Opertation Research – Quantitative Operation Techniques
Opertation Research – Quantitative Operation Techniques
A report on quantitative operation techniquesSubmitted toDr. RICHA CHAUDHARYBy,SUDHIR TALEKAR(M-13-49) TABLE OF CONTENT1OPERATIONS RESEARCH32LINEAR PROGRAMMING PROBLEM4-53INVENTORY MANAGEMENT MODEL6-94CRITICAL PATH METHOD10-155GAME THEORY16-186QUEING THEORY18-20OPERATIONS RESEARCH :Operations research is a discipline that deals with the application of advanced analytical methods to help make better decisions. It is often considered to be a sub-field of mathematics. The terms management science and decision science are sometimes used as synonyms. Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notably industrial engineering and operations management, and draws on psychology and organization science. Operations research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.
LINEAR PROGRAMMING PROBLEMCase 1:Parle AgroLinear programming is the technique for choosing the best alternative from a set of feasible alternatives , in a situation in which function as well as constraints can be expressed as linear mathematical function.Linear programming can be used in business scenario for two purposes :Maximization function where company requires to take it to maximum level likes sales or profit where each company expects to take it to maximum level.Minimization function when company requires to minimize it likes costing where each company expects it to be minimum.In case of parle agro which is an manufacturing unit , sales and profit need to be on maximum level while costing of the product needs to be on minimum level.Parle agro normally produces various products like frooti,njoi shakes, various confectionary but in this analysis we will concentrate only on the product frooti.So the current analysis will require Maximiation of the sales and profit of mango frooti while cost should be minimum under Minimaization function.So consider a situation where parle agro requires to produce product frooti(1 litre) which requires 800ml litre of water, 200ml of sugar and mango pulp syrup and 1hour of labour hours . Whereas other product example x(assume ) 600ml of water and 400ml of sugar and mango product and 2 hours of labor hours. Every week availability of water is around 100litre, of sugar and mango pulp is 50litre, 60labour hour.Product frooti yields Rs 5 per litre while product X yields Rs 4 per liter.Analysis:Each product of frooti requires 800ml water,200ml sugar and mango pulp syrup, 1 labor hour.Each product of X requires 600ml water ,400ml sugar and mango pulp syrup, 2labor hour.Water cannot cross 100litre, sugar syrup and mango pulp cannot cross 50litre, while labor hours cannot exceed 60hours.Formulation:Let P, Q be the number of units produced of frooti and X.Maximize :Z= 5P+4QSubject to,800P+600Q <= 10000……………………………. . Water constraint.