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Linear Programming – Production and Operations Management
Linear Programming is an OR technique or Operations Research technique which emerged in the early 1950s. Having multiple practical applications, this technique has benefitted immensely various organisations in their production and other operations. Prof. G.B. Dantzig is one of the pioneers in formulating the procedure of Linear Programming.
Operations Research can be applied in different settings like – making long range plans, planning the production run, deciding on item and teir quantity to store in warehousing, scheduling of physical distribution of goods, decisions for implementing marketing and product-mix for a company etc.
In short, Linear Programming deals with optimising a desired objective under a situation where there are various constraints. Issues faced by the management is aboout taking the optimum decision but under limitations in a company setup. Therefore, Linear Programming rightly attracts the attention of practising executives.
FORMULATION OF A LINEAR PROGRAMMING PROBLEM
Linear programming problems, typically, have three elements:
1. Decision variables, the determination of whose value is the problem to be solved.
2. Objective function, which is to be either maximised or minimised (e.g. maximisation of profits or minimisation of total costs, as the case may be).
3. Constraints or limitations or conditions related to the decision variables.
The solution of a Linear Programming problem involves:
1. Listing the goal in an algebraic form including the decision variables but in algebraic expression. This expression is called the objective function, which is either to be maximised or minimised.
2. Expressing the constraints in algebraic inequalities involving the decision variables in algebraic notations.
3. The steps listed above, finishes the development of the Linear Programming problem.
Hence, the problem being faced has been resolved with finding of the optimum decision by using the OR technique. Graphical procedure can also be uused to solve simple linear programming problems .
MATHEMATICAL PROCEDURES AND COMPUTER SOFTWARE PACKAGES
One such procedure is called the Simple Method. Such procedures for the solution of the Linear Programming problem can be referred to in any book on Operations Research. The idea behind this chapter is to explain the concepts and applications of Linear Programming in the area of Production and Operations Management. The manual solution by Simplex Method may not be difficult when the number of variables and the number of constraints are one-digit numbers. Today there are computers and readymade Computer Software Packages available to take care of this problem.
ASSUMPTIONS
The assumptions underlying Linear Programming are:
1. Objective Function and the constraints are all linear relationships.
The corollaries of this assumption are that:
(a) We assume that there are no economies of scale or diseconomies of scale; six units of product T require six times as much of raw material as required for one unit of T.
(b) We assume that there are no interactions between the decision variables; the total raw material required for X and T was a simple addition of individual requirements for X and K
2. There is only one objective function. In our product-mix problem there was only one objective and that was to maximise the profit. But, it is not easy in in practice. Often, for a particular decision, an organisation may have a number of objectives with possibly some priorities between them, all of which need to be considered together.
OTHER RELATED METHODS
There are other techniques which can convert a multiple objectives problem to single objective problem. This can be done by considering the trade-offs between different objectives or by ranking different objectives in terms of priorities and converting the problem to a series of single objective problems. A procedure called Goa/ Programming can also be used in such a case.
Integer Programming is used when the decision variables cannot take fractional values.
APPLICATION OF LINEAR PROGRAMMING
Linear programming find vast application in the domain of Production and Operations Management which offer suitable situations. Usually the objective is to either maximise the profit or minimise the total cost or the delay factor. There are always constraints or limitations on production capacity, the quality of the products and constraints on the saleability of a product in a particular period of time. Different time period also impose varied constraints to the decision variables.
COMPUTER SOLUTION OF THE PROBLEM
Information Technology companies have come up with readymade software packages for the solution of Linear Programming problems. One need not be an expert in computer programming; in fact, one need not even know computer programming to solve a Linear Programming problem. A11 that one needs to do is to feed information regarding things such as the number of decision variables, number of constraints, the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints, the maximum or minimum limit of the constraints, and whether the objective function is to be maximised or minimised.
A DECISION-MAKING TOOL
Linear Programming is a very useful and important tool in the hands of the manager. Having diverse practical applications its usefulness for appropriate decision-making solely depends upon the manager and how he takes maximum advantage of the tool.
Production professionals, operations executives, managers, senior executives can use the below links to be updated on Production and Operations Management
- Practice Test for Production and Operations Management
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