Opn Research by Prof Narang

8/3/2019 Opn Research by Prof Narang

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Role Of Operations

Research

In

Managerial DecisionMaking


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Management ScienceOperations ResearchOperational Research

Operations Analysis

It is sometimes believed that operationsresearch refers to constant monitoring of anorganization's ongoing activities such asproduction scheduling and inventory control,facility maintenance and repair, staffing of service facilities etc.

Whereas many management science studies treatother kind of decisions that bear on daily operationsonly indirectly. These studies usually have planningorientation. For example determining the breadth of a firms product line, developing a long term plan

for plant expansion, designing a network of warehouses for a wholesale distribution system,entering a new business by merger or acquisition


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Some Definitions Of

Operations Research1. O.R.Deals with systematic and

scientific research on the operationsof a system .(Mccloskey andTrefethen)

2. O.R. Is the application of scientificmethods, techniques, and tools toproblems involving the operations of asystem so as to provide those incontrol of the system with optimumsolution to the problem.(Churchmann,Ackoff and Arnoff).

3. O.R. Is a scientific approach toproblem solving for executivemanagement. (H.M.Wagner).

4. O.R. Is the art of giving bad answersto problems to which worst answerare sought otherwise. (T.L.Saaty).


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Major O.R.Techniques

1. Linear Programming2. Transportation Models

3. Assignment Models4. Other Mathematical Programming

Techniques Like Goal, Integer,Dynamic Etc

5. Network Techniques LikePERT/CPM Etc.

6. Queuing Theory7. Inventory Management8. Simulation

9. Markov Chains10. Game Theory


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Characteristics Of O.R.

1. Inter-disciplinary Team Approach

2. Holistic Approach To The System

3. Focus On Decision Making


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Phases Of An O.R. Study

1. Identifying The Problem

2. Building A Model

3. Finding The Solution

4. Testing The Model And TheSolution

5. Establishing Control Limits

6. Implementation


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Areas Of Applications OfOperations Research

(Schumacher-Smith Survey)

Forecasting 73Production Scheduling 90Inventory Control 90Quality Control 51Transportation 54

Advertising And Sales Research 27Maintenance And Repairs 32Accounting Procedures 17Plant Location 32Equipment Replacement 27Packaging 7

Capital Budgeting 39

Percent Of

Companies Area Of ApplicationReporting

Activities


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Frequency Of Use

ool/Tech Never Moderate Frequent

atistical Analysis 20 30 75

omputer Simulation 16 57 52ERT/CPM 22 45 58

ventory Mgt. Techniques 22 39 64

inear Programming 30 47 48

ueuing Theory 46 46 33

on-linear Programming 68 39 18

ynamic Programming 62 37 26

ame Theory 64 37 24

(No. Of Companies)

Source:- An Unpublished MBA (Part Time )Project, 1999.

Usage Of OR Techniques Among 125 Companies


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Operations Research Software Available

Bernard W.Taylor, Management Science, Prentice-Hall,Inc., Englewood Cliffs, New Jersey (Contains AB:QM 4.0 By Sang Lee), 1996.

Hamdy A.Taha, Operations Research : An Introduction,Prentice-Hall Of India, New Delhi, (Contains Tora AndSimmnetI1),1995.

Sang M.Lee and Jung P.Shim, Micro ManagementScience, Allyn and Bacon, (Contains Micro Manager

Version2.0),1990.

Yih-long Chang, Quantitative Systems (QS) Version 3.0,Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1995.

Yih-long Chang, Quantitative Systems For Business Plus

(QSB+) Version 3.0, Prentice-Hall, Inc., EnglewoodCliffs,NewJersey,1994.


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enerationTimerame

Description

rst/ 930s-940s

Emphasized The Applications Of The Scientific MethodsTo Problems Involving Operations Of Systems. OR TeamsWere Interdisciplinary And Addressed Complex Problems.

econd / 950s

Emphasized Mathematical/Optimization Techniques.Scientific Methods Still Employed And Computers BeganTo Be Integrated Into Tool Box.

hird/ 960s

Those Who Emphasized Heuristics Programming And Ai-based Methodology Separated From OR, Thus CreatingTwo Approaches To Satisficing. Multiple ObjectiveOptimization And Goal Programming Reflected TheChange In OR. OR Associated With Quantitative; AI WithQualitative.

ourth/ 970s-resent

DSS And ES Methodologies Symbolize This Generation. ESWere Developed By AI In Response To Difficulties It HadEncountered; DSS By MS/OR. Decision Maker In BothCases Becoming More Involved.

fth/?

