Basic theory of selection by relative rank with cost

Suppose there are n objects in a row and we want to choose as good an object as possible. We are allowed to observe one by one starting at an end. We may stop at any point and take the object there, but going back is not allowed. The stopping rule is based on the relative rank of the object among those observed so far. The cost of observation, k is considered to be either zero or positive. This paper presents a basic theory on this problem as well as a set of algorithms which give the optimum stopping rule for given n and k, and the characteristics of the rule.