Friday, June 23, 2017

Victim narrates how he was kidnapped by notorious kidnapper 'Evans' (photos)

Victim narrates how he was kidnapped by notorious kidnapper 'Evans' (photos) follow link and watch this terrifying video narrating his ordeal

Thursday, June 22, 2017

RHAPSODY OF REALITIES THURSDAY, 22ND JUNE, Pastor Chris

TOPIC ✨ THERE ARE GOOD THINGS IN YOU ✨

That the communication of thy faith may become effectual by the acknowledging of every good thing which is in you in Christ Jesus (Philemon 1:6).

For you to be effective in the communication of your faith, there has to be an acknowledgement of the good things in you. There’re no bad things in you. Some people don’t know this, so they’re always looking for something that’s wrong with them. They’re always talking themselves down, focusing always on their inabilities, disabilities, and frustrations. That’s not right! There are good things in you, and you’ve got to acknowledge them.

As a child of God, the very life of God is in you: _*“To whom God would make known what is the riches of the glory of this mystery among the Gentiles; which is Christ in you, the hope of glory”*_ (Colossians 1:27). Christ is in you; He lives in your heart. Acknowledge it. Affirm that greater is He that’s in you than he that’s in the world. This means you’re not an ordinary person. You have the ability of God and excellence of the Spirit in you. You can reign in this life because you have the righteousness of God. You’re special!

Why is it so important to acknowledge the good things in you in Christ Jesus? It’s because they’re spiritual and are actualized or activated by acknowledgement. The Bible says, _*“They know not, neither will they understand; they walk on in darkness: all the foundations of the earth are out of course. I have said, Ye are gods; and all of you are children of the most High. But ye shall die like men, and fall like one of the princes”*_ (Psalm 82:5-7).

The above verses are very revealing. It shows why many live miserably and die like ordinary men, even though they’re gods and children of the Most High. They’ve never acknowledged who they are, what they have, their abilities and potentials in Christ Jesus; this has made their faith ineffective.

CONFESSION*

As I meditate on God’s Word, my spirit is programmed for absolute mastery, success, and transcendental blessings. I’m blessed and highly favoured. The lines are fallen unto me in pleasant places. I have a goodly heritage. Everything that belongs to me is glorious and wonderful. Hallelujah!

FURTHER STUDY: Ephesians 2:10* For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them.

Psalm 139:14-16 I will praise thee; for I am fearfully [and] wonderfully made: marvellous [are] thy works; and [that] my soul knoweth right well. 15 My substance was not hid from thee, when I was made in secret, [and] curiously wrought in the lowest parts of the earth. 16 Thine eyes did see my substance, yet being unperfect; and in thy book all [my members] were written, [which] in continuance were fashioned, when [as yet there was] none of them.

DAILY SCRIPTURE READING

1-Year Bible Reading Plan:* Acts 10:1-23,
Ezra 4-6

2-Year Bible Reading Plan:* Luke 3:1-11,
Deuteronomy 20

EXTRACT FROM: RHAPSODY OF REALITIES DAILY DEVOTIONAL

Thursday, March 17, 2016

PRIVATIZATION OF PUBLIC ENTERPRISES IN NIGERIA: (A CRITICAL ASSESSMENT OF ITS POLITICISATION)

PRIVATIZATION OF PUBLIC ENTERPRISES IN NIGERIA:
(A CRITICAL ASSESSMENT OF ITS POLITICISATION)

CHAPTER ONE
INTRODUCTION
1.1 Background of the Study
In the era of post colonialism, Nigeria has at one time or another, embarked upon certain policies that have political economic implications. For instance, from 1960 to date, Nigeria has introduced indigenization and nationalization policy, operation feed the Nation (OFN), Austerity measure, structural adjustment programme (SAP), Deregulation of oil sector, Resource control Privatization and commercialization of public enterprises to mention but a few. The critical question here remains. How many of these policies have been able to restructure the political economy of Nigeria to the tune of alleviating the yearnings and aspirations of the working class.
The world no doubt is moving towards capitalization and any nation that is not moving towards this direction is seen as either not developing or even retrogressing. A capitalist economy is a free market economy which allows most economic decisions to be guided by the twin forces of demand and supply. Since capitalization discourages monopoly but encourages competitive market, it therefore enhances efficiency and high productivity which is very vital in any developing country’s economy. In Nigeria, most government owned industries and establishments remain citadels of corruption, studies in efficiency and consequently a heavy drain on the economy. As a means of curbing this menace, the Brettonwoods institutions (IMF & WORLD BANK) have advocated the twin policies of privatization and commercialization. Incidentally, Nigeria has fully adopted this policy and is embarking on it with frenzy

