Planning Production of Concrete Products Using Linear Programming: A Case of Small Tile Cement Tile Factory

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1 Volume 11, Number 1, Spring Planning Production of Concrete Products Using Linear Programming: A Case of Small Tile Cement Tile Factory Akram Masoud Haddad College of Business Administration (COBA) American University in the Emirates Abstract Linear programming (LP) is the most popular of the approaches, which was developed during World War II, to make an optimal set of decision, it an attempts to maximize or minimize some objective. The objectives of this study are to study the existing product portfolio and resource constraints of the small tile factory in Amman, analyze existing profitability of tile, and formulate linear programming model and suggest the suitable model to maximize the profit tile production. The study shows that there are high demand for cement tile in Jordan due to rapid growth in building construction activities, which is derived from the increased demand for apartments for housing which is generated from the increase in population. Solving linear programming model that is formulated based on data collected from the study sample and real factory shows that the production mixture of different tiles products increases the monthly profit of the factory. Moreover, results simulate the real world production of tiles that is the more demanded tile products are produced in great quantities. Therefore, using linear programming model will increase the profit and optimizing the usage of available recourse Keywords Production Planning, Linear Programming, Simplex Method, Industrial Production Introduction Management of the modern firms need to make decisions all the time; such as how to allocate the firm's resources to achieve its goal, usually achieve the highest possible return or maximize rate of return, or minimize costs with constrained resources and other fields of decisions. Several quantitative techniques are used to solve the problems facing these firms. Linear programming (LP) is one of the powerful, approved and important scientific methods in quantitative methods, used extensively in various fields to assists managers in planning and decision-making optimal use of resources and achieves the best target. Linear programming (LP) is the most popular of the approaches of a larger area of mathematical optimization techniques called mathematical programming, which is concerned with making an optimal set of decision. It attempts to maximize or minimize some objective, for example, maximize profits or minimize costs. Linear programming was developed during World War II, when a system with which to maximize the efficiency of resources was of utmost importance. George Dantzig, a member of the U.S. Air Force, developed the Simplex method of optimization in 1947 in order to provide an efficient algorithm for solving programming problems that had linear structures. Since then, experts from a variety of fields, especially mathematics and economics, have developed the theory behind linear programming and explored its applications. (Dantzig, 1993 )[1]. Linear programming has several applications in military, government, industry and civil engineering. In addition, it is often used as part of a calculated plan, solving nonlinear programming problem, discrete programming problems, and optimal control problems such as process, inventory and contingency planning. LP has been used in aggregate production planning, service productivity, product planning, product routing, control and distribution scheduling, plant location and material handling (Manley and Threadgill, 1991), (Jacob et al., 1996) (Chopra and Meindl, 2001), (Thomas, 2002), (Stadtler, 2000), (Taghrid and Hassan, 2009), (Fagoyinbo et al., 2011).

