data modelling and optimization report

7/28/2019 Data Modelling and Optimization Report

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2012-14

BATCH

APPLICATION OF LINEAR PROGRAMMING

ACROSS VARIOUS SECTORS CASE BASED

APPROACH

DECISION MODELLING AND OPTIMIZATION

TERM - III

SUBMITTED BY:

GROUP C-9

Suman Maity (12172)

Suvarna Ashwini Nagesh (12173)

Tahir Mushtaq H.M. (12174)

Varun Kumar (12175)Shreetha T.S. (12176)

Vinay A. Hamasagar (12175)

SUBMITTED TO:

Dr. Srilakshminarayan G.

Assistant Professor (QM &OR),

SDMIMD, Mysore

PROJECT REPORT


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APPLICATION OF LINEAR PROGRAMMING ACROSS VARIOUSSECTORSCASE BASED APPROACH

C-9

DECISION MODELLING AND OPTIMIZATION SDMIMD, MYSORE 1

CONTENTSEXECUTIVE SUMMARY .................................................................................................................... 3

INTRODUCTION TO LINEAR PROGAMMING ................................................................................ 4

NUMALIGARH REFINERY LIMITED USES LP FOR BLENDING OF PETROLEM PRODUCTS................................................................................................................................................................ 7

INTRODUCTION TO REFINERY INDUSTRY .............................................................................. 7

ABOUT NRL...................................................................................................................................... 7

PROBLEM DEFINITION .................................................................................................................. 8

MATHAMETICAL FORMULATION .............................................................................................. 9

SOLUTION......................................................................................................................................... 9

SENSITIVITY REPORT:-............................................................................................................... 11

RESULTS ......................................................................................................................................... 12

NESTLE USES LP TO INVENT NEW FORMULA FOR INFANT NUTRITION ........................... 13

INTRODUCTION TO FMCG.......................................................................................................... 13

SCOPE .............................................................................................................................................. 13

ABOUT NESTLE:............................................................................................................................ 14

PROBLEM DEFINITION ................................................................................................................ 16

MATHEMATICAL FORMULATION ............................................................................................ 16

SOLUTION....................................................................................................................................... 17

SENSITIVITY ANALYSIS ............................................................................................................. 18

SENSITIVITY REPORT FOR FORMULATION 1 .................................................................... 18



RESULTS ......................................................................................................................................... 19

OBSERVATIONS AND CONCLUSION........................................................................................ 20

ALLOCATING WORKERS TO MACHINES AND PROJECTS AT ACME FURNITURECOMPANY USING LP........................................................................................................................ 20

INTRODUCTION TO MANUFACTURING SECTOR.................................................................. 20

ABOUT ACME FURNITURE COMPANY .................................................................................... 20

HOW ACME FURNITURE COMPANY USES LINEAR PROGRAMMING? ............................. 21


MATHEMATICAL FORMULATION ............................................................................................ 23

SOLUTION....................................................................................................................................... 25

SENSITIVITY ANALYSIS ............................................................................................................. 28


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INTERPRETATION......................................................................................................................... 37

RESULTS ......................................................................................................................................... 37

CONCLUSION ................................................................................................................................. 38

OPTIMUM PRODUCT MIX AT DONUT SHOP OF WELCOMHERITAGE GROUP.................... 38

INTRODUCTION TO THE HOTEL INDUSTRY .......................................................................... 38

CLASSIFICATION OF HOTELS.................................................................................................... 38

MARKET SEGMENT.................................................................................................................. 40

PROPERTY TYPE ....................................................................................................................... 40

LEVEL OF SERVICES: ............................................................................................................... 41

OWNERSHIP AND AFFILIATION:........................................................................................... 41

AWARDING OF CLASS:................................................................................................................ 41

THREE STAR CATEGORIES:.................................................................................................... 42

FIVE STAR CATEGORIES:........................................................................................................ 43

FIVE STAR DELUXE CATEGORIES:....................................................................................... 43

ABOUT WELCOMHERITAGE GROUP........................................................................................ 43

LP APPLIED IN WELCOMHERITAGE GROUP .......................................................................... 44

HSBC- PORTFOLIO MANAGEMENT USING LP MODEL ............................................................ 47

INTRODUCTION TO BANKING INDUSTRY............................................................................. 47

About HSBC ..................................................................................................................................... 48

PORTFOLIO SELECTION FOR HSBC.......................................................................................... 48


RESULTS ......................................................................................................................................... 51

CONCLUSION ................................................................................................................................. 52


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EXECUTIVE SUMMARY

In this project we have tried to study the importance of Linear programming across varioussectors. The sectors that are covered are:

1) Refinery Sector2) FMCG Sector3) Manufacturing Sector4) Hotel Industry5) Banking Sector

The following companies have been included to study the use of Linear programming at therespective organisations. Hence it is a case based approach.

1)Numaligarh Refinery Limited2) Nestle India Limited

3) Acme Furniture Company4) WelcomHeritage Group5) HSBC Banking Plc.

We have used linear programming to address various concerns of the firms mentioned abovewith the help of different kinds of problems like diet problem, blending problem, assignment

problem, portfolio selection problem, etc.

The use of linear programming in such diverse industries depicts the importance of theSimplex method and the importance of studying LP for the future managers.


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INTRODUCTION TO LINEAR PROGAMMING

Linear programming is a mathematical method adopted to identify the optimum outcome

such as maximum profit or minimum cost in a given scenario. It is also known as linear

optimization. Linear programming can also be termed as the process of taking various linear

inequalities relating to some situation, and finding the "best" value obtainable under those

conditions. A typical example would be taking the limitations of materials and labour, and

then determining the "best" production levels for maximal profits under those conditions. It is

mainly used in the cases where list of requirements listed as mutually relative in terms of

linearity. More formally, linear programming is a technique for the optimization of

a linear objective function, subject to linear equality and linear inequality constraints.

Its feasible region is a convex polyhedron, which is a set defined as the intersection of

finitely many half spaces, each of which is defined by a linear inequality. Its objective

function is a real-valued affine function defined on this polyhedron. A linear

programming algorithm finds a point in the polyhedron where this function has the smallest

(or largest) value if such a point exists.

This linear programming technique has been developed by Russian Economist Leonid

Kantorovich in 1939. He developed this mathematical model during the time of World war(2) to plan expenditures and returns in order to reduce costs to the army and increase losses to

the enemy. The method was kept secret until 1947 when George B. Dantzig published

the simplex method and John von Neumann developed the theory ofduality as a linear

optimization solution, and applied it in the field of game theory. Postwar, many industries

found its use in their daily planning.

Uses:

Today, in "real life", linear programming is part of a very important area of mathematics

called "optimization techniques". This field of study (or at least the applied results of it) are

used every day in the organization and allocation of resources. Company management in

terms of planning, production, transportation, technology and other issues relies more on LP.

It is also used in micro economics. Certain special cases of linear programming, such

as network flow problems and multi commodity flow problems are considered important

enough to have generated much research on specialized algorithms for their solution. A
http://en.wikipedia.org/wiki/Linear_programming#Dualityhttp://en.wikipedia.org/wiki/Linear_programming#Duality


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number of algorithms for other types of optimization problems work by solving LP problems

as sub-problems.

Solving under graphical method:

The general process for solving linear-programming exercises is to graph the inequalities

(called the "constraints") to form a walled-off area on the x, y-plane (called the "feasibility

region"). Then you figure out the coordinates of the corners of this feasibility region (that is,

you find the intersection points of the various pairs of lines), and test these corner points in

the formula (called the "optimization equation") for which you're trying to find the highest or

lowest value.

It uses many methodologies for its calculations mainly

Simplex method and Interior point method

The simplex method: The simplex method has been the standard technique for solving a

linear program since the 1940's. In brief, the simplex method passes from vertex to vertex on

the boundary of the feasible polyhedron, repeatedly increasing the objective function until

either an optimal solution is found, or it is established that no solution exists. In principle, the

time required might be an exponential function of the number of variables, and this can

happen in some contrived cases. In practice, however, the method is highly efficient,

typically requiring a number of steps which is just a small multiple of the number of

variables. Linear programs in thousands or even millions of variables are routinely solved

using the simplex method on modern computers. Efficient, highly sophisticated

implementations are available in the form of computer software packages.

