A New Mathematical Model to Design Optimum Denomination of Coins and Banknotes Range (ODCBR)

When an individual make a cash payment, he needs to consider about the amount to be paid, the coins and banknotes which are available and amount of change. For central banks and retailers, it is of interest to understand how this individual choice process works. The literature of currency use concerns primarily theory; given certain assumptions which can present appreciate denomination range by statistical analysis. Literature surveys try to answer the question that which is the best selection of available coins and banknotes in the wallet to fulfill the charge. There is no mathematical model which can optimize a specific denomination range of coins and banknotes. In this paper, we aim at modeling this process where denomination range of banknotes and coins are optimized through a mathematical model in which all parameters are assumed to be certain in a single period in any economy. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed model.