2 Volume 11, Number 1, Spring Linear programming is an important optimization for several reasons: Many practical problems in operations research can be expressed as a linear programming problem and also a number of other algorithms of optimization problems by linear programming work as sub- problem. Historically, ideas of linear programming inspire many basic concepts of optimization theory such as duality, decomposition and importance of convexity and its generalizations. (Fagoyinbo et al., 2011). Although, the construction sector in Jordan witness very rapid growth during the last decades, the sector facing many challenges among these challenges is the production costs. One of the important subsector of construction sector is tiles production factories that characterized by small scattered factory owned by one person and managed in primitive way. Tiles factories in Jordan face many problems, mainly the planning of production, miss-use of the available resources and financial problems and high cost of production which affect there profitability. This research takes into consideration the sale/production of the main products of cement tiles products in a small size processing units. The objectives of this study are to study the existing product portfolio and resource constraints of the small tile factory in Amman, analyze existing profitability of tile, and formulate linear programming model and suggest the suitable model to maximize the profit tile production. Basic requirement of linear programming problem The technique necessitates the formulation of the problem and fitting it into a mathematical model. This needs a comprehensive study of the components of the problem, namely, a) the decision variables; b) the objective function; c) the alternative course of action; and d) the working environment. (Balakrishnan, et al, (2002) (Murugan and Manivel, 2009) Any linear program consists of four parts: a set of decision variables, the parameters, the objective function, and a set of constraints. That is the basic structure of an LP problem is either to maximize or minimize an objective function, while satisfying a set of constraining conditions called constraints. Linear programming problem requires the availability following requirements: (Andersen at el. 2001) 1. A clear and specific goal so that it can be represented mathematical equation, normally to increase (maximization) profits or (minimization) reduces costs. The objective and its limitations must be expressed as mathematical equations or inequalities, and these must be linear equations and inequalities. 2. Presence of constraints or limitations can't be exceeded. They represent conditions which must be satisfied in determining the values of the decision variables. Most constraints in a linear programming problem are expressed as inequalities. They set upper or lower limits, they do not express exact equalities; thus permit many possibilities. 3. The alternative course of action or a number of alternatives to choose from. 4. The expression of the objective function and constraints in linear programming problems linear equations of the first degree. Linear Programming Assumptions and General Limitations There are five essential conditions in a problem situation for linear programming to pertain. First, there must be limited resources (such as a limited number of workers, equipments, finances, and material); otherwise there would be no problem. Second, there must be an explicit objective (such as maximize profit or minimize cost). Third, there must be linearity (if it takes three hours to make a part, then two parts would take six hours, and three parts would take nine hours). Fourth, there must be homogeneity (the products are identical, or all the hours available from a worker are equally productive). Fifth is divisibility: normal linear programming assumes that products and resources can be subdivided into fractions (Wayne, 2003).

3 Volume 11, Number 1, Spring To solve a real business problem by using Linear Programming, there are many assumptions (limitations) have to be made. These are (Andersen at el. 2001): 1. Linearity: The objective function and all constraints are all linear functions; that is, every term must be of the first degree. Linear means proportional relationship between two or more variables. That is, every increment in one variable results in proportionate change in another variable. Such a relationship is generally found between inputs and outputs. Linearity implies the next two assumptions. 2. Proportionality: For the entire range of the feasible output, the rate of substitution between the variables is constant. That is the contribution of any variable to the objective function or constraints is proportional to that variable. This implies no discounts or economies to scale. 3. Non- negativity: The value of variables must be positive and should not be negative. This suits the production decisions, as negative values of physical quantities are never possible. 4. Finiteness: The number of inputs, outputs and activities need to be finite, as otherwise computation of an optimal solution is not possible. Thus, linear programming is applicable to problems involving quantitative variables, which are linear in nature. Given these quantitative variables, the maximization or minimization objective function can be achieved. 