There Is Now A Realization That To Solve A Larger Set Of Real -World "problems, And So Make A SignificantImpact On Decision Making Technology, One Needs ToEmploy A Much Larger Combination Of Techniques AndTools, Dependent Upon The Situation. Artificial BarriersAnd Constraints Of The Discipline; Should Not BeInhibiting.

The Five Generations Of OR


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ORS FORMULATION APPLIED SCIENTIFIC

METHOD TO PROBLEMSINVOLVING OPERATIONS

OF COMPLEX SYESTEMS(CS)

ATTEMPTED TO USEMATHEMATICAL/ OPTIMIZATION

TECHNIQUES TO SOLVEPROBLEMS INVOLVING

OPERATIONS OF CS

QUANTITATIVE METHODOLOGYAPPLIED TO SOME SUBSETOF PROBLEMS INVOLVING

OPERATIONS OF CS

FIRST GENERATION

SYNERGY OF ALL SCHOOLS OFTHOUGHT

QUANTITATIVE QUALITATIVE

CLASSICAL OR AI

MS/OR/DSS AI/ES

OTHER RELEVANT PARADIGMS

DSS DEVELOPED IN

RESPONSE TO THE LIMITEDSUCCESS ACHIEVED BYTHE

PREVIOUS GENERATION

QUALITATIVE METHODOLOGYAPPLIED TO LARGE CLASS OF

PROBLEMS(GENERAL PROBLEMSOLVERS-GPS)

ES DEVELOPED IN RESPONSETO THE LACK OF SUCCESS INCREATING GPS IN

PREVIOUS GENERATION

CLASSICAL OR

THIRD GENERATION

EARLY OR

SECOND GENERATION

THE FIVE GENERATIONS OF OR

MS/OR

FOURTH GENERATION

SOR(SYNERGISTICOR)

FIFTH GENERATION

( 1930s-1940

( 1950

( 1970s)-PRESEN

AI/E

( 196

AI

(?)


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Some Definitions Of LinearProgramming

1. A Method To Allocate Limited Resources InAn Optimal Manner So As To Satisfy TheLaws Of Supply And Demand For The FirmsProducts.

2. A Method To Optimize A Linear FunctionSubject To Set Of Linear Constraints.

3. Yet Another Class Of OptimizationTechniques.


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Janata fertilizers uses nitrates, phosphates,potash and an inert filler material for fertilizermanufacture. The firm mixes these fouringredients to make two basic fertilizers, 5-10-5and 6-5-10 (nos. represent % wt. Of nitrates,

phosphates and potash in each tonne of fertilizers). The contribution towards profitsand overheads is Rs.300 and Rs.400 per tonnefor (5-10-5) and (6-5-10) respectively. The firmhas 120 tonnes of nitrates ,200 tonnes of

phosphates, 150 tonnes of potash and unlimitedfiller material. They will not receive additionalchemicals until next month. They believe thatthey can sell or store at negligible cost allfertilizer produced during the month.

Determine optimal product mix.


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Ing.A Ing.B

Cost/kg. Rs.10 Rs.40

Fiber content 25% 75%

Fat content 20% 10%

A state agricultural federation manufacturesand markets cattle feed. It uses two ingredientswhich have the following characteristics

Specifications are that fiber content should beat least 50% and fat content should not exceed18% in every one kg. Of the feed. Whatamounts of A and B should be used so thatcost/kg. is minimized?