Interior-point methods: In 1979, Leonid Khaciyan presented the ellipsoid method,

guaranteed to solve any linear program in a number of steps which is a polynomial function

of the amount of data defining the linear program. Consequently, the ellipsoid method is

faster than the simplex method in contrived cases where the simplex method performs poorly.

In practice, however, the simplex method is far superior to the ellipsoid method. In 1984,

Narendra Karmarkar introduced an interior-point method for linear programming, combining

the desirable theoretical properties of the ellipsoid method and practical advantages of thesimplex method. Its success initiated an explosion in the development of interior-point


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methods. These do not pass from vertex to vertex, but pass only through the interior of the

feasible region. Though this property is easy to state, the analysis of interior-point methods is

a subtle subject which is much less easily understood than the behavior of the simplex

method. Interior-point methods are now generally considered competitive with the simplex

method in most, though not all, applications, and sophisticated software packages

implementing them are now available. Whether they will ultimately replace the simplex

method in industrial applications is not clear.

Apart from there are several other types which are as follows:

Integral problems Integer programming Path following algorithms etc.


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NUMALIGARH REFINERY LIMITED USES LP FOR

BLENDING OF PETROLEM PRODUCTS

INTRODUCTION TO REFINERY INDUSTRY

A typical modern Petroleum Refinery comprises a variety of complex processes and plants

depending upon the nature of crude oil being processed and the product slate. This study

deals with the refining of crude oil and the production of various bulk petroleum products.

Production and formulation of lubricating oils as also the manufacture of different petroleum

based specialities becomes, by itself, a subject with extensive coverage.

Current crude refining capacity estimated at 51.85 million tonne/annum is spread over 12

refineries. Petroleum refining industry being entirely in the public sector, is close knit, with a

high level of inter-refinery collaboration and information sharing through forum, such as the

Oil Co-ordination Committee, the Centre for High Technology, inter-refinery meetings and

others.

ABOUT NRL

Numaligarh Refinery Limited (NRL) is a subsidiary of M/s Bharat Petroleum Corporation

Limited (BPCL), a Central Public Sector Undertaking. NRL has an authorized capital of

Rs.1000 cores and the paid up capital is Rs.735.63 cores.

The Companys shareholding pattern as on 31-03-12 is given below:

Bharat Petroleum Corporation Limited - 61.65%

Oil India Ltd. - 26.00%

Government of Assam - 12.35%

NRL has a refinery at Numaligarh in the District of Golaghat in Assam with a refining

capacity of 3 MMTPA of crude oil.

The refinery products like Liquefied Petroleum Gas (LPG), High Speed Diesel (HSD),

Aviation Turbine Fuel (ATF), Superior Kerosene Oil (SKO) and Motor Spirit (MS) are


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marketed mainly through NRLs parent company, M/s BPCL, while some quantities are also

marketed through M/s IOCL and M/s HPCL. The other products like Naphtha, Raw

Petroleum Coke, Calcined Petroleum Coke and Sulphur are marketed directly by the

company or with the help of M/s BPCL

PROBLEM DEFINITION

NRL basically refine three types of oil. Light distilled, middle distilled, and heavy ends.

Under light distilled they produced LPG, Naphtha, and Motor spirit. Under middle distilled

they produced Aviation turbine fuel, superior kerosene oil, and high speed diesel. From heavy

end they produced raw petroleum coke, calcined petroleum coke, and sulfer. We are trying to

solve which product NRL should produce in what quantity to get maximum profit by

fulfilling the entire demand requirement. According to demand light distilled should not be

refine no more than 10% of total weight, middle distilled should not be refine no more than

75% and heavy end should not be more than 15%. Following table shows the information

about minimum requirement of each product, cost price, selling price

product Minimum

requirement

Selling price Cost price

Light distilled

LPG 96 1541 6000

Naphta 19 16320 6000

Motor spirit 185 30250 6000

Medium distilled

Aviation turbine fuel 132 74330 42138

Super kerosene oil 270 74400 42138High speed diesel 1848 37400 42138

Heavy end

Raw petroleum coke 50 7400 11000

Calcined petroleum co 44 33000 11000

sulfer 4 4015 11000


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Requirement of all product quantity are thousand metric ton (TMT), Because of

unavailability of cost prices we assume 3types of raw material is used for 3 different

products. Like medium distilled is made from crude oil. Total requirement is 3000TMT.

MATHAMETICAL FORMULATION

Objective function= MAX Z =(1541-6000)LPG+(16320-6000)NAPHTA+(30250-

6000)MOTOR SPIRIT+(74330-42138)ATF+(74400-42138)SKO+(37400-

42138)HSD+(7400-11000)RPC+(33000-11000)CPC+(4015-11000)SULPHER

Constraints:

1) LPG>=96TMT2) NAPHTA>=19TMT3) MOTOR SPIRIT >=185TMT4) ATF>=132TMT5) SKO>=270TMT6) HSD>=1848TMT7) RPC>=50TMT8) CPC>=44TMT9) SULPHER>=4TMT10)LPG+NAPHTA+MS


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Constarin

ts LHS

SIG

N RHS

lpg 1 96000 >= 96000

nafta 1 19000 >= 19000

motor

spirit 1 185000 >=

18500

0

aviation

turbine

fuel 1 132000 >=

13200

0

superior

kerosine

oil 1 270000 >=

27000

0

high

speeddisel 1 1848000 >=

18480

00

raw

petroleu

m coke 1 50000 >= 50000

calcined

petroleu

m coke 1 396000 >= 44000

sulfer 1 4000 >= 4000

min

requirem

ent of

light

distilled 1 1 1 300000


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SENSITIVITY REPORT:-

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$M$5 LPG 96000 0 1540 28709 1E+30

$N$5 NAPHTA 19000 0 16319 13930 1E+30

$O$5 MOTOR SPIRIT 185000 0 30249 1E+30 13930

$P$5 AVIATION TURBINE FUEL 132000 0 60020 57 1E+30

$Q$5 SUPERIOR KEROSINE OIL 270000 0 60077 1E+30 57

$R$5 HIGH SPEED DISEL 1848000 0 37399 22678 1E+30

$S$5 RAW PETROLEUM COKE 50000 0 7399 25600 1E+30

$T$5 CANCLIEND PETROLEUM COKE 396000 0 32999 1E+30 25600

$U$5 SULPHER 4000 0 4014 28985 1E+30

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$V$10 LPG 96000 -28709 96000

6.54836E-

12 96000

$V$11 NAPHTA 19000 -13930 19000

6.54836E-

12 19000

$V$12 MOTOR SPIRIT 185000 0 185000

6.54836E-

12 1E+30

$V$13 AVIATION TURBINE FUEL 132000 -57 132000

3.49246E-

10 132000

$V$14 SUPERIOR KEROSINE OIL 270000 0 270000

3.49246E-

10 1E+30

$V$15 HIGH SPEED DISEL 1848000 -22678 1848000

3.49246E-

10 1848000

$V$16 RAW PETROLEUM COKE 50000 -25600 50000 352000 50000

$V$17 CANCLIEND PETROLEUM COKE 396000 0 44000 352000 1E+30

$V$18 SULPHER 4000 -28985 4000 352000 4000

$V$19 MIN REQUIREMENT OF LIGHT DISTILLED 300000 -29828 03.49246E-

10 0

$V$20 MIN REQUIREMENT OF MEDIUM DISTILLED 2250000 0 0 0 1E+30

$V$21 MIN REQUIREMENT OF HEAVY END 450000 -27078 0

3.49246E-

10 0

$V$22 TOTAL REQUIREMENT 3000000 53032.5 3000000 1E+30

6.54836E-

11


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RESULTS

After doing LPP now we can see that if NRL produced 96000 ton of LPG, 19000 ton of

naptha,18500 ton of motor spirit,132000ton of ATF,270000 ton of SKO,1848000 ton of

HSD,50000 ton of RPC,396000 ton of CPC and 40000 ton of sulphur, the organisation can

make profit of1120,68,58,000.