5. Additivity: All operations of the problem must be additive with respect to resource usage, returns, and cost. The contribution of any variable to the objective function or constraints is independent of the values of the other variables. This implies independence among the variables. 6. Divisibility: Decision variables can be fractions; this means Non-integer solutions are permissible. However, by using a special technique called integer programming, we can bypass this condition. 7. Certainty: This assumption is also called the deterministic assumption. This means that all parameters (all coefficients in the objective function and the constraints) are known with certainty. Thus, all coefficients of the LP model are assumed to be known with certainty that is LP is a deterministic model. Other adds realistically assumption; however, coefficients and parameters are often the result of guesswork and approximation. The effect of changing these numbers can be determined with sensitivity analysis (Wayne, 2003). However, there are many modifications of these assumption or new techniques that developed to overcome these assumption for example, If this subdivision is not possible, a modification of linear programming, called integer programming, can be used, and when a single objective is to be maximized or minimized, we can use linear programming. When multiple objectives exist, goal programming is used. If a problem is best solved in stages or time frames, this is dynamic programming. Other restrictions on the nature of the problem may require that it be solved by other variations of the technique, such as nonlinear programming or quadratic programming. The certainty assumption is overcome by using (minimization of total deviations) MOTAD Model which is developed by Hazel (Rahahleh, 1989) (Haddad, and Shahwan, 2012). Linear programming problem can be stated as following: Maximize (minimize) Z = C1X1 + C2X2 + +Cn Xn Subject to resource constraints in the form A11X1 + A12X2 + + A1n Xn B1 A21X1 + A22X2 + + A2n Xn B2... Am1X1 + Am2X2 + + Amn Xn Bm

4 Volume 11, Number 1, Spring Non negativity variables: x1, x2, x3, xn > 0 Where: Cn, Amn, and Bm are given constants. Depending on the problem, the constraints may also be stated with equal signs (=) or Greater-than-or-equal-to signs ( ). Tile Production Sector in Jordan The construction sector is of important economic sectors in Jordan, which is characterized by the diversity of its sub-sectors and complexity with a number of other sectors, making it more vulnerable to economic and demographic changes and social development. This sector influence directly by the estate market and heavily depends on the construction sector as a key driver for it, as it. In addition, the sector is associated with the manufacture and trade sector elevators and solar water heaters, doors and windows and supplies blacksmithing, carpentry, industrial and number of glass and mirrors. The construction sector has witnessed a steady development in the last decade as results of many factors, such as overall political climate, and safe investment environment, and good infrastructure. This sector ranked as the fifth among industrial sectors in terms of the number of workers. The number of workers reached around (17) thousand workers working in 2886 establishments operating in the construction sector.the year Records shows that the increase in the capital invested in this sector increased by (34%) during the years 2012, reach about JD 382 million in Tiles production Cement tiles are wall & floor tiles made of cement together with sand, gravel and optionally adding marble chips to the ingredient. Cement tile is a type of tiles, which is made from black Cement, white cement, mosaic usually cracking marble stone, and colored pigments. This is very durable and sturdy, with a range of patterns and colors. Cement tile tends to be about twice as heavy as ceramic tile, and it is less subject to breakage and chipping. More properly, these tiles are actually made from concrete, a mixture of the binding agent known as cement and some type of aggregate. In basic cement tile products, the cement is blended with a pigment while it is being mixed, so that the resulting tiles are colored. Tile is composed of two layers, layer the face in which mosaic and white cement is used and the background layer in which black cement and sand is used. The broken marbles are different according to the sources of these marbles. Normally the factories use European imported broken marbles, Egyptian marbles, local sources marbles. Cement tiles of various sizes can be produced. The popular size and thickness of tiles are: 1. Tile 20x20 cm or 25 x 25 cm and 25 mm thickness and facial layer thickness is not less than 6 mm. 2. Tiles 30 x 30 cm or 40 x 40 cm and 30 mm thickness and the thickness of the face layer is not less than (8 mm). 3. Panel tile 20 X 7 or 25 X 7 or 30 X 7 as measured by the tile thickness (15 mm) layer thickness of not less than face (6 mm). The demand for cement tile is derived from building construction activities. Since transporting and selling cement tiles over a long distance are not a profitable operation, the relevant market is the local or regional market. The total area constructed in Jordan is (17.34) during the years 2012, this implies high demand on this product. Demand for tiles products The demand for cement tile is derived from building construction activities, as well as the increased demand for apartments for housing which is generated from the increase in population either from high nature growth rate in population which is account for 2.8% or from the migrations to Jordan due to political situations in the neighboring countries. Table (1) shows the number, the growth rate in