Monday, February 15, 2016

Nigeria Trade Union Congress (NTUC)

Nigeria Labour Congress (NLC) is an umbrella organisation for trade unions in Nigeria. It was founded in 1978 following a merger of four different organisations: Nigeria Trade Union Congress (NTUC), Labour Unity Front (LUF), United Labour Congress (ULC) and Nigeria Workers Council (NWC). The numerous affiliated unions were restructured into 42 industrial unions. Its founding President was Wahab Goodluck.
During its history, conflicts with the military regime twice led to the dissolution of the NLC's national organs, the first in 1988 under the military regime of General Ibrahim Babangida and the second in 1994, under the regime of General Sani Abacha. Under Nigeria's military governments, labour leaders were frequently arrested and union meetings disrupted. Following democratic reforms in the country, some of the anti-union regulations were abolished in January 1999. The same month Adams Oshiomhole was elected President of the reformed organisation.
Today, the NLC has 29 affiliated unions. In total, they gather around 4 million members, according to their own figures. This makes the NLC one of the largest trade union organisations in Africa.
Recently conflict between the government and the NLC has escalated due to the organisation's opposition to higher fuel prices. The price increases are the result of decisions by the Olusegun Obasanjo government to dramatically reduce subsidies and to deregulate the purchase and sale of fuel. The NLC has led several general strikes protesting the government's fuel price policy.
In September 2004, the NLC gave the federal government an ultimatum to reverse the decision to reintroduce the controversial fuel tax or face a nationwide protest strike. The strike threat was made despite the fact that a Federal High Court judgement in an earlier dispute had declared the organisation lacking legal power to call a general strike over government policies. [1]
Following the announcement of the strike plans, the NLC claims President Adams Oshiomhole was arrested October 9, 2004 at a protest at Nnamdi Azikiwe Airport. According to the organisation, Oshiomhole was "abducted by a team of operatives of the State Security Services (SSS) numbering over fifteen, who overpowered him, wrestled him to the ground and bundled him into a standby Peugeot 504 station wagon, which bore no licence plates." [2] The State Security Services called the claim "sensational and inaccurate reporting", saying that the NLC president had a misunderstanding with field operatives, but that the matter was soon resolved. A presidential spokesperson claimed that Oshiomhole was only invited for a "chat" at the airport, no arrest having taken pla
CHALLENGES
It was Franz Fanon who argued that ‘every generation must out of its relative obscurity discover its mission’. It will fulfil it or betray. This is true for generations of individuals, organisations, leaders, communities or societies. What defines the mission of any generation would flow from the challenges facing it and in terms of organisations; it would further be shaped by its mandate or objectives.

The debate around the missions of leaders and organisations in the country is so personalised that specification of the mandate or objective of organisations are reduced to some narrow agendas of individual leaders. This is quite problematic and could undermine processes of organisational strengthening and development. While appreciating the role of leaders in the process of shaping organisational priorities and direction, a situation where leaders assume domineering role is authoritarian, no matter how well intentioned, articulated and correctly defined.

Perhaps the thing to emphasise is that organisations are only relevant to the extent that they are able to contribute to addressing the problems of people at any given point. In terms of trade unions therefore they are only relevant to the extent that they are able to redress the problem of injustice in the workplace and ensure improved welfare and working conditions. This is at the core of the discussion of the relevance, effectiveness or even validity of the mission of Nigerian trade unions and in particular Nigeria Labour Congress (NLC).

Since the February 16, 2007 election of the new leadership of the NLC, there are so many expressed opinions about what to expect from the new leadership. Having worked at a relatively high level in the organisation and being privileged to be part of the Oshiomhole team, it is important that one contribute to the discussion by raising issues around what could be the mission of the leadership.

One thing that must be placed in proper perspective is that external image of any organisation does not necessary depict its strength, capacity or even potential. The image of the NLC today is largely reflection of its role against the deregulation of the downstream sector of the petroleum industry. The capacity of the Oshiomhole leadership to spearhead the struggle against arbitrary price adjustments of petroleum products was the source of its relative popularity.