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PROBLEM-I

5-10-5 6-5-10 Available

NITRATES 5% 6% 120 TONNES

PHOSPHATES 10% 5% 200 TONNES

POTASH 5% 10% 150 TONNES

CONTRIBUTION Rs.300 Rs.400Per Tonne


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Problem-2

Ing.A Ing.B

Cost/Kg. Rs.10 Rs.40

Fiber 25% 75%

Fat 20% 10%

Required

Fiber Content At least 50%Fat Content - Not More Then 18%


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A MEDIA PLANNING PROBLEM

EXPOSURE RATESTA TB

MAGAZINE 2% 1%(Rs.80,000)

TV COMMERCIAL 1% 3%(Rs.3,20,000)

MINIMAL EXPOSURE 50% 30%

A PRODUCT MIX PROBLEM

A COSTS RS.150/- PER PAIRB COSTS RS.100/- PER PAIR

BUYER WANTS:-

1. EXACTLY 5000 PAIRS2. NOT MORE THAN 2000 PAIRS OF A3. FOR EVERY ONE PAIR OF A NOT MORE

THAN TWO PAIRS OF BOBJECTIVE: MINIMIZE THE COSTS


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A Product Mix Problem

Cont/Pair Rs 150 Rs.100

HIKING BOOTS SKING BOOTS AVAILABLEEWING 2 3 13 HOURTRETCHING 5 2 16 HOURS

SOLUTION :- HB-2, SB-3TC = Rs 600.

Another Product Mix Problem

Cont/Pair Rs.100 Rs.150

A( moccasin) B (derby)

Cutting & 100 Or 150Upper Closing

Lasting 50 Or 200

Sole Adhesion 250 Or 125

Solution :- A - 21.42857B - 114.2857TC Rs 19285.71


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PRODUCTS MATERIALS CONT/UNITA B C

P1 1 2 3 Rs.3P

2 2 1 1 Rs.4

P3 3 2 1 Rs.5AVAILABLE 10 12 15

PRIMAL PROBLEMMAX Z = 3X 1+4X 2+5X 3

X1+2X 2+3X 3< 102X 1+X 2+2X 3< 123X 1+X 2+X 3< 15X1, X 2, X 3 > 0

SV CONT Q 3 4 5 0 0 0

COEFF. X 1 X2 X3 S1 S2S2 0 1 0 0 4/5 -1/5 1 -3/X1 3 4 1 0 -1/5 -1/5 0 2/X2 4 3 0 1 8/5 3/5 0 -1

OC -4/5 -9/5 -2

DUAL PROBLEMMm Z* = 10Y 1+12Y 2+15Y 3

Y1+2Y 2+3Y 3 > 32Y 1+Y 2+Y 3 > 43Y 1+2Y 2+Y 3 > 5Y1, Y 2,Y 3 > 0


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SV COST Q 10 12 15 0 0 0COEFF. Y 1 Y2 Y3 S1 S2

Y3 15 2/5 0 3/5 1 -2/5 1/5 0S3 0 4/5 0 -4/5 0 1/5 -8/5 1Y1 10 9/5 1 1/5 0 1/5 -3/5 0

OC 1 4 3


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Applications Of Linear Programming InProduction Management

1. Product Mix

2 Production Smoothing

3. Assembly Line Balancing

4. Sub Contracting

5. Some Purchasing Decisions6. Location Of Production Facilities

Applications Of Linear Programming InMarketing Management

1. Media Planning

2. Routing Of Salesmen

3. Physical Distribution

4. Warehousing Decisions


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APPLICATIONS OF LINEAR PRORAMMINGIN FINANCIAL MANAGEMENT

1. Capital Budgeting

2. Financing Decisions

3. Portfolio Selection4. Profit Planning

5. Financial Audit

Applications Of Linear Programming

In Personnel Management1. Job Assignment

2. Manpower Scheduling

3. Manpower Planning

4. Equitable Salaries

5. Manpower Deployment


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Limitations Of Linear Programming

1. Linearity

2. Additivity

3. Continuity

4. Certainty

5. Single Objective


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A TOOTHPICK MANUFACTURER MAKES TWO KINDS OFTOOTHPICKS: ROUNDS AND FLATS. MAJOR PRODUCTIONFACILITIES INVOLVED ARE CUTTING AND PACKING. THECUTTING DEPARTMENT CAN PROCESS 300 BOXES OF ROUNDSOR 600 BOXES FLATS PER HOUR. THE PACKING DEPARTMENTCAN PACKAGE 600 BOXES OF ROUNDS OR 300 BOXES OFFLATS PER HOUR.

IF THE CONTRIBUTION OF PROFIT FOR A BOX OF ROUNDSIS EXACTLY SAME AS THAT FOR A BOX OF FLATS, WHAT ISTHE OPTIMUM PRODUCTION LEVEL?