5 Volume 11, Number 1, Spring the number of licenses issued by the authorized authorizes in Jordan. The total number is increased from (10.07) million m2 in 2008 to (17.3) million m2 in 2012, that is 70% increase. Most of this area is for housing buildings purposes, the percentage of the housing area ranging from 73.9% to 81.9%, and exceeds 81.9% of the total area licensed in Table 1: number of building license issued by big Jordanian Municipalities Housing Commercial and other uses Total Housing Commercial and other uses Total % of Housing Therefore, there are growing high demand for tiles products and the total production should exceed the licensed area by at least 50% as there are many buildings are build without license or license from other authorizes not included in the statistics. The basic raw materials used in the manufacture of flooring mosaic tiles are grey cement, white cement stone/marble chips, fine aggregates or sand, dolomite powder and coloring oxide ordinary Portland cement can be used for mosaic tiles of dull colors. All these row materials are available in the local markets like are sand, cement (Grey and white) and white, gravel and marble chips from local sources or imported sources mainly marbles chips. Raw materials for manufacturing pathway tiles are grey cement, fine aggregates or sand, and gravels. The current price of cement tiles ranges between 3-12 JD per m2 at factory gate depending on composition (marble chips, granite chips, etc.) design and coloring matter. Review of Literature In objective of investigate the extent the industrial sector is applying the research methods in the planning and production control processes Al-Samoum ( 1998) The use of Research Methods in The Planning and Production Control Processes in industrial sector. The research sample was selected from (90) factories working in foodstuff mineral and chemical industries. The study shows that approximately half of the sample constituent does not apply the operational research methods in planning and production control; they are using simple statistical methods such as graphs and personal experience. The use of operational research methods in planning and production control is connected with the kind of industry and factory size. Success of applying operational research methods depends on the type of fields to be used in. However, the operational research methods were successfully used in minimizing customer waiting time, resources particularization, maintenance and profit analysis, and used in planning to add new products. There are many obstacles facing the use of operational research methods in planning and production control such as availability of reliable information systems at some of the factories, high cost of its use, managers' ignorance of the available methods, unavailability of specialized personnel to use these methods and the small size of the factories. Saad and Shbow (2003) apply integer Linear Programming to publishing sector in Lebanon, a case of Arab Scientific Publishers, printing and publishing and distribution, which is one of Leading companies in Lebanon and the Arab world, we can obtain an optimal production plan, which aims primarily to increase return the company, within the existing data, while maintaining the quality and the required quality Globally. The result of the study, conducted over a period of years of production,

6 Volume 11, Number 1, Spring to show that Adoption of this the best way to achieve the company's revenue surplus of $ , which is of the surplus in profit, compared with the returns achieved in current production in the company Al-Ghamdi (2008) Applied linear programming method to the Arab Company for the manufacture of vegetable oils in order to determine the overall planning of production, and determining the quantities of production and inventory of oil per month for the company and thus determining the total cost of production during the 12 hours per month. By applying this method, the company reached a number of the most important results, determine the amount of the monthly production and inventory all the company's products, in addition to reduced cost for all oil products. Khan et al (2011) Linear Programming And Sensitivity analysis to optimal Production Planning For ICI Pakistan and estimates an optimal production levels for the different products manufactured at ICI, a multinational company in Pakistan. The revised simplex method is used to maximize the profit generated in 2010 subjected to cost