Although there are contending views about the efficacy of the management of the mass actions led by the NLC under Oshiomhole, one thing that cannot be denied is the fact Adams Oshiomhole was able to provide a high measure of courageous leadership. However, in terms of assessment of contribution of the NLC under Oshiomhole’s leadership towards raising welfare standards of workers, we may have to come to terms with some basic realities. These realities basically call for some humble recognition of the structural limitations and weaknesses that are embedded in the NLC and its affiliates.

One unaccomplished task of the Oshiomhole leadership has to do with the challenge of reinventing the structures of the NLC and ensure that they are efficient and positioned to competently service the needs of unions and workers. A major problem that confronted the Oshiomhole’s leadership throughout the eight-year tenure has to do with the burden of managing ineffective affiliates either on account of fundamental changes in the structures of work organisations in some sectors or having generation of leaders that are alienated from realities facing workers and therefore not able to gauge and service the needs of workers. In fact, if anything, one can conveniently argue that there are cases where unions or at least their leaders are a liability to workers and their expectation for improved welfare and working conditions. In some respect their actions or inactions worsened conditions of workers. Typical example was the case of anti-causualisation struggles and the role of some unions in protecting some management in the steel, hotel and food industry.

There is the big question of internal democracy both within the NLC itself and the unions. One immediate indicator is the fact that constitutional structures of particularly the NLC have not functioned properly, at least since 2001. Virtually all meetings of the NLC, either at the level of the National Executive Council (NEC) or Central Working Committee (CWC) were emergency meetings. As a result regular organisational challenges have suffered. Partly on account of absent of regular institutional reflections around the challenges facing workers and unions, and to the extent of that reflections, assessment of capacity to deliver effective services to workers and unions, it could be argued that the workings of the trade unions and the NLC have suffered stagnation.

Let me also quickly point out that the absence of institutional reflection is also to a large extent a function of the weakness of the Secretariat. Again, this could also be a measure of the unfinished task of the Oshiomhole leadership, but perhaps also compounded by historical factors, which includes conservative retention of a secretariat structure that may not be relevant to contemporary realities and challenges facing unions. But what are these contemporary challenges facing unions?

First, the structures of Nigerian trade unions, which the NLC secretariat reflect, have largely been the outcome of the 1978 restructuring with some slight amendments of the 1996 restructuring. They were therefore structures created based on 1970s work organisations that were largely Taylorian founded around hierarchies and command structures. To some considerable extent, they were also reflections of cold war politics, which incorporated an underlying responsibility for unions to be part of nationalist and anti-imperialist movement. The legal framework regulating both labour and union administration is similarly influenced by these factors.

Taking the issue of the Taylorian model, the rise of post-Fordist work organisations based on tasks and knowledge since the 1940s in industrialised countries is producing a paradigm shift, which since the 1990s, with the end of the cold war, has been influencing the emergence of giant, less-regulated and knowledge driven work organisations. In the process, many unions and their structures are fast becoming either moribund or incompetent in addressing the problems of workers.

A good reference point would be the case of the rise of what is commonly referred to as new generation banks. In the UBA, for instance, around the mid 1990s, a whole generation of staff were laid off and the new generation of IT driven staff could not just fit into the old analogue National Union of Banks, Insurance and Financial Institutions Employees (NUBIFIE). Related to that is the fact that given that the officers of the union were largely recruited from the old Taylorian industrial structure, the union is not able to address the challenges of workers. One can further prove this very point citing the 2005 agreement facilitated by Ministry of Employment, Labour and Productivity to the effect that management of all the new generation banks should recognise the existence of unions. About 2 years after that agreement, the union was not able to take advantage of that agreement and unionise the workers.

Second related issue is the case of private telecom operators and even the challenges of adjusting to NITEL privatisation. The leadership of the National Union of Post and Telecommunication Employees (NUPTE) were found to be grossly incompetent and corrupt in handling the matter leading to their sacking. There is also the case of the so-called senior and junior dichotomy, which is so entrenched most especially in the public sector.

These are issues that would serve as guide in assessing today’s challenges. What perhaps need to be further acknowledged is that these are to considerable extent internal issues. One will argue that one big external issue that appear to have constraint the capacity of unions is the moribund Ministry of Labour, Employment and Productivity. It is moribund in terms of injecting new initiatives that have capacity of strengthening the regulatory framework for the administration of labour and employment relations in the country. Similarly, its officials, like the unions, are also living in the Taylorian age and therefore not able to address challenges associated with the rise of modern knowledge driven work organisations.

