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Discrete Optimization Model in Constructing Optimal Decision Tree

Decision trees have been well studied and widely used in knowledge discovery and decision support systems. One of the applications of binary integer programming to form decision trees or decision making is the knapsack problem. The knapsack problem is an integer programming problem that involves only one constraint. The knapsack problem is generally illustrated with a bag and an item. The problem to be solved is to maximize the price of goods with a certain capacity that can be loaded by a bag with a certain capacity too. In solving the knapsack problem, it can generally be done directly. In this paper we are interested to show how the implicit enumeration method solves the knapsack problem to form an optimal decision tree