resource constraints. The production of Polyester, Soda Ash, Paints and Chemicals are taken into consideration. The production of the Soda Ash is most productive contributing more to the objective function. In the year 2010, the company was earning R.s 3, 273,756,000 from the production of these products. This amount raises by R.s 189,708, R.s 989,238, R.s 15,594,377 and R.s 45,408,040 by changing production patterns within the first, second, third and fourth digits respectively. The company can earn significant profit by operating on the proposed production forecasts. The top management and decision makers can maximize the profit of the company within the nameplate production capacity, setting up the future goals and outlook of the company. Methodology Any modern industrial manufacturing unit faces many problems, especially in this rapid changeable business environment, such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by the marketing and competition. To be able to find the best uses of an organization s resources, a mathematical technique called Linear Programming can be used. The adjective linear is used to describe a relationship between two or more variables, a relationship that is directly and precisely proportional. The data for the study were collected from a sample of factories that manufacturing tiles in Amman governorates. The product wise actual expenditure incurred on material, labour and overheads details on production, sales and profit earned were obtained from formal and informal interviews of the respondents. In addition, watching and records notes about the production of representative tile factory for separate 6 days distributed in one. In the present study, the following steps outline the process of solving any linear system of equations using an available LP solver. Formulation of LP model The process of building linear programming model passes through three basic steps, these are: a. Indicate the decision variable b. State the objective function c. Indicate the constraints Decision variables: The factory which is used in this study produces two main types of tile. The first is cement tile, which is used for outdoor areas such as yards and footpaths and the second is Mosaic tiles that used either in the open areas or indoors for areas that can be covered by carpets or salons depending in the quality of the raw materials of the face layers especially the origin of marble chips. The most popular dimensions of cement tile are 30*30*3cm or 40*40*3cm, the face layer is made of pure grey cement or gravel face layer. While the most popular dimension of mosaic tiles are 30*30*2.5cm normally used for salons or sitting rooms or 20*20*2.5cm, that is used normally for sleeping rooms. The layer

7 Volume 11, Number 1, Spring face is consist of four types of import first quality marble chips, local first quality marble, law quality local marble, karar marble chips. The mosaic tiles need banal tiles with the same length and height of 10cm, the production of banal tiles is approximately 20% of the quantity produced of the mosaic tiles. The analysis of the gross margins shows that there is no significant difference between the profits due to different in dimension but the difference is due to the type of marble used in the face layer. Let X1, X2, X3, X4, X5, X6, X7, X8 represent the number of square meter of pure grey cement, gravel face of cement tile of dimensions of 30*30*3 cm, and imported, local first quality marble, karar marble with dimensions of 30*30*2.5 cm, law quality local marble with dimensions of 20*20*2 cm and banal tiles respectively. Objective function The key decision is to determine the most variables and profitable of the tiles product and the optimum volume of production of each item of tile product. The profit per unit of X1, X2,.X8, factory's gate prices and the variable cost (capital need) to produce one M 2 of tile are shown in table (2). Constraints The constraints in the model are the following: i. Raw materials cost constraint, there limited amount of capital available to buy raw material that cover the period between buying the raw material and getting the prices of sold tiles in cash, normally about 1.5 month. ii. Labour cost constraint; there are two types of labours, technicians (skilled) labour and non skilled labours, the first types work in machines, while the second type of labour can work in work in the factory. Both usually get monthly salaries. That is the salaries of skilled labour considered as loses if they don t work. iii. Machines capacity constraints, the capacity of two types of machines needed, one for moldy and pressing tiles, and the second for glazing and smoothing the mosaic tiles. The factory has two machines for moldy and pressing tiles and one machine for glazing and smoothing the mosaic tiles. The amount of production of each machine varies according to different types of tiles products dimensions. iv. Production constraints: the amount of banal tiles should be 25% of the total mosaic tiles. Shifting from one type to another means at least production of the moldy and pressing machine for one day v. The envisaged plant is considered to operate in a single shift of 8 hours a day, six days a week and 300 days a year. Production can be doubled or tripled, if the plant is made to operate in two or three shifts. The technical coefficients for each of the selected tile products, available resources, the capacity of the machines and gross margins are show in table (2). the objective is to maximize the total profit of the selected tile products through manufacture and sale of tile products can be stated as follow: (Anderson et al, 2003). Subject to: Maximize Z = X1+ X2+ X3+ X4+ X5+ X6+ X7+ X X X X (Raw material cost) 7.36 X X X (Labour cost) 5.79 X X X (Overhead cost) X3+ X4+ X5+ X6+ X7 = 4 X8 Xi daily amount of production of Xi