With the emergence of civilian government, a critical challenge facing the unions is that of adjusting to the requirement of democratic practices. This issue would appear to be quite desolate particularly when taken in context of the internal operations of the trade unions both at national and at state levels. What is very glaring is that internal union administrations are undemocratic both at the level of the NLC, affiliates, national and state levels. This may be contestable by my colleagues in the trade unions largely on account of instinct for self-defence. However, it needs to be appreciated that democracy is about formal recourse to structures and ensuring that decisions of structures are complied with. I will argue that this is very weak and in the case of the NLC, in the last eight years, regular meetings of these structures never held as and when due. If anything, this is in part accountable to inability of the organisation to focus itself to attend to new and emerging challenges and perhaps re-organise, re-configure or amend its structures.

For those who seek to engage the discussion of challenges before the NLC around personalities, would miss these vital issues. Therefore my position is that anybody interested in locating the challenges facing the trade unions and most especially the NLC and to that extent seeking to influence the agenda of the new leadership, these are indications. Having raised these issues, one thing that should be emphasised is that the capacity of the NLC leadership to address some or all of the challenges would be determined by how it set out to approach key organisational questions, some of which have been identified above. A major determinant would be the capacity of the Secretariat.

From my little knowledge, I fear that the secretariat and its officers will be more concerned with negotiating power issues rather than focusing on developing broad strategic agenda proposals. This is because in reality the powers of the secretariat was greatly reduced not by any constitutional review but on account of having limited capacity to assert itself at the face of a towering and high profile leader in the last eight years. The process for actualising this may take varying forms, from formal to subtle and even crude but informal strategies. In the process, there may be some distractive consequences, including usual leadership personality conflicts and time lost, which as far as I am concerned should be avoided.

One issue that would appear to be very disadvantageous has to do with the fact that there is very little focus on the internal workings of the NLC and the trade unions, except when a national strike is looming. It will therefore be important that if truly we believe in the potency of the union movement to the process of socio-economic and political transformation of our society, we need to subject the internal workings of the NLC and the trade unions to greater national focus and in the process contribute to strengthening organisational capacity. The Umar leadership would find such an approach very helpful rather than the current one of simplistically measuring him up to Oshiomhole, which I would say at this point, is only meant to write him off. I am sure given the right space and with the correct assessment of challenges facing workers, the young leadership has its potential to record its own achievements. The question would be the quality of advice and input.
Addressing Workers’ Challenges in the Informal Sector
The informal sector in Nigeria refers to economic activities in all sectors of the economy that are operated outside the purview of government regulation. It encompasses a wide range of small-scale, largely self-employment activities as most of them operate the traditional method of production. Though activities in the informal sector are difficult to measure; they are highly dynamic and contribute substantially to the general growth of the economy.
Available statistics from the Ministry of Labour and Productivity indicates that the informal sector contributes about 60 per cent of the nation’s Gross Domestic Product (GDP). Like many other developing countries, the sector is considered crucial to job creation as it accounts for about 90 per cent of jobs in the country.
Despite these contributions, the Nigerian informal sector is faced with a number of challenges which include: lack of access to credit facilities, multiple taxations and levies. It is pertinent to also note that the sector is often not recognised and protected under existing legal and regulatory framework of government and are characterised by a high degree of vulnerability and poverty.
Deputy Director/Controller, Lagos office of the Federal Ministry of Labour, Mrs. Nofisat Abiola Arogundade, said government is aware of the informal sector contribution to economic development in the area of job creation, but however noted that “our concern is to create quality job and not just any job. It is long established that the ambition of people is to live a dignified life and the essence of dignity is work”.
“In realisation of this fact of life, our current Labour administration in Nigeria has made access to good quality jobs for all workers as a central policy, hence our commitment to the promotion and enforcement of Decent Work Agenda at all workplaces. Decent work is central to efforts to reduce poverty, and is a means for achieving equitable, inclusive and sustainable development,” she said.