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NESTLE USES LP TO INVENT NEW FORMULA FOR

INFANT NUTRITION

INTRODUCTION TO FMCG

Fast-moving consumer goods (FMCG) orconsumer packaged goods (CPG) are products

that are sold quickly or fully used up over a short period of days, weeks, or months, and

within one year, at relatively low cost. Examples include non-durable goods such as soft

drinks, toiletries, and grocery items. Though the absolute profit made on FMCG products is

relatively small, they generally sell in large quantities, so the cumulative profit on such

products can be substantial.

SCOPE

This The Fast Moving Consumer Goods (FMCG) industry in India is one of the largest

sectors in the country and over the years has been growing at a very steady pace. The sector

consists of consumer non-durable products which broadly consists, personal care, household

care and food & beverages. The Indian FMCG industry is largely classified as organised and

unorganised. This sector is also buoyed by intense competition. Besides competition, thisindustry is also marked by a robust distribution network coupled with increasing influx of

MNCs across the entire value chain sector continues to remain highly fragmented.

FMCG have a short shelf life, either as a result of high consumer demand or because the

product deteriorates rapidly. Some FMCGssuch as meat, fruits and vegetables, dairy

products, and baked goodsare highly perishable. Other goods such as alcohol, toiletries,

pre-packaged foods, soft drinks, and cleaning products have high turnoverrates. An excellent

example is a newspaperevery day's newspaper carries different content, making one

useless just one day later, necessitating a new purchase every day.

The following are the main characteristics of FMCGs:

From the consumers' perspective: Frequent purchase Low involvement (little or no effort to choose the item products with strong brand

loyalty are exceptions to this rule)
http://en.wikipedia.org/wiki/Soft_drinkhttp://en.wikipedia.org/wiki/Inventory_turnoverhttp://en.wikipedia.org/wiki/Newspaperhttp://en.wikipedia.org/wiki/Brand_loyaltyhttp://en.wikipedia.org/wiki/Brand_loyaltyhttp://en.wikipedia.org/wiki/Brand_loyaltyhttp://en.wikipedia.org/wiki/Brand_loyaltyhttp://en.wikipedia.org/wiki/Newspaperhttp://en.wikipedia.org/wiki/Inventory_turnoverhttp://en.wikipedia.org/wiki/Soft_drink


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Low price From the marketers perspective:

High volumes Low contribution margins Extensive distribution networks High stock turnover

ABOUT NESTLE:

Nestl's relationship with India dates back to 1912, when it began trading as The Nestl

Anglo-Swiss Condensed Milk Company (Export) Limited, importing and selling finished

products in the Indian market.

After India's independence in 1947, the economic policies of the Indian Government

emphasised the need for local production. Nestl responded to India's aspirations by forming

a company in India and set up its first factory in 1961 at Moga, Punjab, where the

Government wanted Nestl to develop the milk economy. Progress in Moga required the

introduction of Nestl's Agricultural Services to educate, advice and help the farmer in a

variety of aspects. From increasing the milk yield of their cows through improved dairy

farming methods, to irrigation, scientific crop management practices and helping with the

procurement of bank loans.

Nestl set up milk collection centres that would not only ensure prompt collection and pay

fair prices, but also instil amongst the community, a confidence in the dairy business.Progress involved the creation of prosperity on an on-going and sustainable basis that has
http://en.wikipedia.org/wiki/Contribution_marginhttp://en.wikipedia.org/wiki/Distribution_(business)http://en.wikipedia.org/wiki/Stock_turnoverhttp://en.wikipedia.org/wiki/Stock_turnoverhttp://en.wikipedia.org/wiki/Distribution_(business)http://en.wikipedia.org/wiki/Contribution_margin


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resulted in not just the transformation of Moga into a prosperous and vibrant milk district

today, but a thriving hub of industrial activity, as well.

Nestl has been a partner in India's growth for over nine decades now and has built a veryspecial relationship of trust and commitment with the people of India. The Company's

activities in India have facilitated direct and indirect employment and provides livelihood to

about one million people including farmers, suppliers of packaging materials, services and

other goods.

The Company continuously focuses its efforts to better understand the changing lifestyles of

India and anticipate consumer needs in order to provide Taste, Nutrition, Health and

Wellness through its product offerings. The culture of innovation and renovation within the

Company and access to the Nestl Group's proprietary technology/Brands expertise and the

extensive centralized Research and Development facilities gives it a distinct advantage in

these efforts. It helps the Company to create value that can be sustained over the long term by

offering consumers a wide variety of high quality, safe food products at affordable prices.

Nestl India manufactures products of truly international quality under internationally famous

brand names such as NESCAF, MAGGI, MILKYBAR, KIT KAT, BAR-ONE,

MILKMAID and NESTEA and in recent years the Company has also introduced products of

daily consumption and use such as NESTL Milk, NESTL SLIM Milk, NESTL Dahi and

NESTL Jeera Raita.

FMCG major Nestle India had an 20.83 % increase in its net profit at Rs 278.93 crore for the

fourth quarter ended December 31, 2012 on the back of good domestic and export

performance. The company had posted a net profit of Rs 230.83 crore in the same period of

2011. For the year ended December 31, 2012, the company posted a net profit of Rs 1,067.93crore, up 11.06 per cent from Rs 961.55 crore in 2011. Nestle employs 7,000 people in the

country and its products are sold in 40 lakh outlets across India.

Nestl India is a responsible organisation and facilitates initiatives that help to improve the

quality of life in the communities where it operates.


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PROBLEM DEFINITION

Three chickpea-based infant food formulations were designed using a efficiency ratio, net

protein ratio, and apparent protein digestibility was linear programming model to minimize

total cost while meeting the also performed. Results showed no significant protein efficienty

ratio or net FAO/ WHO requirements for lysine and sulfur amino acids. Each protein ratio

differences between the casein control and any of the formulation was prepared by cooking

and blending the ingredients into a experimental formulations tested. Although they were

produced at viscous paste that was later drum-dried and analyzed for chemical minimum cost,

all products complied with the infant food specifications composition. Biological evaluation

of protein quality by means of protein established by the Codex Alimentarius Commission.

MATHEMATICAL FORMULATION

Three types of restrictions were set upon the variables: 1) minimum and maximum quantities

of ingredients to be included, 2) amino acid supply of each ingredient, and 3) material

balance. The objective function established was: MinZ= Ywhere Z is the cost per kilogram of

each formulation,

Ingredients cost Lysine Cytine

Rice 34 .59 .52

Chickpea 40 1.46 .46

Methionine 1140 95

Soybean meal 56 3.19 1.46

Table presents the list of variables, ingredients, and costs at the time of formulation.For formulations 1 and 2, the only restriction imposed on the linear programming model was

X2 > 0.7, and the latter included banana and soybean meal. Restrictions on formulation 3

were a maximum of 50% chickpea (X2 < 0.5) and a minimum of 10%,soybean meal (X3 >

0.1).


