Linear Programming

RODUCT MIX (USING LINEAR PROGRAMMING):

Linear programming is a quantitative tool for optimal allocation of limited resources
amongst competing activities. It is perhaps the most popular amongst OPERATIONS RESEARCH techniques and has
found application in several functional areas of business- production, finance, marketing, distribution,
advertising and so forth.

Any resource allocation problem is characterised by specification of an objective such as minimising cost,
or maximising profit. The constraints can be of a financial, technological, marketing or anyother nature.

Linear programming involves formulating the problem in linear terms and solving it to provide a plan for
deploying the resources in an optimal manner.

This technique is being used by many managements to maximise the profit or to minimise the cost.
In earlier days, fomulating a linear programming model and solving the same was a tedious process.

frontsys software company has developed a tool called solver which will be used with MICROSOFT EXCEL
SPREADSHEETS to solve LINEAR PROGRAMMING MODELS. This is a very simple tool which can be used by
everyone who can use MICROSOFT EXCEL and understand little about formulating the constraints.

Bottom of Form

PRODUCT MIX USING LP FOR A SPINNING MILL

Let us assume C1,C2,C3 and C4 are quantities of four counts to be produced in cotton
TC1,TC2 and TC3 are quantities of three counts to be prodced in Poly/Cotton blend.

CX1,CX2,CX3 and CX4 are Contribution in US$/KG for four cotton counts. TCX1,TCX2 and
TCX3 are contribution IN US$/KG for three POLY/COTTON counts correspondigly.

HOW TO FORMULATE A LP MODEL: EXAMPLE

TARGET FUNCTION: (TO MAXIMISE)

(C1*CX1)+(C2*CX2)+(C3*CX3)+(C4*CX4)+(TC1*TCX1)+(TC2*TCX2)+(TC3*TCX3) = CONTBN. MAXIMUM

BY CHANGING : ( THE FOLLOWING QUANTITIES)
C1,C2,C3,C4,TC1,TC2,TC3

CONSTRAINTS:· C1+C2+C3+C4 less than or equal to 180 tons
· TC1+TC2 less than or equal to 100 tons
· C1 should be 19.6 tons ( committed to the customer)
· TC2 more than 19.6 tons ( committed to the customer)
· C1+C2+C3+C4 no of m/cs allotted should not be more than 20 (m/c constraint)
· TC1+TC2+TC3 no of m/cs allotted should not be more than 10 (m/c constraint)
· C1 less than or equal to 20
· C2 less than or equal to 20
· C3 less than or equal to 20
· C4 less than or equal to 20
· TC1 less than or equal to 10
· TC2 less than or equal to 10
· TC3 less than or equal to 10

HOW TO SOLVE THIS:

MICROSOFT EXCELL Spreadsheet has a tool called SOLVER. This can be
used to solve any LINEAR AND NON-LINEAR EQUATIONS.

· OPEN an EXCEL SHEET
· FEED the PARAMETERS in the Excell Sheet
· SELECT SOLVER in the Tools Menu, Now Solver parameters are seen
· SET the TARGET cell and it should contain the target function
· FEED the range of cells to be changed
· FEED the constraints
· press SOLVE, THE RESULTS ARE ALREADY THERE