Challenges of Informal Sector
The Nigerian government, at various levels, has adopted policies aimed at enhancing the performance of the informal sector. For instance, policies have variously been designed to promote small and medium scale enterprises. Some of the policies include the Entrepreneurship Development Policy, International Financial Assistance, Monetary policy through Microfinance banks; among others.
Whereas government has set up all sorts of intervention agencies such as Better Life Programme, Peoples’ Bank, National Agency for Poverty Eradication, (NAPEP), Small and Medium Enterprises Development Agencies (SMEDAN), National Directorate of Employment (NDE) etc. over the past two decades to ameliorate the sufferings of people toiling away in the informal economy, these policies have not translated into meaning development for the sector.
The sector has continued to suffer from comprehensive absence of social protection, vocational education facilities, access to business friendly credits, unfair competition through dumping of manufactured goods from more industrialised countries, lack of representation and participation in decision making processes resulting in unworkable, corruption prone public policies and programmes that have abysmally failed to significantly address the basic needs of Nigerian working people.
General Secretary of the Federation of Informal Workers of Nigeria (FIWON), Mr. Gbenga Komolafe, expressed dismay over various forms of extortion by government agencies from members in the sector. Specifically, he said workers in the informal sector are unduly subjected to multiple taxation and different types of levies by government.
“The informal sector has created employment opportunities for millions of workers in the formal sectors of the economy who lost their jobs since the 1980s when implementation of neo-liberal economic policies intensified in Nigeria and contributed 60 per cent of the nation’s GDP.
“Despite the contributions of the informal sector to the growth of the economy, informal workers are subjected to multiple taxations, levies and other forms of extortion by Government and its agencies,” he said.
Also, President of the Nigerian Labour Congress (NLC), Comrade Abdulwaheed Omar, who stated that the NLC is not unaware of the challenges in the sector, noted that workers in the sector are subjected to multiple levies and taxes by government. “They are affected by unilateral decisions and actions by local governments, incessant harassment by the police and numerous task forces and agencies of government”, he said
He listed other challenges to include "capitalisation, lack of funds, and endless manipulation by political parties and politicians for their selfish ends.
However, Arogundade maintained that the Federal Government, through the labour ministry, is poised to address these challenges under the Nigeria Decent Work Country Programme.
“The Ministry wishes to address the multitude of workers and enterprises who are often not recognised and protected under existing legal and regulatory frameworks and who are characterised by a high degree of vulnerability and poverty, and to redress these decent work deficits”.
According to Arogundade, the vision of the present administration is to make life meaningful and worthwhile for citizens of this country as well spelt out in the 7-point Agenda of government.
Labour’s Organising Efforts
Organising workers in the informal sector is quite challenging in view of the peculiar nature of the sector. With their diverse and widely dispersed enterprises and settlements, and their general orientation towards their rural hometowns, they are usually more difficult to organise and to develop much needed civic engagement.
But they need better organisation and self-regulation to be able to engage more constructively with government and other development partners, and to increase their power to lobby, negotiate, and influence public policy in favour of their sector.
For some years, the organised labour movement have been strategising on how to bring the informal sector into its fold. Moreso, the trade unions are losing members to the informal sector as a result of job losses, due to the effect of the global meltdown.
The need therefore to embrace the informal sector has become a front burning issue for the labour movement. In a bid to address this issue, the NLC recently organised a summit for operators in the informal sector where experts, stakeholders x-rayed the 'problems of the informal sector,' the challenges and the way forward.
In his address, the NLC President recalled the numerous efforts it has made at trying to organise the sector and better the life of workers, stressing that the Congress is not unaware of the problems of the informal sector.
He stressed the need for trade unions to help informal sector operators to organise themselves better and build a formidable base among others as the reason for bringing the sector into its fold.
“It is a known fact that compared to the self employed, the workers in the formal sector are far smaller. Another truth is that with the gales of mass retrenchment that has been sweeping through our country since 1975 and which were exacerbated during the General Muhammadu Buhari regime in 1984/85 and the President Olusegun Obasanjo administration in 2006-2007, most of the victims find sustenance as self employed peoples,” he said.
"Trade unions look at the vast ocean of humanity trapped in informal work and feel challenged about doing something about organising informal work. The question however is how to do it, given the different forms of challenges faced in the informal economy and the confused nature of the bargaining partner”, he added. Also, Secretary of the NLC in Lagos State Council, Comrade Ismaila Bello, listed some of the challenges of organising the informal sector to include: organisation building, financial management, capacity building for leaders, trade union education, skill development and vocational training.
He said those in the informal sector would like to find solutions to these challenges in the trade union movement and suggested that it is high time trade unions embraced informal sector workers.
Sharing his union's experience, Bello said, “Early 2005, the union established linkage with the Nigerian Union of Tailors in Lagos, Oyo and Ogun states. Further linkages were made were made in Kaduna, Kwara, and Benue states. While the organic organisational linkages have taken firm roots in Lagos, Benue and Kaduna, the relationship in other states are yet to be formalised.”
As a result of the successful experience with the tailors group, there are on-going attempts at formalising the union's relationship with the Kampala Makers Association in Lagos.
General Secretary of the Nigeria Automobile Technicians Association (NATA), Comrade David Ajetunmobi, explained that trade unions may not find it easy organising the informal sector because of the “diverse nature of this sector.”
According to him: “Trade unions look at the vast ocean of humanity trapped in informal work and feel challenged about doing something about organising informal work. The question however is how to do it, given the different forms of challenges faced in the informal economy and the confused nature of the bargaining partner”.
"The bargaining partners for informal workers are diverse: local governments for space and sane taxation system, state governments for appropriate policies, space and social protection, Federal Government for policies that address social protection needs in the informal economy, health insurance, vocational training".
Ajetunmobi however said his view does not in any way suggest that informal sector workers do not need trade union. His view is that the “Informal workers need the organisational experience of the trade unions while unions also need the vast number of informal workers to build more power to leverage more concessions on larger macro-economic issues such as the deregulation policy for example".
Trade unions he suggested, could help build informal workers' organisations through education, training and collaboration in developing policies that could make life better for informal sector workers.
Conclusion
The contribution of the informal sector to growth of the Nigerian economy is quite significant. The sector contributes mainly to national economy in terms of output and employment.
Therefore government must encourage and empower the sector through the provision of conducive macroeconomic policies aimed at boosting the performance of the sector.
Also, informal sector operators should not be content merely with self-help and being left alone to fend for themselves. The informal sector in itself may not be able to achieve due to inaccessibility to credit, but with the policy of the Central Bank of Nigeria through micro-finance banks, the macroeconomic objective of reducing unemployment in the country will become a reality. The microfinance policy has empowered the many microfinance institutions to provide credit to the informal sector.
Also, international development assistance needs to be reviewed and better coordinated in order to give greater priority to poverty reduction and improved social services.There is also the need for government at all levels to directly involve representatives of informal workers in the formulation, implementation, monitoring and evaluation of government intervention agencies.