8 Volume 11, Number 1, Spring The amount of each type must be number of working days of each moldy and pressing machines time working days X X X (Raw material cost) 7.36 X X X (Labour cost) 5.79 X X X (Overhead cost) And X1, X2, and X3 0 Result and Discussion The results of solving the linear programming model or tiles factory for maximizing the profit from the present level taking into consideration all possible constraints faced by that factory is presented in table (2). The table shows that the factory can generate a maximum profit of (6351JD) of producing (3767m2) of different quantities of tiles of the different products. The result shows that the large amount of tiles is from mosaic tiles of 20*20 cm, and mosaic tiles of imported marble with amount of (1097) and (1317) respectively. The quantities of other tiles produces are small, because the factory must have verities of tile product which is very important from marketing point view. The tiles factories owners use diversification of products strategy in marketing. In this context, these results are long with the real world production noticed from the sample. In additions the growing demand for these types in particular as a result of rapid growth in constructing sector mainly the buildings for housing purposes. Records show that the licensed area exceeds (17.3) million square meters in 2012 with increase of (8.5%) over the last year, 81.9% of this area is for housing purposes. Table 2: Comparison between LP Result and Specialized on One Type of Production Product Maximum Daily Gross Maximum Monthly LP LP Production Margins Production Production Profit Unit m2 JD JD m2 JD Local High Imported Import Local * Gravel Cement Tile Pure Cement Banal no produced alone Total Comparing the profit with the profit generated from producing one type of tile products considered in this case and the profit of the sample with the result of the linear programming models shows that the profit of linear programming model is exceed that generated from the highest profit of specialized on one product that generate only (5983JD) per month of specialized in production of tiles from local marble class 1. It is worth to mention that no one can specialize in production of banal tiles. Sensitivity analysis is a means of assessing the impact of potential changes to the parameters (the numerical values) of an LP model. Such changes may occur due to forces beyond a manager s

9 Volume 11, Number 1, Spring control; or a manager may be contemplating making the changes, say, to increase profits or reduce costs. The sensitivity analysis of the model demonstrates the impact of changing the recourses and other right hand side of the constraints. The sensitivity report of the model is given in table (3). These figures provide very important information about the manufacturing process in the tiles production unit. The sensitivity analysis of objective function coefficient shows the allowable increase and decrease in these coefficients that is the changes of the products prices that maintained the profit without any changes. Form marketing point view, this means that the owner of tiles factory can reduce the prices without any impact on the total profit. Table 3: the Sensitivity Analysis of the Objective Function Coefficient Coefficients of Objective Allowable Function Increase Allowable Decrease Local High unlimited Imported unlimited Import Local unlimited 20* Cement with Gravel unlimited Pure Cement unlimited Banal 1.65 unlimited 0.04 Each constraint has a corresponding shadow price, which is a marginal value that indicates the amount by which the value of the objective function would change if there were a one-unit change in the RHS value of that constraint. In the contrary, there are many non binding constraints, which are making the right hand values of the non binding constraints less restrictive will have no impact on the solution. Only the is bending constraint, this constraint limits the value of the objective function; if the constraint could be relaxed (less restrictive), an improved solution would be possible. The results of right hand side sensitivity analysis that the labour cost, and marketing and production constraints are bending and have shadow prices. The results indicate that there are surplus of capital that is allocated to cover raw materials cost and variable cost items, this means that this surplus can be invested in other activities and generate income instead of frozen without any benefit, and limit the amount of capital to that shown in the table. Table 4: Sensitivity Analysis for the Right Hand Side (RH) Constraint RH side Final Shadow Allowable Allowable Value Prices Increase Decrease Raw Material Cost unlimited Labor Cost unlimited 851 Other Variable Cost unlimited 2232 Total Variable Cost unlimited 5194 Machine 1 Capacity unlimited 0 Machine 2 Capacity unlimited 6 Marketing and Production

