
world. The world demand for wheat requires 125 million acres of land devoted to wheat
production. Similarly, 60 million acres of la

Dynamic Programming
Examples
Page 1
Equipment Replacement Model
The longer a machine stays in service, the higher will be its
maintenance cost, and the lower will be its productivity. When a
machine reaches a certain age, it may be more economical to
repl

College of Management, NCTU
Operation Research II
Spring, 2009
Chap10 Dynamic Programming
Dynamic programming provides a systematic procedure for determining the
optimal combination decision.
In contrast to linear programming, there does not exist a stand

1) Suppose that England, France, and Spain produce all the wheat, barley, and oats in the
world. The world demand for wheat requires 125 million acres of land devoted to wheat
production. Similarly, 60 million acres of land are required for barley and 75

Dynamic Programming
Page 1
DYNAMIC PROGRAMMING
The OR problems presented previously dealt with situations involving a single decision.
Management, however, must frequently consider a sequence of decisions where each decision
affects future decisions. The