UNDER WHAT CIRCUMSTANCES WOULD THEMANUFACTURER BE BETTER OFF TO PRODUCE ONLYROUNDS?

A TRUCKING FIRM HAS RECEIVED AN ORDER TO MOVE 3,000TONNES OF INDUSTRIAL MATERIAL TO A DESTINATION 1,000KM. AWAY. THE FIRM HAS AVAILABLE AT THE MOMENT AFLEET OF 150 CLASS A 15 TONNE TRAILER TRUCKS ANDANOTHER FLEET OF 100 CLASS B 10 TONNE TRAILER TRUCKS.THE OPERATING COSTS OF THESE TRUCKS ARE RS. 3 AND RS.4 PER TONNE KM RESPECTIVELY. BASED ON PASTEXPERIENCE, THE FIRM HAS A POLICY OF RETAINING ATLEAST ONE CLASS-A TRUCK WITH EVERY TWO CLASS-BTRUCKS IN RESERVE. IT DESIRES TO KNOW HOW MANY OF

THE TWO CLASSES OF VEHICLES SHOULD BE DISPATCHEDTO MOVE THE MATERIALS AT MINIMAL OPERATING COSTS.


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A FARMER HAS A 100- HECTARE FARM. HE CANSELL ALL THE TOMATOES, LETTUCE, OR RADISHESHE CAN RAISE. THE PRICE HE CAN OBTAIN IS RE.1PER KILOGRAM FOR TOMATOES, RE. 0.75 A HEADFOR LETTUCE AND RS. 2 PER KILOGRAM FORRADISHES. THE AVERAGE YIELD PER HECTARE IS2,000 KILOGRAM OF TOMATOES, 3000 HEADS OFLETTUCE AND 1,000 KILOGRAMS OF RADISHES.FERTILIZER IS AVAILABLE AT RE. 0.50 PERKILOGRAM AND THE AMOUNT REQUIRED PERHECTARE IS 100 KILOGRAMS EACH FOR TOMATOESAND LETTUCE AND 50 KILOGRAMS FOR RADISHES.LABOUR REQUIRED FOR SOWING, CULTIVATINGAND HARVESTING PER HECTARE IS 5 MAN-DAYSEACH FOR TOMATOES AND RADISHES AND 6 MAN-DAYS FOR LETTUCE. A TOTAL OF 400 MAN-DAYS OFLABOUR ARE AVAILABLE AT RS.20 PER MAN-DAY.FORMULATE THIS PROBLEM AS A LINEARPROGRAMMING MODEL TO MAXIMIZE THEFARMERS TOTAL PROFIT.


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FOUR PRDUCTS HAVE TO BE PROCESSED THROUGHTHE PLANT, THE QUANTITIES REQUIRED FOR THE

NEXT PRODUCTION PERIOD BEING:PRODUCT 1 2,000 UNITSPRODUCT 2 3,000 UNITSPRODUCT 3 3,000 UNITSPRODUCT 4 6,000 UNITS

THERE ARE THREE PRODUCTION LINES ON WHICH THEPRODUCTS COULD BE PROCESSED. THE RATES FORPRODUCTION IN UNITS PER DAY AND THE TOTALAVAILABLE CAPACITY IN DAYS ARE GIVEN IN THEFOLLOWING TABLE. THE COST OF USING THE LINES ISRS. 600, RS. 500, RS. 400 PER DAY,RESPECTIVELY,

ASSIGNMENT OF FOUR PRODUCTS: RATES OFPRODUCTION IN UNITS PER DAY.

PRODUCTION PRODUCT MAX.LINELINE 1 2 3 4 CAPACITY(DAYS)

A 150 100 500 400 20B 200 100 760 400 20C 160 80 890 600 18

FORMULATE THE ABOVE AS A LINEAR PROGRAMMINGPROBLEM TO MINIMIZE THE COST OF PRODUCTION


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PRQ FEED COMPANY MARKETS TWO FEED MIXESFOR CATTLE. THE FIRST MIX, FERTILEX, REQUIRESAT LEAST TWICE AS MUCH WHEAT AS BARLEY. THESECOND MIX, MULTIPLEX REQUIRES AT LEASTTWICE AS MUCH BARELY AS WHEAT. WHEAT COSTSRS.1.50 PER KG. AND ONLY 1,000 KG. ARE AVAILABLE

THIS MONTH. BARLEY COSTS RS. 1.25 PER KG. AND1200 KG. ARE AVAILABLE. FERTILEX SELLS FORRS.1.80 PER KG. UPTO 99 KG, AND EACH ADDITIONALKG. OVER 99 KG. SELLS FOR RS.1.65. MULTIPLEXSELLS AT RS. 1.70 PER KG. UPTO 99 KG. AND EACHADDITIONAL KG.OVER 99 KG. SELLS FOR RS.1.55.