10 Volume 11, Number 1, Spring Constraints for Each Type of Tiles Products unlimited unlimited unlimited Days of Production Each constraint has a corresponding shadow price, which is a marginal value that indicates the amount by which the value of the objective function would change if there were a one-unit change in the RHS value of that constraint. The shadow price of nonbinding constraint is zero, that implies increasing or decreasing its RHS value by one unit will have no impact on the value of the objective function. The shadow price shows that a one day added to productions as the cost of goods sold is contributing to the maximization of the profit. In other words adding one shift will increase the production. However, most of the tiles factories working for only one shift (eight hours per day). Conclusion This study use linear programming techniques to maximize the profit of typical Jordanian small tiles factory. Solving linear programming model that is formulated based on data collected from the study sample and real factory shows that the production mixture of different tiles products increases the monthly profit of the factory. Moreover, results simulate the real world production of tiles that is the more demanded tile products are produced in great quantities. Therefore, using linear programming model will increase the profit and optimizing the usage of available recourse. References Alghamedi, W. (2008) Aggregate Production Planning by using Linear Programming Empirical study on Arabian Company, Master thesis, Faculty of Economics and Administration King Abdu-Aziz University, Jeddah, Saudi Arabia Al-Samoum (2010) The use of Research Methods in The Planning and Production Control Processes in industrial sector Master thesis, Faculty of Economics and Administration King Abdu-Aziz University, Jeddah, Saudi Arabia Al-samoum A.A (1998) The use of Research Methods in The Planning and Production Control Processes, Master thesis, Faculty of Economics and Administration King Abdu-Aziz University, Jeddah Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2002). An introduction to management science. (10th ed.). Cincinnati, OH: South-Western. Balakrishnan, N. Kannan, N, and Srinivasan, M.R, (2002) Statistical methods and practice - Recent advances, Norosa publishing house, New Delhi.pp Chopra, S. and Meindl, P., Supply Chain Management: Strategy, Planning and Operation, Prentice- Hall Inc., 2001 Dantzig, G. B. (1963). Linear programming and extension. Priceton University Press.

11 Volume 11, Number 1, Spring Dantzig, G.,1993, Computational Algorithm of the Revised Simplex Methods, RAND Memorandum RM-1266 Fagoyinbo, I. S., Akinbo, R. Y., Ajibode, I. A., & Olaniran, Y.O.A. (2011). Maximization of Profit in Manufacturing Industries Using Linear Programming Techniques: Geepee Nigeria Limited Mediterranean Journal of Social Sciences Vol. 2 (6) November 2011 Haddad, A. M. and Shahwan, Y (2012) Optimization Agricultural Production under Financial Risk of Water Constraint in the Jordan Valley Applied Economics,volume 44 numbers APRIL 2012 ISSN Jacobs, D. A., Silan, M. N., & Clemson, B. A.(1996). An analysis of alternative locations and service areas of American Red Cross blood facilities. Interfaces, 26, Khan, Izaz Ullah, Norkhairul Hafiz Bajuri and Imran Abbas Jadoon (2011) Optimal Production Planning for ICI Pakistan Using Linear Programming And Sensitivity Analysis International Journal of Business and Social Science Vol. 2 No. 23 [Special Issue December 2011] 206 Manley, B. R., & Threadgill, J. A. (1991). LP used for valuation and planning of New Zealand plantation forests. Interfaces, 21, Murugan N. and S. Manivel Profit Planning of an NGO Run Enterprise Using Linear Programming Approach International Research Journal of Finance and Economics - Issue 23 (2009) Rahahleh, M.A.S.(1989) Measures of Variation in Net Return and Their Impact on Risk- Efficiency Farm Plans for Annual Rainfed Crops in Jordan, master thesis, University of Jordan, Amman, Jordan. Saad and Shbow (2003) apply integer Linear Programming to publishing sector in Lebanon, a case of Arab Scientific Publishers, printing and publishing and distribution, journal of King Abdu- Aziz University, Economic and Management, vol 19 No. 2 Stadtler, H., Supply Chain Management and Advanced Planning: Concepts, Models, software and Case Studies, Springr-Verlag Berlin Heidelberg New York, 2000 Taghrid, I., & Hassan, F. (2009). Linear programming and sensitivity analysis in production planning. IJCSNS International Journal of Computer Science and Network Security, 9, Thomas R., A de novo programming model for optimal distribution network design in a supply chain, Center for business and economics, Midwest Business Administration Association Annual meeting, 2002 Wayne L. Winston. (2003) Operations Research: Applications and Algorithms. Duxbury Press, fourth edition,