WEEK-2

LINEAR PROGRAMMING

Waheed UllahPhD Scholar

INU

PRESENTATION OUTCOMES; WHAT IS LINEAR PROGRAM? OBJECTIVE/ PURPOSE OF LP CHARACTERISTICS/ WHERE TO USE? EXAMPLE

What is LP? It is a Mathematical programming which is

used to find the best or optimal solution to a problem that requires a decision or set of decisions about how best to use a set of limited resources to achieve a state goal of objectives.

PURPOSE & OBJECTIVE SCARCE RESOURCES LP IS A METHOD OF ALLOCATING

RESOURCES IN A OPTIMAL WAY LP IS A DECISION AIDING TOOL WIDELY

USED IN INDUSTRY FOR DRAWING INFERENCE

OBJECTIVE FUNCTION COSTS CAN BE MINIMIZED PROFITS CAN BE MAXIMIZED

CHARACTERISTIC AND USAGE (Production Management) PRODUCT MIX

TO DETERMINE THE QUANTITY OF EACH PRODUCT

PRODUCTION PLANNING TO DETERMINE THE MINIMUM COST

PRODUCTION PLAN WITH AN ITEM FLUCTUATIN DEMAND

ASSEMBLY LINE BALANCING TO MINIMIZE THE TOTAL ELAPSE TIME

PORTFOLIO SELECTION TO FIND THE ALLOCATION OF WHICH

MAXIMIZES THE TOTAL EXPECETED RETURN OR MINIMIZE THE RISK UNDER CERTAIN LIMITATIONS

PROFIT PLANNING MAXIMIZATION OF THR PROFIT MARGING FROM

INVESTMENT IN PLANT FACILITIES AND EQUIPMENTS, CASH IN HAND, & INVENTORY

(FINANCIAL MANAGEMENT)

MEDIA SELECTION TO DETERMINE THE ADVERTISING MEDIA MIX SO

AS TO MAXIMIZE THE EFFECTIVE EXPOSURE, SUBJECT TO LIMIT OF BUDGET, SPECIFIED EXPOSURE RATES TO DIFFERENT MARKET SEGMENT

TRAVELLING SALESMAN PROBLEM TO FIND THE SHOR5TEST ROUTE FROM A GIVEN

CITY TO EACH OF THE SPECIFIED CITIES & THEN RETURNING TO THE ORIGINAL POINT OF DEPARTURE, PROVIDED NO CITY WOULD BE VISITED TWICE

(MARKETING MANAGEMENT)

PHYSICAL DISTRIBUTION TO DETERMINE THE MOST ECONOMIC AND

EFFICIENT MANNER OF LOCATING MANUFACTURING PLANT & DISTRIBUTION CENTRE FOR PHYSICAL DISTRIBUTION

PROBLEMS (MARKETING MANAGEMENT)

STAFFING PROBLEM TO ALLOCATE OPTIMUM MANPOWER TO A

PARTICULAR JOB SO AS TO MINIMIZE THE TOTAL OVERTIME COST OR MANPOWER

EQUITABLE SALARIES TO DETERMINE EQUITABLE SALARIES & SALES

INCENTIVES JOB EVALUATION & SELECTION

SELECTION OF SUITABLE PERSON FOR A SPECIFIED JOB

(PERSONNEL MANAGEMENT)

EXAMPLE A FURNITURE MANUFACTURES PRODUCES

WOODEN TABLE & CHAIRS. UNIT PROFIT FOR TABLE – 6Rs/- UNIT PROFIT FOR CHAIR – 8Rs/-

LETS ASSUME THERE ARE ONLY TWO RESOURCES COMPANY

USES TO PRODUCE TABLE & CHAIR WOOD (BOARD FEET) LABOUR (HOUR)

IT TAKES 30 WOOD & 5 HOURS TO MAKE A TABLE &

20 WOOD (BF) & 10 HOURS TO MAKE A CHAIR THERE ARE 300 BOARDFEET OF WOOD

AVAILABLE & 110 HOURS OF LABOUR AVAILABLE THE COMPANY WISHES TO MAXIMIZE THE PROFIT

(OBJECTIVE VARIABLE) RESOURCES (WOOD & LABOUR) ARE DECISION

VARIABLES THE LIMITATION ON RESOURCES AVAILABILITY

FORM THE CONSTRAINT

SIMPLEX METHOD MOST COMMON WAY TO SOLVE THE

LARGE LP PROBLEMS MATHEMATICAL TERM SIMPLEX IS A LINE SEGMENT CONNECTING

TWO POINTS TWO DIMENSIONAL THREE DIMENSIONAL

EXAMPLE LP FORMULATION

RESOURCES TABLE (x1) CHAIR (x2) AVAILABLE

WOOD 30 20 300

LABOUR 5 10 110

UNIT PROFIT 6 8 -

TO SIMULTENIOUSLY SOLVE THE TWO CONSTRAINT EQUATION, FIRST MULTIPLY THE LABOUR EQUATION BY -2, & ADD IT TO THE WOOD EQUATION

30x1 + 20x2 = 300 (WOOD)-2(5x1 + 10x2 = 110) (LABOUR)

20x1 + 0 = 80x1 = 4 TABLES

WOOD CONSTRAINT

LABOR CONSTRAINT

THANK YOUQUESTIONS ? IF ANY ?