BHARAT FARMS WILL BUY ANY AND ALL AMOUNTSOF BOTH MIXES PQR FEED COMPANY WILL MIX. SETUP THE LINEAR PROGRAMMING PROBLEM TODETERMINE THE PRODUCE MIX THAT RESULTS INMAXIMUM PROFITS .


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A MANUFACTURER HAS CONTRACTED TO PRODUCE 2,000 UNITSOF A PARTICULER PRODUCT OVER THE NEXT EIGHT MONTHS.

DELIVERIES ARE SCHEDULED AS FOLLOW:JANUARY 100FEBRUARY 200MARCH 300APRIL 400MAY 100JUNE 100JULY 500AUGUST 300

TOTAL 2,000

THE MANUFACTURER HAS ESTIMATED THAT IT COSTS HIM RE.1 TO STORE ONE UNIT OF PRODUCT FOR ONE MONTH. HE HAS AWAREHOUSE CAPACITY OF 300 UNITS.

THE MANUFACTURER CAN PRODUCE ANY NUMBER OF UNITS INA GIVEN MONTH, SINCE THE UNIT CAN BE PRODUCED MOSTLYWITH PART-TIME LABOUR, WHICH CAN BE EASILY OBTAINED.HOWEVER,THERE ARE THE COST OF TRANING NEWPERSONNEL AND COSTS ASSOCIATED WITH LAYING OFFPERSONNEL WHO HAVE BEEN HIRED. THE MANUFACTURERHAS ESTIMATED THAT IT COSTS APPOXIMATELY 75 PAISE PERUNIT TO INCRESE THE PRODUCTION LEVEL FROM ONE MONTHTO THE NEXT(E.G. IF PRODUCTION IN JANUARY IS 200 AND ISINCREASED TO 300 IN FEBRUARY, THE COST IS RS.75 FORTRANING THE ADDITIONAL PEOPLE REQUIRED TO PRODUCE

AT THE 300 UNIT LEVEL.)SIMILARLY IT COSTS 50 PAISE PERUNIT TO REDUCE PRODUCTION FROM ONE MONTH TO THENEXT. (AT THE END OF EIGHT MONTHS, ALL EMPLOYEE WILLBE LAID OFF WITH THE CORRESPONDING PRODUCTION-REDUCTION COSTS). ASSUME THE PRODUCTION LEVEL BEFORE

JANUARY IS ZERO .FORMULATE THE ABOVE AS A LINEAR PROGRAMMINGPROBLEM.


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Transportation Models

There are a number of availabilitycentres such as factories, warehouses etc.With known availabilities.

There are a number of consumptioncentres such as warehouses, markets etc.With known requirements.

The distribution cost (freight, handlingcosts etc.) Per unit from an availabilitycentre to a consumption centre is given

The problem is to find an optimaldistribution plan i.e. how many units

should be allocated from which availabilitycentre to which consumption centre so thatthe total distribution cost is minimized

.

Single commodity

Direct shipment


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The Assignment Model

The assignment model is a special type of linear programming problem in which nitems are assigned among n receivers, oneitem to a receiver,such that the total returnresulting from the assignment is optimized.

The returns associated with eachassignment are assumed to be known andindependent of each other.

Ex-1 A marketing manager may have foursalesmen and four sales territories. Whichassignment will help in maximizing sales?

Ex-2 A foreman may have five mechanicsand five jobs, how the assignment shouldbe made so as to minimize the total timetaken for completing the jobs.