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SOLUTION

FORMULATION

1

RICE CHICKPEA MYTHIONINE

Cost 0.297862 0.7 0.002138019

objective minimum cost 34.5 40 1140 40.71357959

Constraint

Ingredient limits 1 0.7 >= 0.7

Sulfur amino acid

requirements 0.52 0.46 95 0.68 >= 0.68

Lysine requirements 0.59 1.46 1.197738569 >= 1.06

overall limit 1 1 1 1 = 1

FORMULATION

2


Cost 0.00582 0.99079869 0.003381117

Objective 34.5 40 1140 43.68721748

Constraint

Ingredient limits 1 0.990798688 >= 0.7

Sulfur amino acid

requirements 0.52 0.46 95 0.78 >= 0.78

Lysine requirements 0.59 1.46 1.45 >= 1.45

overall limit 1 1 1 1 = 1

FORMULATION

3


SOYABEAN

MEAL

0.9 0 0 0.1

34.5 40 1140 56 36.65

Constrain

Ingredient limits 1 0 =


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Sulfur amino acid

requirements 0.52 0.46 95 1.46 0.614 >=

Lysine requirements 0.59 1.46 3.19 0.85 >=

overall limit 1 1 1 1 1 =

SENSITIVITY ANALYSIS

SENSITIVITY REPORT FOR FORMULATION 1

Variable Cells



$D$6 cost RICE 0.297861981 0 34.5 6.198117199 1E+30

$E$6 cost CHICKPEA 0.7 0 40 1E+30 6.202053345

$F$6 cost MYTHIONINE 0.002138019 0 1140 1E+30 1105.5

Constraints



$G$12 overall limit 1 28.41553768 1 0.388461538 0.232177342

$G$9 Ingredient limits 0.7 6.202053345 0.7 0.297672943 0.158388407

$G$10 Sulfur amino acid requirements 0.68 11.70088908 0.68 22.05684746 0.202

$G$11 Lysine requirements 1.197738569 0 1.06 0.137738569 1E+30


Variable Cells



$D$17 cost RICE 0.005820195 0 34.5 6.198117199 1E+30

$E$17 cost CHICKPEA 0.990798688 0 40 1E+30 6.202053345

$F$17 cost MYTHIONINE 0.003381117 0 1140 1E+30 1109.229885

Constraints




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$G$20 Ingredient limits 0.990798688 0 0.7 0.290798688 1E+30

$G$21 Sulfur amino acid requirements 0.78 11.74542551 0.78 0.327534247 0.319310345

$G$22 Lysine requirements 1.45 7.131868426 1.45 0.005058176 0.252885902

$G$23 overall limit 1 24.18457636 1 0.426274041 0.003447729


Variable Cells



$D$28 RICE 0.9 0 34.5 5.5 1E+30

$E$28 CHICKPEA 0 5.5 40 1E+30 5.5

$F$28 MYTHIONINE 0 1105.5 1140 1E+30 1105.5

$G$28 SOYABEAN MEAL 0.1 0 56 1E+30 21.5

Constraints



$H$31 Ingredient limits = 0 0 0.5 1E+30 0.5

$H$32 Ingredient limits = 0.1 21.5 0.1 0.9

4.27009E-

17

$H$33 Sulfur amino acid requirements = 0.614 0 0.54 0.074 1E+30

$H$34 Lysine requirements = 0.85 0 0.85

1.11022E-

16 1E+30

$H$35 overall limit = 1 34.5 1 1E+30

1.88173E-

16

RESULTS

Gerber's Mixed Cereal gave the same results as for PER. Protein apparent digestibility was

higher for the ANRC casein diet at 86%, and nearly the same for formulations 1, 2, and 3.

They are close to those of Gerber's High Protein Cereal, which is manufactured in the same

manner as the experimental formulations. Results from this experiment confirm the similarity

in nutritive value of the formulated products. Formulation 2 showed a higher nutritive value

with respect to one of the commercial products because of improved essential amino acid

complementation and supplementation.


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OBSERVATIONS AND CONCLUSION

Chemical analysis and biological evaluation of the linear programming model formulated

products confirmed their highly nutritive value in agreement with infant food specifications

outline. It was also established that the application of optimization methodologies, such as

linear programming, offer a special versatility as far as formulation of low-cost, highly

nutritive food products. In particular, underutilized chickpea resources available in many

parts of the world have been successfully used as the main ingredient to formulate infant

cereals to improve nutrition.

ALLOCATING WORKERS TO MACHINES AND PROJECTS

AT ACME FURNITURE COMPANY USING LP

INTRODUCTION TO MANUFACTURING SECTOR

Manufacturing is the production of goods for use or sale using labour and machines, tools,

chemical and biological processing, or formulation. The term may refer to a range of human

activity, from handicraft to high tech, but is most commonly applied to industrial production,

in which raw materials are transformed into finished goods on a large scale. Such finished

goods may be used for manufacturing other, more complex products, such as aircraft,

household appliances or automobiles, or sold to wholesalers, who in turn sell them

to retailers, who then sell them to end usersthe "Consumers".

Modern manufacturing includes all intermediate processes required for the production and

integration of a product's components. Some industries, such as

semiconductor and steel manufacturers use the term fabrication instead.

The manufacturing sector is closely connected with engineering and industrial design.

Examples of major manufacturers in North America include General Motors

Corporation, General Electric, and Pfizer. Examples in Europe include Volkswagen

Group, Siemens, and Michelin. Examples in Asia include Toyota, Samsung, and Bridgestone.

ABOUT ACME FURNITURE COMPANY

ACME started doing business in Los Angeles, California in 1985. Today they have six

branches located in New York City, New Jersey, Atlanta, Miami, Dallas, and San Franscico.


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From the beginning they have set out to provide our customers with service, value and

quality.

Service

In their new 400,000 square foot fully racked warehouse in Los Angeles, they can ship out

most orders within 48 hours. In most instances they can ship 90% of the items requested. This

is possible due to the fact that they maintain a 12 million dollar inventory at all times. They

also offer their customers a traffic department that offers the most competitive freight rates

available.

Value

Over the years ACME has been working with many of the same factories in Malaysia,

Taiwan, Vietnam, Indonesia, and Brazil and of course China. Because of their long-term

relationships with these factories, they have been able to purchase their products at the most

competitive prices in the industry.

Quality

Nothing is more important than quality. That is why ACME maintains its own quality control

personnel in every country in which they do business. Every item must meet their exactstandards. Nothing less will do.

Integrity

Besides the three branches they also maintain showrooms in Tupelo, Mississippi, High Point,

North Carolina, San Francisco, California and their newest showroom in Las Vegas, Nevada.

HOW ACME FURNITURE COMPANY USES LINEAR

PROGRAMMING?

At ACME Furniture Company, they use linear programming to determine which employee to

allocate to which machining centre and also to determine the allocation of a worker on a

particular job.

They basic model used here is the assignment problem where one employee has to be allotted

to one machining centre based on the time he takes to complete the task. In the case of

assigning a particular employee to a particular project the same assignment model is used.They allocate the employee on the basis of minimizing the cost to the company.


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PROBLEM DEFINITION

PROBLEM -1:

Six individuals are to work on six different machines at the ACME Furniture Company. The

machines used shape, surface, and drill to make a finished wood component. The work will

be sequential so that a finished component is produced at the end of the manufacturing

process. All individuals are skilled on all machines, but each worker is not equally skilled on

each machine.

Table1: Average time (in seconds) required to complete a task by each worked

PROBLEM2

The same six individuals are to work on six different projects which involve all the tasks

mentioned in the table above. The allocation is based on minimizing the cost. All individuals

are skilled on all machines, but each worker is not equally skilled on each machine and

depending upon the complexity of a job demand unique cost for working on each project.

Project

Individual

Project

1

Project

2

Project

3

Project

4

Project

5

Project

6

Worker 1 871 1466 1276 1091 1417 840

Worker 2 902 758 1185 1302 1283 1123

Worker 3 807 1460 836 1231 1368 1083

Worker 4 751 900 1189 820 1412 1356

Worker 5 794 891 1142 790 917 1099


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Worker 5 1153 1428 707 1488 1220 942

Table - 2: Labour Wage (in $) to be paid to complete a project by each worker

MATHEMATICAL FORMULATIONPROBLEM 1

The problem can be formulated as given below

Xij = Flow on arc from node denoting worker i to node denoting machine j

Where

i = Worker 1, 2, 3, 4, 5, 6

j = Surfacer, Lathe, Sander 1, Router, Sander 2 and Drill Machine

Objective Function

Minimize the total time spent for manufacturing

Z = 13X1S + 22X1L + 19X1S1 + 21X1R+ 16X1S2 + 20X1D +

18X2S + 17X2L + 24X2S1 + 18X2R+ 22X2S2 + 27X2D +

20X3S + 22X3L + 23X3S1 + 24X3R+ 17X3S2 + 31X3D +

14X4S + 19X4L + 13X4S1 + 30X4R+ 23X4S2 + 22X4D +

21X5S + 14X5L + 17X5S1 + 25X5R+ 15X5S2 + 23X5D +

17X6S + 23X6L + 18X6S1 + 20X6R+ 16X6S2 + 24X6D +

Subject to the constraints

-X1S - X1L - X1S1 - X1R- X1S2 - X1D = -1 (Worker 1 Availability)

