Integer LFP

Abstract

In some practical applications the unknown variables of a linear-fractional problem are constrained to a discrete set. Such a discrete set may consist of enumerated arbitrary (integer or real) values. If this set of feasible values for unknown variables consists of integer values, such a class of LFP problems is usually called integer linear-fractional programming or ILFP. Examples of applications of integer LFP are mostly in the field of economics and engineering, where it is very important to find such solution that provides the biggest value of a ratio expressed as an objective function — it may be a ratio of revenues and allocations subject to restriction on the availability of the goods involved in the location problem, or a maximal density of integrated elements of an electronic chip designed, etc. If the set of enumerated feasible values for unknown variables contains not only integers but real values too, we usually refer to such of LFP problems as discrete LFP. For example, the following LFP problem is a discrete LFP problem.