WEEK-2 LINEAR PROGRAMMING Waheed Ullah PhD 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 RESOURCESTABLE (x1)CHAIR (x2)AVAILABLE WOOD LABOUR UNIT PROFIT68-

 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= 80 x1= 4 TABLES

WOOD CONSTRAINT

LABOR CONSTRAINT

THANK YOU QUESTIONS ? IF ANY ?