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AN ASSIGNMENT PROBLEMWORKERS

I II III IV

A 16 15 18OBS B 13 16 14

C 14 13 11D 16 18 17

A ROUTING PROBLEM

TO CITYA B C D E

A - 4 7 4ROM B 4 - 3 4ITY C 7 6 - 7

D 3 7 - 7E 4 5 7 -

TO/ FROM D E F G CAPACIT

A 42 48 38 37 160

B 40 49 52 51 150

C 39 38 40 43 190

REQD. 80 90 110 220 500/500

160

10 6080

80110

A TRANSPORTATION PROBLEMWAREHOUSES

14

12

3

5

12

15

6

34

ACTORIES


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For Maximization Case

The numerical value of a given objectivefunction with respect to the integer solutioncan never exceed the numerical value of that objective function with respect to thenon-integer solution.

For Minimization Case

The numerical value of a given objectivefunction with respect to the integer solutioncan never be less than the numerical value of that objective function with respect to thenon-integer solution.


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The cutting division of the photo filmcorporation requisitions from stock controldepartment plastic films of 85 feet (fixed unitlength) which can be cut according to two

patterns. First pattern will cut each film lengthinto 35 feet pieces with the remaining 15 feet toscrap. Second pattern will cut each film lengthinto a 35 feet piece and two 25 feet pieces withnothing to scrap. The present order from a

customer is for 8 pieces of 35 feet length and 6pieces of 25 feet length. What minimum numberof plastic films of 85 feet should be cut to meetcustomer requirement?


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Problems On Integer Linear Programming

1. The ABC company requires an outputof at least 200 unit of a product per day andto accomplish this target it can buymachine A or B or both. Machine A costsRs.20,000 while machine B costs Rs.15,000and company has a budget of Rs.2,00,000for the same. Machines A and B willproduce 24 and 20 units respectively of thisproduct per day. However, machine A willrequire a floor space of 12 square feet while

machine B will require 18 square feet andcompany has total floor space of 180 squarefeet only. Determine the minimum numberof machines that should be purchased.


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ABC COMPANY HAS 4 INDEPENDENTNVESTMENT PROJECTS AND MUST ALLOCATE A

XED CAPITAL TO ONE OR MORE OF THEM SOHAT THE COMPANYS NET PRESENT VALUE ISAXIMIZED. THE ESTIMATED NET PRESENT VALUEND THE ANTICIPATED CASH OUTFLOWSSSOCIATED WITH THESE PROJECTS IS GIVEN INHE FOLLOWING TABLE:

NPV CASH OUTFLOWS(RS.1000)

PR. NO (RS. 1000) YEAR(I) YEAR(II)

1 100 50 150

2 50 105 30

3 140 318 143

4 90 100 68

IN SELECTING THESE PROJECTS, THE COMPANY ISONSTRAINED TO LIMIT ITS EXPENDITURE IN THE FIRSTEAR TO RS.5, 15,000 AND IN THE SECOND YEAR TO RS.38,000.

IF PROJECTS 1 AND 3 ARE MCTUALLY EXCLUSIVE,OW SHOULD THE INVESTMENT BE MADE SO THAT THEOTAL NET PRESENT VALUE IS MAXIMIZED?


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SET-UP COST PER MAX.

MACHINE COST(Rs) UNIT (Rs) PRODUCTION

1 8000 5 40002 5000 4 30003 4000 8 1000

QUANTITY REQUIRED:5000 UNITS AT MINIMUM COST.

PRODUCT

PLANT P Q R CAPACITY

A 35 24 20 600B 30 28 25 1,000C 20 25 37 800D 24 32 28 800

DEMAND 500 800 600


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1. GOALS HAVE PREEMPTIVE PRIORITIES.

2. MINIMIZE DEVIATIONS FROM GOALS.

3. ATTACH WEIGHTS TO DIFFERENTACTIVITIES AT THE SAME GOAL LEVEL.

BASIC CONCEPTS OF GOAL PROGRAMMING


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,UPHOLSTERY MATERIAL AND A REGULAR DRESSMATERIAL. THE UPHOLSTERY IS PRODUCED ACCORDINGTO DIRECT ORDERS FROM FURNITURE MANUFACTURERS.THE DRESS MATERIAL ON THE OTHER HAND, ISDISTRIBUTED TO RETAIL FABRIC STORES. AVERAGEPRODUCTION RATES FOR THE TWO MATERIALS ARE

