Linier Programming

By Agustina Shinta

What is it?

LP is essentially a mathematical technique for solving a problem that has certain characteristics.

There is a function or objective to be maximized or minimized, there are limited resources to be used in the satisfaction of this objective, and numerous means of using the resources are available

Ex:Farmers may have : land, machinery and

equipments and labor resources that they can use to produce corn, soybeans, wheat, hay, oats and other crops, and they would like to combine these resources in such a fashion as to maximize net income.

Although most farm management applications of LP involve short run planning where resource supplies are fixed, long run planning where additional resources can be acquired over time can be done with LP

LP can be used industrial sector such as transportation, petroleum, and meatpacking industries and other sectors involving production, transportation and distribution of goods and services.

The technique is also being used extensively in the planning of individual farm business through the use of prerestructured LP packages that are available through many extension services.

LP have been well tested and proven applicable to a wide variety of problems in the farm and business management area

LP is a set of mathematical rules for solving specific problems. Standard computer programs are available to accomplish these tasks.

Why study LP ?

The reasons for studying LP are numerousFirst, the procedure is applicable to almost any

resource allocation problem faced by the farm manager.This ability to handle different issues with one analysis procedure means that time allocated to understanding the procedure can be “spread over many potential uses”

Second, the procedure can handle more complex problems than budgeting or marginal analysis. We can specify more complex, realistic problems without concern for the cost or feasibility of obtaining an answer

Third, LP provide not only information on the best or optimal way of allocating resources and the best production marketing financial plan, but also additional information concerning the value of various resources used in that plan.

Ex :LP would indicate :- How much family labor is used- How much is unused in a whole farm planning

problem- How much the operator could pay for

additional hired labor- etc

Fourth, It can easily be used to evaluate how the results would change it changes occurred in product prices or technical efficiency- the sensitivity or stability of the farm plan.

Ex. - How the whole farm organization will change as the

relative prices of products increase or decrease- What would happen to income if additional labor was

available and how would it be best used- How would additional credit or capital be allocated and

how much additional income would it generate- etc

Fifth, it handles the issues of “opportunity cost”. It can reflect income forgone in using a resource in an alternative enterprise

In sum up, LP is one of the few techniques available that can solve a realistically defined farm management problem using mathematical procedures consistent with the economic concept of marginal analysis.

The concept of a process (activity)

A process is a method of transforming resources or inputs into a specific output.

Although this definition sound quite similar to that of a production function, a process is much more restrictive in that the relative proportion of all inputs and outputs is fixed in a process.

It implies that there are many alternative ways to produce a single product in a LP model.

In addition to determining the optimal combination of products or enterprises to include and the allocation of scarce resources to those enterprises, the LP procedure can also indicate the optimal technology or method of production that should be used.

Assumptions of LP

4 basic assumptions are1. Additivity and Linearity2. Divisibility3. Finiteness4. Single-valued Expectations

Additivity and Linearity

• The total amount of resources used by two or more processes must be the sum of the amount of resources used by each process.

• Linearity implies that multiplying all inputs used in a process by a constant results in a constant change in the output of that process.

Finiteness

The assumption specifies a limit to the number of alternative processes and resource restrictions that can be included in the analyisis.

Farm managers can only allocate so much time to the evaluation of alternatives and must restrict their analysis to a subset of the possible production and marketing alternatives available of them.

Single Valued Expectations

This assumption specifies that resource supplies, input output coefficients, and commodity and input prices must be known with certainty

Conclusion:Linearity of production relationshipsCompletely divisible outputs and inputsA finite set of production alternativeConstantSingle valued expectations of prices and production efficiencies