Friday, February 12, 2016

Characteristics of Linear Programming Problems

Characteristics of Linear Programming Problems

Now that we have had the opportunity to construct several linear programming models, let's review the characteristics that identify a linear programming problem.

The components of a linear programming model are an objective function, decision variables , and constraints.


A linear programming problem requires a choice between alternative courses of action (i.e., a decision). The decision is represented in the model by decision variables. A typical choice task for a business firm is deciding how much of several different products to produce, as in the Beaver Creek Pottery Company example presented earlier in this chapter. Identifying the choice task and defining the decision variables is usually the first step in the formulation process because it is quite difficult to construct the objective function and constraints without first identifying the decision variables.
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The problem encompasses an objective that the decision maker wants to achieve. The two most frequently encountered objectives for a business are maximizing profit and minimizing cost.

A third characteristic of a linear programming problem is that restrictions exist, making unlimited achievement of the objective function impossible . In a business firm these restrictions often take the form of limited resources, such as labor or material; however, the sample models in this chapter exhibit a variety of problem restrictions. These restrictions, as well as the objective, must be definable by mathematical functional relationships that are linear. Defining these relationships is typically the most difficult part of the formulation process.
Properties of Linear Programming Models

In addition to encompassing only linear relationships, a linear programming model also has several other implicit properties, which have been exhibited consistently throughout the examples in this chapter. The term linear not only means that the functions in the models are graphed as a straight line; it also means that the relationships exhibit proportionality. In other words, the rate of change, or slope, of the function is constant; therefore, changes of a given size in the value of a decision variable will result in exactly the same relative changes in the functional value.

Proportionality means the slope of a constraint or objective function line is constant.


Linear programming also requires that the objective function terms and the constraint terms be additive. For example, in the Beaver Creek Pottery Company model, the total profit ( Z ) must equal the sum of profits earned from making bowls ($40 x 1 ) and mugs ($50 x 2 ). Also, the total resources used must equal the sum of the resources used for each activity in a constraint (e.g., labor).