-X2S - X2L- X2S1 - X2R- X2S2 - X2D = -1 (Worker 2 Availability)


- X4S - X4L - X4S1 - X4R- X4S2 - X4D = -1 (Worker 4 Availability)



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X1S +X2S + X3S +X4S +X5S +X6S = 1 (Surfacer Availability)

X1L+X2L+ X3L +X4L +X5L +X6L = 1 (Lathe Availability)

X1S1 +X2S1 + X3S1 +X4S1 +X5S1 +X6S1 = 1 (Sander1 Availability)

X1R+X2R+ X3R+X4R+X5R+X6R= 1 (Router Availability)

X1S2 +X2S2 + X3S2 +X4S2+X5S2 +X6S2 = 1 (Sander2 Availability)

X1D +X2D + X3D +X4D +X5D +X6D = 1 (Drill Availability)

All variables >=0 (Non-negativity constraints)

PROBLEM 2

The problem can be formulated as given below

Xij = Flow on arc from node denoting worker i to node denoting project j

Where

i = Worker 1, 2, 3, 4, 5, 6

j = Project 1, 2, 3, 4, 5, 6

Objective Function

Minimize the total time spent for manufacturing

Z = 871X1S + 1466X1L + 1276X1S1 + 1091X1R+ 1417X1S2 + 840X1D +

902X2S + 758X2L + 1185X2S1 + 1302X2R+ 1283X2S2 + 1123X2D +

807X3S + 1460X3L + 836X3S1 + 1231X3R+ 1368X3S2 + 1083X3D +

751X4S + 900X4L + 1189X4S1 + 820X4R+ 1412X4S2 + 1356X4D +

794X5S + 891X5L + 1142X5S1 + 790X5R+ 917X5S2 + 1099X5D +

1153X6S + 1428X6L + 707X6S1 + 1468X6R+ 1220X6S2 + 942X6D +


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Subject to the constraints


-X2S - X2L- X2S1 - X2R- X2S2 - X2D = -1 (Worker 2 Availability)





X1S +X2S + X3S +X4S +X5S +X6S = 1 (Project 1 Availability)

X1L+X2L+ X3L +X4L +X5L +X6L = 1 (Project 2 Availability)

X1S1 +X2S1 + X3S1 +X4S1 +X5S1 +X6S1 = 1 (Project 3 Availability)

X1R+X2R+ X3R+X4R+X5R+X6R= 1 (Project 4 Availability)

X1S2 +X2S2 + X3S2 +X4S2+X5S2 +X6S2 = 1 (Project 5 Availability)

X1D +X2D + X3D +X4D +X5D +X6D = 1 (Project 6 Availability)

All variables >=0 (Non-negativity constraints)

SOLUTION

PROBLEM 1:

Machine

Individual Surfacer Lathe Sander 1 Router Sander 2 Drill Flow inWorker 1 1 0 0 0 0 0 1

Worker 2 0 0 0 1 0 0 1

Worker 3 0 0 0 0 1 0 1

Worker 4 0 0 1 0 0 0 1

Worker 5 0 1 0 0 0 0 1

Worker 5 0 0 0 0 0 1 1

Flow out 1 1 1 1 1 1


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Project

Individual Surfacer Lathe Sander 1 Router Sander 2 Drill

Worker 1 13 22 19 21 16 20Worker 2 18 17 24 18 22 27

Worker 3 20 22 23 24 17 31

Worker 4 14 19 13 30 23 22

Worker 5 21 14 17 25 15 23

Worker 5 17 23 18 20 16 24

Project

Cost 99

Flow In

Flow

Out

Net

Flow Sign RHS

Surfacer 1 -1 = -1

Lathe 1 -1 = -1

Sander

1 1 -1 = -1

Router 1 -1 = -1

Sander

2 1 -1 = -1

Drill 1 -1 = -1

Worker

1 1 1 = 1

Worker

2 1 1 = 1

Worker

3 1 1 = 1

Worker

4 1 1 = 1

Worker

5 1 1 = 1

Worker

6 1 1 = 1

PROBLEM 2:


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Project

Individual

Project

1

Project

2

Project

3

Project

4

Project

5

Project

6 Flow in

Worker 1 0 0 0 0 0 1 1

Worker 2 0 1 0 0 0 0 1

Worker 3 1 0 0 0 0 0 1

Worker 4 0 0 0 1 0 0 1

Worker 5 0 0 0 0 1 0 1

Worker 5 0 0 1 0 0 0 1

Flow out 1 1 1 1 1 1

Project

Individual

Project

1

Project

2

Project

3

Project

4

Project

5

Project

6

Worker 1 871 1466 1276 1091 1417 840

Worker 2 902 758 1185 1302 1283 1123

Worker 3 807 1460 836 1231 1368 1083

Worker 4 751 900 1189 820 1412 1356

Worker 5 794 891 1142 790 917 1099

Worker 5 1153 1428 707 1488 1220 942

Project

Cost 4849

Flow In

Flow

Out

Net

Flow Sign RHSProject

1 1 -1 = -1

Project

2 1 -1 = -1

Project

3 1 -1 = -1

Project

4 1 -1 = -1


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Project

5 1 -1 = -1

Project

6 1 -1 = -1Worker

1 1 1 = 1

Worker

2 1 1 = 1

Worker

3 1 1 = 1

Worker

4 1 1 = 1

Worker

5 1 1 = 1

Worker

6 1 1 = 1

SENSITIVITY ANALYSIS

PROBLEM 1:

Microsoft Excel 14.0 Answer Report

Worksheet: [Book1]Sheet1

Report Created: 12/03/2013 20:32:32

Result: Solver found a solution. All Constraints and optimality conditions are satisfied.

Solver Engine

Engine: Simplex LP

Solution Time: 0.015 Seconds.

Iterations: 23 Subproblems: 0

Solver Options

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume

NonNegative

Objective Cell (Min)


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Cell Name Original Value Final Value

$C$21 Project Cost Project 1 4849 4849

Variable Cells

Cell Name Original Value Final Value Integer

$C$4 Worker 1 Project 1 0 0 Contin

$D$4 Worker 1 Project 2 0 0 Contin

$E$4 Worker 1 Project 3 0 0 Contin

$F$4 Worker 1 Project 4 0 0 Contin

$G$4 Worker 1 Project 5 0 0 Contin

$H$4 Worker 1 Project 6 1 1 Contin















$E$7 Worker 4 Project 3 0 0 Contin$F$7 Worker 4 Project 4 1 1 Contin









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Constraints

Cell Name Cell Value Formula Status Slack

$N$3 Project 1 Net Flow -1 $N$3=$P$3 Binding 0






$N$9 Worker 1 Net Flow 1 $N$9=$P$9 Binding 0






Microsoft Excel 14.0 Sensitivity Report

Worksheet: [Book1]Sheet1

Report Created: 12/03/2013 20:32:32

Variable Cells

Final

Reduce

d Objective

Allowabl

e

Allowabl

e

Cell Name Valu Cost Coefficien Increase Decrease


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e t

$C$4 Worker 1 Project 1 0 0 871 4 195

$D$4 Worker 1 Project 2 0 295 1466 1E+30 295

$E$4 Worker 1 Project 3 0 376 1276 1E+30 376

$F$4 Worker 1 Project 4 0 0 1091 195 151

$G$4 Worker 1 Project 5 0 4 1417 1E+30 4

$H$4 Worker 1 Project 6 1 0 840 295 1E+30

$C$5 Worker 2 Project 1 0 444 902 1E+30 444

$D$5 Worker 2 Project 2 1 0 758 283 1E+30


$F$5 Worker 2 Project 4 0 624 1302 1E+30 624


$H$5 Worker 2 Project 6 0 696 1123 1E+30 696

$C$6 Worker 3 Project 1 1 0 807 195 4


$E$6 Worker 3 Project 3 0 0 836 4 195



$H$6 Worker 3 Project 6 0 307 1083 1E+30 307$C$7 Worker 4 Project 1 0 151 751 1E+30 151

$D$7 Worker 4 Project 2 0 0 900 216 283


$F$7 Worker 4 Project 4 1 0 820 151 216







$G$8 Worker 5 Project 5 1 0 917 195 1E+30




$E$9 Worker 5 Project 3 1 0 707 195 4



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$G$9 Worker 5 Project 5 0 0 1220 4 195


Constraints

Final Shadow

Constrain

t

Allowabl

e

Allowabl

e

Cell Name

Valu

e Price R.H. Side Increase Decrease

$N$3 Project 1 Net Flow -1 -600 -1 0 0






$N$9 Worker 1 Net Flow 1 271 1 1 0

$N$1

0 Worker 2 Net Flow 1 -142 1 0 0

$N$1

1 Worker 3 Net Flow 1 207 1 0 0

$N$1

2 Worker 4 Net Flow 1 0 1 0 1E+30

$N$1

3 Worker 5 Net Flow 1 -225 1 0 0

$N$1


PROBLEM 2

Microsoft Excel 14.0 Answer Report

Worksheet: [ACME.xlsx]Sheet2

Report Created: 12/03/2013 21:49:50

Result: Solver found a solution. All Constraints and optimality conditions are satisfied.

