Introduction. Integer programming is a branch of mathematical programming or optimization. A general mathematical programming problem can be stated as. Integer programming. From Wikipedia, the free encyclopedia. An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.‎Proof of NP-hardness · ‎Variants · ‎Applications · ‎Algorithms. Integer Programming is a subset of Linear Programming. It has all the characteristics of an LP except for one caveat: the solution to the LP must be restricted to.


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They integer programming are seeking optimal values either in the minimization or maximization sense of a objective function of a set of decision variables, which represent actions that can be taken in the problem being modeled.

Integer programming - Wikipedia

In some cases, the decisions have to be discrete e. The integer programming is integer programming IP, and the latter for LP. The applications scenarios are not the big difference between IP and LP.

Integer programming When formulating LP's we often found that, strictly, certain variables should have been regarded as taking integer values but, for the sake of convenience, we let them take fractional values reasoning that the variables were likely to be so large that any fractional part could be neglected.

Whilst this is acceptable in some situations, in many cases it is not, and in such cases we must find a numeric solution in which the variables take integer values. Problems in which this is the case are called integer programs IP's and the subject of solving such programs is called integer programming also referred to by the initials IP.

Note here that problems in which integer programming variables can take only integer programming values and some variables can take fractional values are called mixed-integer programs MIP's.

As for formulating LP's the key to formulating IP's is practice. Although there are a number of standard "tricks" available to cope with situations that often arise in integer programming IP's it is probably true to say that formulating Integer programming is a much harder task than formulating LP's.

We consider an example integer program below.

What is the difference between integer programming and linear programming? - Quora

Capital budgeting There are four possible projects, which each run for 3 years and have the following characteristics. Which projects would you choose in order to maximise the total integer programming

Capital budgeting solution We follow the same approach as we used for integer programming LP's - namely: We do this below and note here that the only significant change in formulating IP's as opposed to formulating Integer programming is in the definition of the variables.

One "trick" in formulating IP's is to introduce variables which take the integer values 0 or 1 and represent binary decisions e.


integer programming Constraints The constraints relating to the availability of capital funds each year are 0. Integer programming effectively the zero-one nature of the decision variable means that we always capture in the single term 0. In this course we deal only with linear integer programs IP's with a linear objective and linear constraints.

It is plain though that there do exist non-linear integer programs - these are, however, outside the scope of this course. Extensions to this basic problem include: How to amend our basic IP to deal with integer programming extensions is given here.

Integer Programming - MATLAB & Simulink

Solving IP's For solving LP's we have general purpose independent of the LP being solved and computationally effective able to solve large LP's algorithms simplex or interior point. For solving IP's no similar general purpose and computationally effective algorithms integer programming.

Indeed theory suggests that no general purpose computationally effective algorithms will ever be found. This area is known as integer programming complexity and concerns NP-completeness.

Integer programming

It was developed from the early 's onward and basically is a theory concerning "how long it takes algorithms to run". This means that IP's are a lot harder integer programming solve than LP's. Integer programming methods for IP's can be categorised as: It is used in a special case of integer programming, in which all integer programming decision variables are integers.

It can assume the values either as zero or one. Telecommunications networks[ edit ] The goal of these problems is to design a network of lines to install so that a predefined set of communication requirements are met and the total cost of the network is minimal. In many cases, the capacities are constrained to be integer quantities.