The terms in the objective function or constraints are additive .


Another property of linear programming models is that the solution values (of the decision variables) cannot be restricted to integer values; the decision variables can take on any fractional value. Thus, the variables are said to be continuous or divisible , as opposed to integer or discrete . For example, although decision variables representing bowls or mugs or airplanes or automobiles should realistically have integer (whole number) solutions, the solution methods for linear programming will not necessarily provide such solutions. This is a property that will be discussed further as solution methods are presented in subsequent chapters.

The values of decision variables are continuous or divisible .


The final property of linear programming models is that the values of all the model parameters are assumed to be constant and known with certainty . In real situations, however, model parameters are frequently uncertain because they reflect the future as well as the present, and future conditions are rarely known with certainty.

THE USE OF LINEAR PROGRAMMING IN SOLVING BUSINESS PROBLEMS

THE USE OF LINEAR PROGRAMMING IN SOLVING BUSINESS PROBLEMS
Applications of linear programming for solving business problems:
1. Production Management: LP is applied for determining the optimal allocation of such re¬sources as materials, machines, manpower, etc. by a firm. It is used to determine the optimal product- mix of the firm to maximize its revenue. It is also used for product smoothing and assembly line balancing.
2. Personnel Management: LP technique enables the personnel manager to solve problems relating to recruitment, selection, training, and deployment of manpower to different departments of the firm. It is also used to determine the minimum number of employees required in various shifts to meet production schedule within a time schedule.
3. Inventory Management: A firm is faced with the problem of inventory management of raw materials and finished products. The objective function in inventory management is to minimize inven¬tory cost and the constraints are space and demand for the product. LP technique is used to solve this problem.
4. Marketing Management: LP technique enables the marketing manager in analyzing the audience coverage of advertising based on the available media, given the advertising budget as the constraint. It also helps the sales executive of a firm in finding the shortest route for his tour. With its use, the marketing manager determines the optimal distribution schedule for transporting the product from different warehouses to various market locations in such a manner that the total transport cost is the minimum.
5. Financial Management: The financial manager of a firm, mutual fund, insurance company, bank, etc. uses the LP technique for the selection of investment portfolio of shares, bonds, etc. so as to maximize return on investment.
6. Blending Problem: LP technique is also applicable to blending problem when a final product is produced by mixing a variety of raw materials. The blending problems arise in animal feed, diet problems, petroleum products, chemical products, etc. In all such cases, with raw materials and other inputs as constraints, the objective function is to minimize the cost of final product.
Linear programming: The technique of linear programming was formulated by a Russian mathematician L.V. Kantorovich. But the present version of simplex method was developed by Geoge B. Dentzig in 1947. Linear programming (LP) is an important technique of operations research developed for optimum utilization of resources.

According to famous Economist Robbins, the resources (land, labour, capital, materials, machines, etc.) are always limited. But each resource have various alternative uses. The problem before any manager is to select only those alternatives which can maximize the profit or minimize the cost of production. The linear programming technique is used for selecting the best possible strategy from a number of alternatives.
Linear programming consists of two words:
‘Linear and programming’: The world linear stand for indicating the rela-tionships between different variables of degree one whereas another word programming means planning and refers to the process of selecting best course of action from various alternatives.

Thus, linear programming is a mathematical technique for allocating limited resources is optimum manner. In the words of William M. Fox, “Linear programming is a planning technique that permits some objective function to be minimized or maximized within the framework of given situational restrictions.”
Characteristics:

All linear programming problems must have following five characteristics:
(a) Objective function: There must be clearly defined objec¬tive which can be stated in quantitative way. In business problems the objective is generally profit maximization or cost minimization.
(b) Constraints: All constraints (limitations) regarding resources should be fully spelt out in mathematical form.
(c) Non-negativity: The value of variables must be zero or positive and not negative. For example, in the case of production, the manager can decide about any particular product number in positive or minimum zero, not the negative.
(d) Linearity: The relationships between variables must be linear. Linear means proportional relationship between two ‘or more variable, i.e., the degree of variables should be maximum one.
(e) Finiteness: The number of inputs and outputs need to be finite. In the case of infinite factors, to compute feasible solution is not possible.

Assumptions:
(i) There are a number of constraints or restrictions- expressible in quantitative terms.
(ii) The prices of input and output both are constant.
(iii) The relationship between objective function and constraints are linear.
(iv) The objective function is to be optimized i.e., profit maximization or cost minimization.