Solver Engine

Engine: Simplex LP

Solution Time: 0.031 Seconds.


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Iterations: 26 Subproblems: 0

Solver Options

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name

Original

Value Final Value

$D$22 Project Cost Surfacer 99 99

Variable Cells

Cell Name

Original

Value Final Value Integer

$D$5 Worker 1 Surfacer 1 1 Contin

$E$5 Worker 1 Lathe 0 0 Contin

$F$5 Worker 1 Sander 1 0 0 Contin

$G$5 Worker 1 Router 0 0 Contin

$H$5 Worker 1 Sander 2 0 0 Contin$I$5 Worker 1 Drill 0 0 Contin





$H$6 Worker 2 Sander 2 0 0 Contin

$I$6 Worker 2 Drill 0 0 Contin











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Constraints

Cell Name Cell Value Formula Status Slack

$O$4 Surfacer Net Flow -1 $O$4=$Q$4 Binding 0

$O$5 Lathe Net Flow -1 $O$5=$Q$5 Binding 0

$O$6 Sander 1 Net Flow -1 $O$6=$Q$6 Binding 0

$O$7 Router Net Flow -1 $O$7=$Q$7 Binding 0

$O$8 Sander 2 Net Flow -1 $O$8=$Q$8 Binding 0

$O$9 Drill Net Flow -1 $O$9=$Q$9 Binding 0

$O$10 Worker 1 Net Flow 1 $O$10=$Q$10 Binding 0

$O$11 Worker 2 Net Flow 1 $O$11=$Q$11 Binding 0$O$12 Worker 3 Net Flow 1 $O$12=$Q$12 Binding 0




Microsoft Excel 14.0 Sensitivity Report

Worksheet: [ACME.xlsx]Sheet2


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Report Created: 12/03/2013 21:49:50

Variable Cells

Final

Reduce

d Objective

Allowabl

e

Allowabl

e

Cell Name

Valu

e Cost

Coefficien

t Increase Decrease

$D$5 Worker 1 Surfacer 1 0 13 0 1E+30

$E$5 Worker 1 Lathe 0 7 22 1E+30 7

$F$5 Worker 1 Sander 1 0 5 19 1E+30 5

$G$5 Worker 1 Router 0 5 21 1E+30 5$H$5 Worker 1 Sander 2 0 4 16 1E+30 4

$I$5 Worker 1 Drill 0 0 20 4 0

$D$6 Worker 2 Surfacer 0 3 18 1E+30 3

$E$6 Worker 2 Lathe 0 0 17 2 4

$F$6 Worker 2 Sander 1 0 8 24 1E+30 8

$G$6 Worker 2 Router 1 0 18 3 2

$H$6 Worker 2 Sander 2 0 8 22 1E+30 8

$I$6 Worker 2 Drill 0 5 27 1E+30 5


$E$7 Worker 3 Lathe 0 2 22 1E+30 2

$F$7 Worker 3 Sander 1 0 4 23 1E+30 4

$G$7 Worker 3 Router 0 3 24 1E+30 3

$H$7 Worker 3 Sander 2 1 0 17 2 1E+30

$I$7 Worker 3 Drill 0 6 31 1E+30 6

$D$8 Worker 4 Surfacer 0 2 14 1E+30 2$E$8 Worker 4 Lathe 0 5 19 1E+30 5

$F$8 Worker 4 Sander 1 1 0 13 2 1E+30

$G$8 Worker 4 Router 0 15 30 1E+30 15

$H$8 Worker 4 Sander 2 0 12 23 1E+30 12

$I$8 Worker 4 Drill 0 3 22 1E+30 3


$E$9 Worker 5 Lathe 1 0 14 4 1E+30

$F$9 Worker 5 Sander 1 0 4 17 1E+30 4


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$G$9 Worker 5 Router 0 10 25 1E+30 10

$H$9 Worker 5 Sander 2 0 4 15 1E+30 4

$I$9 Worker 5 Drill 0 4 23 1E+30 4

$D$1

0 Worker 5 Surfacer 0 0 17 1E+30 0

$E$10 Worker 5 Lathe 0 4 23 1E+30 4

$F$10 Worker 5 Sander 1 0 0 18 4 2

$G$1

0 Worker 5 Router 0 0 20 2 3

$H$1

0 Worker 5 Sander 2 0 0 16 4 2

$I$10 Worker 5 Drill 1 0 24 0 4

Constraints

Final Shadow

Constrain

t

Allowabl

e

Allowabl

e

Cell Name

Valu

e Price R.H. Side Increase Decrease

$O$4 Surfacer Net Flow -1 -12 -1 1 0

$O$5 Lathe Net Flow -1 -14 -1 0 0

$O$6 Sander 1 Net Flow -1 -13 -1 1 0

$O$7 Router Net Flow -1 -15 -1 0 0

$O$8 Sander 2 Net Flow -1 -11 -1 0 0

$O$9 Drill Net Flow -1 -19 -1 1 0

$O$1


$O$11 Worker 2 Net Flow 1 3 1 0 0

$O$1


$O$1

3 Worker 4 Net Flow 1 0 1 0 1E+30

$O$1


$O$1 Worker 6 Net Flow 1 5 1 1 0


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5

INTERPRETATION

The sensitivity reports for both the problems are shown above. The sensitivity report has two

distinct tables, titled Variable Cells and Constraints. These tables permit us to answer several

what-if questions regarding the problem solution.

The Variable Cells table presents information regarding the impact of changes to the OFCs

on the optimal solution. The constraints table presents information related to the impact of the

changes in constraint RHS values on the optimal solution.

The sensitivity report also gives the allowable increase and decrease on each variable.

RESULTS

PROBLEM 1

Individual Machine Assigned

Worker 1 Surfacer

Worker 2 Router

Worker 3 Sander 2

Worker 4 Sander 1

Worker 5 Lathe

Worker 6 Drill

PROBLEM 2

Individual Project Assigned

Worker 1 Project 6

Worker 2 Project 2

Worker 3 Project 1

Worker 4 Project 4

Worker 5 Project 5

Worker 6 Project 3


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CONCLUSION

Thus from the above results we can observe that ACME assigns its workers to projects and to

machines using LP. Thus LP model is an effective tool in determining the allocation of

worker to jobs and machines.

OPTIMUM PRODUCT MIX AT DONUT SHOP OF

WELCOMHERITAGE GROUP

INTRODUCTION TO THE HOTEL INDUSTRYAccording to the British laws a hotel is a place where a bonafied traveler canreceive food

and shelter provided he is in a position to for it and is in a fit condition toreceive.Hotels have

a very long history, but not as we know today, way back in the 6th century BC when the first

inn in and around the city of London began to develop. Thefirst catered to travelers and

provided them with a mere roof to stay under. This conditionof the inns prevailed for a long

time, until the industrial revolution in England, which brought about new ideas and progress

in the business at inn keeping.The invention of the steam engine made traveling even more

prominent. Whichhad to more and more people traveling not only for business but also for

leisure reasons.This lead to the actual development of the hotel industry as we know it

today.Hotel today not only cater to the basic needs of the guest like food and shelter provide

much more than that, like personalized services etc.Hotels today are a Home away from

home.

