Linear Programming Essay

September 21, 2017 Management

Integer Programming is a mathematical attack which maintains that the solution of any mathematical jobs should be in footings of whole Numberss or whole numbers. The intent of whole number scheduling is to happen a close whole figure solution to the Linear Programming ( LP ) job within the restraints imposed. For illustration. the denary solutions like 30. 5 tabular arraies. 3. 96 autos. 9. 25 chairs or 2. 66 individuals may be realistic without go againsting the restraints of job ; nevertheless. merely rounding off the values to the nearest whole number would non bring forth a executable solution.

Integer Programming can be considered as portion of LPM or Linear Programming Models. LPMs seek to minimise or maximise the variable which is subjected to restraints or restrictions. The value of the variable. obtained by work outing the LPM can be in decimals while in instance of whole number scheduling. it has to be in whole numbers ( Taylor. 2009 ) . 2. Identify the three basic types of whole number programming theoretical accounts mentioned in the Taylor text ( entire whole number theoretical account. 0-1 whole number theoretical account. assorted integer theoretical account ) . In your ain words. distinguish these.

Many combinative jobs can be stated as Linear programming jobs with the demand which is over and above the bing as that all or some of the variables can merely hold built-in values. As per Taylor in his book of Management Science. the Integer Linear Programming ( ILP ) can be divided into three classs as given below – • Total Integer Model – In this type of ILP. all the variables are whole numbers. The job does non hold any relaxation for denary consequences. The theoretical account is designed to ensue in whole Numberss or the end product is either rounded up or down by using the logic provided in the job demands itself.

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• 0-1 Integer Model – This type of Linear Programming theoretical account is besides known every bit Boolean as the additive plan variables in this instance can take values 0 or 1. • Assorted Integer additive plan – This is another class of additive scheduling in which some of the lone some of the variables are allowed to be whole numbers. This standard in this instance is small relaxed in footings of consequences being obtained in decimals or whole Numberss ( Taylor. 2009 ) . 3. Explain the statement: Sensitivity analysis can be much more critical in whole number scheduling that it may be in traditional LPMs.

Integer plans for managerial analysis under conditions of uncertainness must be used with great attention. The trouble of executing systematic sensitiveness analyses on whole number theoretical accounts further limits the advantages of the theoretical account. Rounding uninterrupted additive programming solutions to whole numbers alternatively of utilizing an whole number programming modus operandi may take to non- optimum whole number solution. But such conditions do non needfully justify the usage of an whole number instead than a rounded linear programming solution for intents of managerial analysis.

Integer solution as an ideal it suggests that all relevant variables in the determination state of affairs have been decently incorporated in the theoretical account and the values of the coefficients are sufficiently accurate. The uncertainnesss of demand. monetary values. costs etc do such type of premises impractical and sensitiveness analysis is used as a direction tool to analyse the consequence of these uncertainnesss. The restriction in the usage of whole number scheduling is that in “in executing sensitiveness analysis on an whole number additive scheduling theoretical account. it may be necessary to trust on intuition and inventiveness instead than on systematic processs.

” Further. the trouble associated with measurement and construing double variables is still another job connected with the whole number scheduling ( Karlof. 2006 ) . 4. By and large talking. why is whole number ( additive ) programming preferred to merely rounding the solution determined by traditional LPMs? Are at that place any exclusions where merely rounding the additive scheduling solution is equal? If yes. explicate in concern content. During the preparation of any Linear Programing it is found that certain variables can be regarded as taking whole number values.

However. for the convenience interest they are regarded to be taking fractional values as they can be ignored because of high whole number values. Sometimes. this could be possible but there are instances when happening a numeral solution in which the variables take whole number values is necessary. As discussed. Integer Programming is advantageous. in state of affairss where solution need non be integer. when the fractions can be ignored. the LP with rounding off can be the best attack. For illustration. if the solution to a job comes to be 3. 55 chairs. the following best figure i. e. 3 can be chosen but its non the right determination as fraction is of higher value. Hence. an optimized figure demands to be arrived by utilizing integer additive scheduling.

However. if the reply to a job is 30000. 55 chairs so rounding it off to 30000 is all right as. 55 is a little fraction compared to the whole number. 30000 ( Karlof. 2006 ) . References Taylor. Bernard W ( 2008 ) . Introduction to Management Science. Prentice Hall. ISBN 0136064361. 9780136064367 Karlof. John K. ( 2006 ) . Integer Programing – Theory & A ; Practice. CRC Press. ISBN 0849319145. 9780849319143


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