Advantages and limitations:
LP has been considered an important tool due to following reasons:
1. LP makes logical thinking and provides better insight into business problems.
2. Manager can select the best solution with the help of LP by evaluating the cost and profit of various alternatives.
3. LP provides an information base for optimum alloca¬tion of scarce resources.
4. LP assists in making adjustments according to changing conditions.
5. LP helps in solving multi-dimensional problems.
LP approach suffers from the following limitations also:
1. This technique could not solve the problems in which variables cannot be stated quantitatively.
2. In some cases, the results of LP give a confusing and misleading picture. For example, the result of this technique is for the purchase of 1.6 machines.
It is very difficult to decide whether to purchase one or two- machine because machine can be purchased in whole.
3. LP technique cannot solve the business problems of non-linear nature.
4. The factor of uncertainty is not considered in this technique.
5. This technique is highly mathematical and complicated.
6. If the numbers of variables or constrains involved in LP problems are quite large, then using costly electronic computers become essential, which can be operated, only by trained personnel.
7. Under this technique to explain clearly the objective function is difficult.
Managerial uses and applications:
LP technique is applied to a wide variety of problems listed below:
(a) Optimizing the product mix when the production line works under certain specification;
(b) Securing least cost combination of inputs;
(c) Selecting the location of Plant;
(d) Deciding the transportation route;
(e) Utilizing the storage and distribution centre’s;
(f) Proper production scheduling and inventory control;
(g) Solving the blending problems;
(h) Minimizing the raw materials waste;
(i) Assigning job to specialized personnel.
The fundamental characteristic in all such cases is to find optimum combination of factors after evaluating known constraints. LP provides solution to business managers by understanding the complex problems in clear and sound way.
The basic problem before any manager is to decide the manner in which limited resources can be used for profit maximization and cost minimization. This needs best allocation of limited resources—for this purpose linear programming can be used advantageously.
Graphical method:
The business problems involving two variables can be easily solved by drawing the graph for various constraints. Following are the steps in graphical solution of linear programming problem (LPP):
1. Formulate LPP by writing the objective function (generally maximize profit) and the constraints.
2. Constraints are changed into equalities.
3. Plot the constraints on the graph.
4. Identify the feasible region and ascertain their coordinates.
5. Test which point is most profitable.

Applications of linear programming for solving business problems

APPLICATIONS OF LINEAR PROGRAMMING FOR SOLVING BUSINESS PROBLEMS

 

A mathematical optimization model consists of an objective function and a set of constraints in the form of a system of equations or inequalities. Optimization models are used extensively in almost all areas of decision-making, such as engineering design and financial portfolio selection. This site presents a focused and structured process for optimization problem formulation, design of optimal strategy, and quality-control tools that include validation, verification, and post-solution activities.
Applications of linear programming for solving business problems;

1. Production Management: LP is applied for determining the optimal allocation of such re­sources as materials, machines, manpower, etc. by a firm. It is used to determine the optimal product- mix of the firm to maximize its revenue. It is also used for product smoothing and assembly line balancing.

2. Personnel Management: LP technique enables the personnel manager to solve problems relating to recruitment, selection, training, and deployment of manpower to different departments of the firm. It is also used to determine the minimum number of employees required in various shifts to meet production schedule within a time schedule.


3. Inventory Management: A firm is faced with the problem of inventory management of raw materials and finished products. The objective function in inventory management is to minimize inven­tory cost and the constraints are space and demand for the product. LP technique is used to solve this problem.


4. Marketing Management: LP technique enables the marketing manager in analyzing the audience coverage of advertising based on the available media, given the advertising budget as the constraint. It also helps the sales executive of a firm in finding the shortest route for his tour. With its use, the marketing manager determines the optimal distribution schedule for transporting the product from different warehouses to various market locations in such a manner that the total transport cost is the minimum.


5. Financial Management: The financial manager of a firm, mutual fund, insurance company, bank, etc. uses the LP technique for the selection of investment portfolio of shares, bonds, etc. so as to maximize return on investment.


6. Blending Problem: LP technique is also applicable to blending problem when a final product is produced by mixing a variety of raw materials. The blending problems arise in animal feed, diet problems, petroleum products, chemical products, etc. In all such cases, with raw materials and other inputs as constraints, the objective function is to minimize the cost of final product.