IDENTICAL; 1000 METRES/HR. BY RUNNING TWO SHIFTS,NET OPERATIONAL CAPACITY OF THE PLANT IS 80HOURS/WK. THE MARKETING DEPARTMENT REPORTSTHAT THE MAXIMUM ESTIMATED SALES FOR THEFOLLOWING WEEK IS 70,000 M. OF UPHOLSTERY AND45,000 M. OF DRESS MATERIAL. ACCORDING TO THEACCOUNTING DEPARTMENT, THE APPROXIMATE PROFIT

FROM A METRE OF UPHOLSTERY MATERIAL IS RS.2.50 ANDFROM A METRE OF DRESS MATERIAL IS RS.1.50.

THE M.D. OF THE COMPANY BELIVES THAT A GOODEMPLOYER- EMPLOYEE RELATIONSHIP IS IMPORTANT INBUSINESS. HENCE HE DECIDES THAT A STABLEEMPLOYMENT LEVEL IS A PRIMARY GOAL FOR THE

FIRM. THEREFORE, WHENEVER THERE IS EXCESSDEMAND OVER NORMAL PRODUCTION, HE SIMPLYEXPANDS PRODUCTION CAPACITY BY PROVIDINGOVERTIME. HOWEVER HE FEELS THAT OVERTIME OFMORE THAN 10 HOURS/WK. SHOULD BE AVOIDEDBECAUSE OF ACCELERATING COSTS.

CONTD.P/2.


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FIRST GOAL : AVOID UNDER UTILISATION OFPRODUCTION CAPACITY,I.E. MAINTAIN STABLE EMPLOYMENT AT NORMALCAPACITY

SECOND GOAL : LIMIT OT OPERATION TO 10 HOURS. THIRD GOAL :ACHIEVE SALES GOALS OF 70,000 M. OF

UPHOLSTERY AND 45,000 M. OF DRESS MATERIAL. FOURTH GOAL : MINIMISE OT OPERATION AS MUCH AS

POSSIBLE. FORMULATE AND SOLVE THIS PROBLEM AS A GOAL

PROGRAMMING PROBLEM.


40/43

BHARAT TELEVISION COMPANY PRODUCES CTV SETS.IT HAS TWO PRODUCTION LINES. PRODUCTION RATEOF LINE-1 IS 2 SETS/HR. AND IT IS 1.1/2 SETS/ HR. INLINE-2. THE REGULAR PRODUCTION CAPACITY IS 40HR./WK. FOR BOTH LINES. EXPECTED PROFIT FROM ANAVERAGE CTV SET IS RS.1000/- . THE TOPMANAGEMENT OF THE FIRM HAS THE FOLLOWINGGOALS FOR THE WEEK (IN ORDINAL RANKING):

GOAL -1: PRODUCTION GOAL 180 SETS.GOAL 2 : LIMIT OT OF LINE-1 TO 10 HOURS.GOAL 3 : AVOID UNDERUTILISATION OF

REGULAR WORKING HOURS FORBOTH LINES.

GOAL 4 : LIMIT THE SUM OF OT FOR BOTHLINES. (ASSIGN WTS. ACCORDING TO

RELATIVE COST OF OT HOUR. ASSUMECOST OF OPREATIONS IS IDENTICALFOR BOTH PRODUCTION LINES)

FORMULATE THE PROBLEM AS A GLP MODEL. IFTHE TOP MANAGEMENT DESIRES TO PUT A PROFITGOAL OF RS.1,90,000 FOR THE WEEK AS THE TOPPRIORITY GOAL ABOVE THE STATED FOUR GOALS,HOW WOULD THE MODEL CHANGE.