CLASSIFICATION OF HOTELS

Hotel can be classified into different categories or classes, based on their operational criteria.For example the type of accommodation they provide, location of the property, type of

services provided, facilities given and the clientele they cater to can helpcategories hotels

today.

Hotels today are basically classified into the following categories:

1Market segment:

Economy / limited services hotel


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Mid market hotel

All suite hotels

Time-share hotels

Condotel / Condiminium

Executive hotels

Luxury / Deluxe hotels

Property type:

Traditional hotel

Motels

Bread and break fast inns

Commercial hotel

Chain hotel

Casino hotel

Boutique hotels

Resorts

Spas Conference resorts

2) According to size:

Small hotels [150 rooms]

Medium hotels [up to 299rooms]

Large hotels [up to 600rooms]Other classification can be based on:a)Market segment

b)Property typec)Sized)Level of servicese)Owner ship and applicationf)Plansg)Type of

patronageh)Length of guAccording to size:


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Small hotels [150 rooms]

Medium hotels [up to 299rooms]

Large hotels [up to 600rooms]Other classification can be based on:a)Market segment

b)Property typec)Sized)Level of servicese)Owner ship and applicationf)Plansg)Type of

patronageh)Length of guest staest stayi)Location etc

MARKET SEGMENT

Economy hotel:It provides efficient sanity private rooms with bath. The furnishing and decor

areacceptable to majority of travelers. Food and beverage service may or may not

beavailable.Mid market hotels:They offer comfortable accommodation with private on

premises bath. Food and beverage services and uniformed bell staff. They offer above

average luxury.All Suite hotels:It offers separate sleeping and living areas along with a

kitchenette and a stocked bar, and offer class service.First class hotels:They are luxury hotels

with exceptional decor better than average food and beverage service, uniformed bell

services. They often have 2 or 3 dining rooms swimming pool, spas etc.Deluxe hotels

They are better and offer more specialized services than first class hotels. Theyalso provide

limousine services.

PROPERTY TYPE

Traditional hotels: They have the basic concept of rooms with breakfast, bell desk services

and the other usual services.

Motels: They are located on highways. Guest is given parking right outside their rooms. The

usually have a gas station / workshop attached to them.

Resorts: They are usually situated in tourist locations like on rivers, mountains, jungles, or

the sea. They give more privilege to sports activities leisure and re-creation activities like

manages, sightseeing, adventure sports, etc.

Resident hotels: Where guest stay for longer duration, stay like weeks, months even years.

Casino hotel

They are hotels usually in tourist spots and mainly cater to people who are on holidays.

Casino hotels like the name suggest offer gambling facilities along with accommodations.SIZE


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Small hotelup to 150 rooms Medium hotels150 to 299 rooms Large hotels299 to 600

rooms Extra large hotelsabove 600 rooms

LEVEL OF SERVICES:World-class services: They target top business executives and provide service s that cater to

needs of such people like lap tops in the rooms, business center, sectarian services.

Mid- range services: They appeal to the larger segment of traveling public [tourist]. The

services provided by the hotel are moderate and sufficient to budgeted travelers.

Economy / Limited services hotel: They provide comfortable and inexpensive rooms and

meet the basic requirement of the guest. These hotels may be large of small in size depending

on the kind of business they get. The key factor behind the survival of these hotels is that they

are priced very low and are in the budget of most of the travellers.

OWNERSHIP AND AFFILIATION:

Independent hotels: They have no application with other properties. They have their own

management and are single properties with one owner.

Chain hotels: They impose certain minimum standards, levels of service, policies and

procedures to be followed by their entire establishment. Chain hotels usually have corporate

offices that monitor all their properties and one management runs these properties. That is all

the hotels under the chain are completely owned and run by thechain itself.

Franchisee hotels: The franchisee grants the entities, the right to conduct business provided

they follow the established pattern of the franchisee, maintains their standards, levels of

service, practice their policies and procedures.

AWARDING OF CLASS:

Awarding of class is done by the HRACC in India. These are a few things listed down that

are taken into consideration while awarding star category to any hotels.

Number and types of rooms the hotel has

Elegant and comfortable surroundings

Rooms efficiency


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Cleanness and sanitation

Staff size and specialization

Range and level of services

Number of Restaurants

Bars and Beverage services

Concierge services

Accessibility to entertainment

Availability of transportation

Spa and swimming pool facility

Reservation and referral services.

Star category of hotels [India]

One star [*]Two star [**]Three star [***]Four star [****]Five star [*****]Five star deluxe

[***** deluxe]

THREE STAR CATEGORIES:

For a hotel to be recognized as a three star property the architectural features and general

features of the building should be very good there should be adequate parking facilities. At

least 50% of the rooms must be air-conditioned. Also the ambience and dcor of the place

must be ecstatic.

They should provide reservation and information facility apart from reception, information,bell service at least two gourmet dining facility should be available. The establishment may

or may not have banqueting facility.

They should provide high levels of personalized services. The staff must be well-trained and

proper standards for hygiene and sanitation must be followed. Also all properties have to

keep in mind that proper waste management is done.


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FIVE STAR CATEGORIES:

Five star categories is only allotted to properties, which have all the qualities of a three star

property and a few additional. Like the entire property must be centrally air-conditioned. The

building of the property must be an attractive one. All the rooms must be spacious. The

property must have proper banqueting facility, business center. Proper and well-maintained

pool and health club a spa is optional. The property must have 24 hour coffee shop, round the

clock room service, a bar and a minimum of 1 gourmet restaurant. The staff must be highly

trained and a degree of specialization must be shown. State of art equipment must be used

and the facility provided in the rooms must be sophisticated.

FIVE STAR DELUXE CATEGORIES:

They are more or less like five star properties with the only difference is that they are on a

larger scale. Five star deluxe properties maintain a very high staff to guest ratio and very high

levels of service is maintained. They in addition to five star properties have5 to 7 dining

rooms, a bar, 24-hour coffee shop, banqueting facility. Spas, fitness centers, business centers

ETC

ABOUT WELCOMHERITAGE GROUP

WelcomHeritage, a joint venture between ITC Ltd. and Jodhana Heritage, represents some ofthe best traditions of heritage hospitality and tourism in India. It offer's over 37 exclusive

heritage destinations, ranging from grand palaces to traditional havelis and magnificent forts;

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Madhya Pradesh, Uttarakhand, Himachal Pradesh Jammu & Kashmir, West Bengal,

Karnataka, Tamil Nadu, Punjab, Sikkim, Arunachal Pradesh, Uttar Pradesh, Puducherry &

Goa

A holiday with WelcomHeritage is always special: timeless bazaars, elephant and camel

safaris, local festivals, desert camps and a variety of adventure and sport activities. steeped in

history are stories of heroic warriors and illustrious queens; of royal courts and princes; pomp

and pageantry and gracious and splendid living. Through the relentless passage of time, many

a legend has been relegated to the pages of history, others are extolled in verse and sung by

traditional bards and folk singers. Some live on in the palaces, forts and royal retreats even

today. Their private homes beckon the visitor, with elegant WelcomHeritage hospitality. We

offer you a slice of history, with one major difference.


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WelcomHeritage Hotels offers the secrets for a great escape. At each WelcomHeritage hotel,

you can experience our rich heritage and culture. A fort resort at the rim of a desert, or a

country manor in the lap of a green valley. A jungle lodge in a wildlife forest reserve, or a

palace or haveli, resonant with the past. A picture-postcard cottage ensconced in mystic

mountains or a splendid mansion on the spur of a hill. A spa in a heritage home, a houseboat

on a sparkling lake, a colonial hill residence with tea gardens for a view, a mist-wrapped

palace in fragrant plantations. Each hotel has a secret to share, a story to tell - and so will

you.Moreover, each WelcomHeritage hotel has the blueprint of a great holiday all laid out for

you. Every hotel offers you an opportunity to go where you get away to all that is not

ordinary.All that is exclusive, while being affordable. Unusual, without being over-the-top.

