We investigate the structure of the currencies (systems of coins) for which the greedy change-making algorithm always finds an optimal solution (that is, a one with minimum number of coins). We present a series of necessary conditions that must be satisfied by the values of coins in such systems. We also uncover some relations between such currencies and their sub-currencies.

In this paper we address the problem of planning a temporary storage area in a shampoo making system. Everyday, the packing service of the company, which gathers several packing lines, transmits plans of orders to produce (also called batches) to the making service. Each plan corresponds to the work that will be performed by one packing line for the next production horizon. A batch, which consi...

One problem with taking advice arises when the advice is expressed in terms of data or actions unavailable to the advicetaker. For example. in the card game Hearts, the advice “don’t lead a suit in which some opponent has no cards left” is nonoperational because players cannot see their opponents’ cards. Operationalization is the process of converting such advice into an executable (perhaps heu...

The change making problem is the problem of representing a given value with the fewest coins possible We investigate the prob lem of determining whether the greedy algorithm produces an opti mal representation of all amounts for a given set of coin denominations c c cm Chang and Gill show that if the greedy algorithm is not always optimal then there exists a counterexample x in the range c x cm...

A learner who has already acquired a solution-method can not always use it adequately. Therefore, the practice to use a solution-method is indispensable to master it. The problem solving practice is the most popular, but it is not the only way to make the learner master the solution-method. To make problems which can be solved by a solution-method is a promising way to master the solution-metho...

abstract: although all university majors are prominent and the necessity of their presences is of no question, they might not have the same priority basis considering different resources and strategies that could be spotted for a country. this paper focuses on clustering and ranking university majors in iran. to do so, a model is presented to clarify the procedure. eight different criteria are ...

one of important problems in supply chains management is supplier selection. in a company, there are massive data from various departments so that extracting knowledge from the company’s data is too complicated. many researchers have solved this problem by some methods like fuzzy set theory, goal programming, multi objective programming, the liner programming, mixed integer programming, analyti...

the linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. this paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. in this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to ...