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APPLICATION AREAS OF GOAL PROGRAMMING

GOAL PROGRAMMING HAS BEEN WIDELY APPLIED TOVARIOUS DECISION PROBLEMS IN BUSINESS FIRMS,GOVERNMENT AGENCIES, AND NON PROFIT INSTITUTIONS.SOME OF THE BEST KNOWN APPLICATIONS OF GOALPROGRAMMING INCLUDE THE FOLLOWING PROBLEMAREAS: ACADEMIC PLANNING AND

ADMINISTRATION ACCOUNTING ANALYSIS ADVERTISING MEDIA

SCHEDULING BLOOD COLLECTION ANDDISTRIBUTION

CAPITAL BUDGETING COMPUTER RESOURCE

PLANNING ANDALLOCATION

DECISION-SUPPORT

SYSTEM DESIGN ECONOMIC POLICYANALYSIS

EDUCATIONAL SYSTEMPLANNING

ENVIRONMENTALPROTECTION

PORTFOLIO

DETERMINATION PRODUCTION SCHEDULING PROJECT SCHEDULING QUALITY CONTROL

FACILITIES LOCATION ANDLAYOUT PLANNING

FINANCIAL PLANING HEALTH-CARE DELIVERY

SYESTEM DESIGN INVENTORY MANAGEMENT LOCATION AND

ALLOCATION DECISIONS MANPOWER PLANNING MARKETING LOGISTICS MILITARY STRATEGIES

AND PLANNING

NETWORK SCHEDULING ORGANIZATIONAL

ANALYSIS PERSONNEL

ADMINISTRATION POLICY ANALYSIS RESEARCH AND

DEVELOPMENT TRANSPORTATION

LOGISTICS URBAN PLANNING WATER RESOURCES

PLANNING


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OCATION 1 2 3 4 5 6 7

1 - 12 27 14 45 36 15

2 - 10 25 32 M 22

3 - 28 50 28 10

4 - 16 20 32

5 - 26 35

6 - 20

7 -.

TOTAL OF 30, 50 & 20 TONNES OF THIS COMMODITY ARETO BE SENT FROM LOCATIONS 1, 2 & 3 RESPECTIVELY. ATOTAL OF 15, 30 25 & 30 TONNES ARE TO BE SENT TOLOCATIONS 4, 5, 6 & 7 RESPECTIVELY. SHIPMENTS CAN BESENT THROUGH INTERMEDIATE LOCATIONS AT A COSTEQUAL TO THE SUM OF THE COSTS FOR EACH OF THE LEGSOF THE JOURNEY. THE PROBLEM IS TO DETERMINE THE

A CERTAIN CORPORATION MUST SHIP A CERTAINPERISHABLE COMMODITY FROM LOCATIONS 1, 2, 3, TOLOCATIONS 4, 5, 6 &7. A

THE AIR FREIGHT PER TONNE (IN 100 RS.)BETWEEN SEVEN LOCATIONS IS GIVEN IN THE FOLLOWINGTABLE. WHERE NO DIRECT AIR FREIGHT SERVICE ISAVAILABLE, A VERY HIGH COST M HAS BEEN USED.


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A PROBLEM ON DYNAMIC PROGRAMMING

A GOVERNMENT SPACE PROJECT IS CONDUCTINGRESEARCH ON A CERTAIN ENGINEERING PROBLEM THATMUST BE SOLVED BEFORE MAN CAN FLY TO THE MOONSAFELY. THREE RESEARCH TEAMS ARE CURRENTLYTRYING THREE DIFFERENT APPROACHES FOR SOLVINGTHIS PROBLEM THE ESTIMATE HAS BEEN MADE THATUNDER PRESENT CIRCUMSTANCES, THE PROBABILITYTHAT THE RESPECTIVE TEAMS-CALL THEM A,B AND C

WILL NOT SUCCEED IS 0.40,0.60 AND 0.80 RESPECTIVELY.THUS THE CURRENT PROBABILITY THAT ALL THE THREETEAMS WILL FAIL IS= 0.192. SINCE THE OBJECTIVE IS TOMINIMIZE THIS PROBABILITY THE DECISION HAS BEENMADE TO ASSIGN TWO MORE TOP SCIENTISTS AMONG THETHREE TEAMS IN ORDER TO LOWER IT AS MUCH ASPOSSIBLE. THE FOLLOWING TABLES GIVES THEESTIMATED PROBABILITIES OF FAILURE WHEN 0, 1 AND 2

.SCIENTISTS ARE ADDED TO THE TEAMS.TEAM

A B CNO.OF 0 0.40 0.60 0.80NEW SCIENTISTS 1 0.20 0.40 0.50

2 0.15 0.20 0.30

HOW SHOULD THE TWO SCIENTISTS BE ALLOCATED TTHE TEAMS?

Opn Research by Prof Narang

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