WelcomHeritage's over 40 hotels are sited conveniently - often in stunningly scenic locations

- with easy connections from cities, making them the perfect holiday option.

Most of all, you will find an atmospheric, boutique experience, far removed from

standardised sameness. Hospitality that comes from the heart. Accommodation that combines

a slice of heritage with modern amenities. A local flavour in the cuisine, the craft and the

cultural vignettes. Views to fill albums, walls dotted with frames, trophies and treasures. A

feeling of being at a home away from home.And, last but not the least, that uncommon

unforgettable quality that makes your holiday a holiday to remember - and recount.

These are some of the hotels

Welcome Heritage Bal Samand Lake Palace (Jodhpur)

Welcome Heritage Ferrnhills Royale Palace (Ooty)

Welcome Heritage Khimsar Fort (Khimsar)

Welcome Heritage Lallgarh Palace (Dist. Bikaner)

Welcome Heritage Noor-Us-Sabah Palace (Bhopal)

Welcome Heritage Shivavilas Palace (Sandur)

Welcome Heritage Taragarh Palace (Palampur)

Welcome Heritage Umed Bhawan Palace (Kota)

Welcome Heritage Windamere (Darjeeling)

LP APPLIED IN WELCOMHERITAGE GROUP

Mathematical formulation:A typical mathematical problem consists of a single objective

function, representing either profits to be maximised or costs to be minimised, and a set of


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constraints that circumscribe the decision variables. In the case of a linear program (LP), the

objective function and constraints are all linear functions of the decision variables.

Linear programming is a widely used model type that can solve decision problems withthousands of variables. Generally, the feasible values of the decision variables are limited by

a set of constraints that are described by mathematical functions of the decision variables.

The feasible decisions are compared using an objective function that depends on the decision

variables. For a linear program, the objective function and constraints are required to be

linearly related to the variables of the problem.

A linear programming problem (LPP) is a special case of a mathematical programming

problem wherein a mathematical program tries to identify an extreme (i.e. minimum ormaximum) point of a function f(x1, x2, .. , xn) , which furthermore satisfies a set of

constraints, e.g. g(x1, x2, . Xn) b. Linear programming is the specialisation of

mathematical programming to the case where both function f, to be called objective function,

and the problem constraints are linear.

Problem: Manager of a donut store that sells two types of donuts: regular and chocolate.

Making one batch of regular donuts takes 1 hour of an employee As time and 2 hours of

employee Bs time. Making one batch of chocolate donuts takes 2 hours of employee As

time and 1 hour of employee Bs time. One batch of regular and chocolate donuts sells at $35

and $55 respectively. It costs $30 and $45 to make a batch of regular and chocolate donuts

respectively. Employee A works 8 hours a day and employee B works only 7 hours a day.

Your donuts are so good that there is unlimited amount of demand for them. Everyday, you

want to produce at least one batch of regular donuts. You always have enough to make only 4

batches of chocolate donuts every day.

Now you need to decide how many batches of regular and chocolate donuts to be made so

that your objective of maximising profit is met. You have the constraints As and Bs time,

ingredients of chocolate donuts, production rule of 1 batch of regular donuts, no negative

number of donuts and no partial batches.

Sensitivity Analysis


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Let us denote batches of regular donuts to produce as R and batches of chocolate donuts to

produce as C. By writing the objective function in terms of the above , we have Maximise 5R

+ 10C.

{Regular donuts profits are 3530 = 5$ and chocolate donuts profits are 55- 45 = 10$}

Let us now express all constraints using decision codes:

Employee As time = 8 hours. Hence, 1R + 2C 8

Employee Bs time = 7hours. Hence 2R + 1C 7

Ingredients for chocolate donuts= 4, Hence C 4

Atleast one batch of regular donuts; R 1

No negative number of donuts of either type: Hence R 0,C 0

No partial batches allowed R & C are integers.

Figure:1 Graphical presentation of LP problem

Solution: The shaded area is where the inequalities of four equations are satisfied. The

objective function to maximise 5R + 10C is attained at the point C(3,2). Hence the optimal

solution is to prepare 3 batches of Chocolate and 2 batches of Regular donuts.


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Observation & Conclusion: In this paper we studied that linear programming , which is

very successfully used in many industries can also be used in food & beverage department of

a hotel. We have discussed here how we could use LP to maximise the objective function and

obtain an optimal solution. Though only two variables have been used here, the same could

be extended for more variables and solution could be attained by using Excel solver.

HSBC- PORTFOLIO MANAGEMENT USING LP MODEL

INTRODUCTION TO BANKING INDUSTRY

Finance is the life blood of trade, commerce and industry. Now-a-days, banking sector acts as

the backbone of modern business. Development of any country mainly depends upon the

banking system.

A bank is a financial institution which deals with deposits and advances and other related

services. It receives money from those who want to save in the form of deposits and it lends

money to those who need it. Oxford Dictionary defines a bank as "an establishment for

custody of money, which it pays out on customer's order."


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About HSBC

HSBC Holdings plc is a British multinational banking and financial services company

headquartered in London, United Kingdom. HSBC is a universal bank and is organized

within four business groups: Commercial banking; Global banking and Markets (investment

banking); Retail Banking and Wealth Management; and Global Private Banking. It has

around 7,200 offices in 85 countries and territories across Africa, Asia, Europe, North

America and South America, and around 89 million customers. As of 31 March 2012 it had

total assets of $2.637 trillion, of which roughly half were in Europe, the Middle East and

Africa, and a quarter each in Asia-Pacific and the Americas.

HSBC Holdings plc was founded in London in 1991 by The Hong Kong and ShanghaiBanking Corporation to act as a new group holding company and to enable the acquisition of

UK-based Midland Bank. The origins of the bank lie in Hong Kong and Shanghai, where

branches were first opened in 1865. Today, HSBC remains the largest bank in Hong Kong,

and recent expansion in mainland China, where it is now the largest international bank has

returned it to that part of its roots.

PORTFOLIO SELECTION FOR HSBC

HSBC is one such company which uses Linear Programming Technique to solve the issues

regarding portfolios like shares, bonds, Mutual funds etc. In this report, according to the

survey conducted on how many number of shares, bonds and mutual funds HSBC owns, the

information is gathered and LP model is used to solve the problem. The following are the

investment options for HSBC

PROBLEM DEFINITION

Expected annual return of investments

Investment Expected annual return rate (%)

Share Amanufacturing sector 15.4

Share Bmanufacturing sector 19.2

Share C - food and beverage sector 18.7


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Share D - food and beverage sector 13.5

Mutual fund A 17.8

Mutual fund B 16.3

Requirements

Total amount = 90000 Amount in shares of a sector no larger than 50% of total available Amount in shares with the larger return of a sector less or equal to 80% of sectors

total amount

Amount in manufacturing company less or equal to 10% of the whole share amount Amount in mutual funds less or equal to 25% of the amount in manufacturing

shares

To select a portfolio package from set of investment options and to maximize the return orminimize the risk in each of these investments with the given capital using Linear

Programming model.

Solution

Define Decision variables

x1 = invested amount in share A of the manufacturing sector

x2 = invested amount in share B of the manufacturing sector

x3 = invested amount in share C of the food and beverage sector

x4 = invested amount in share D of the food and beverage sector

x5 = invested amount in mutual fund A

x6 = invested amount in mutual fund B


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Mathematical Formulation

Objective Function:

Max z = 0.154x1 + 0.192x2 + 0.187x3 + 0.135 x4 + 0.178x5 + 0.163x6

Subject to constraints:

x1 + x2 + x3 + x4 + x5 + x6


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RESULTS

Investment Amount invested Annual return rate

expected (%)

Total expected return

of

the investment

Share A 27900 15.4 4296.6

Share B 8100 19.2 1555.2

Share C 36000 18.7 6732

Share D 9000 13.5 1215

Mutual fund A 9000 17.8 1602

Mutual fund B 0 16.3 0


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APPLICATION OF LI

data modelling and optimization report

Documents