9. Linear programming models are used by many Wall Street firms to select a desirable bond portfolio. The following is a simplified version of such model. Solodrex is considering investing in four bonds: $1,000,000 is available for investment. The expected annual return, the worst-case annual return on each bond, and the duration of each bond are given in Table 15. The duration of a bond is measure of the bond’s sensitivity to interest rates. Solodex wants to maximize the expected return from its bond investments, subject to three constraints. Constraint 1. The worst-case return of the bond portfolio must be at least 8%. Constraint 2. The average duration of the portfolio must be at most 6. For example, a portfolio that invested $ 600,000 in bond 1 and $400,000 in bond 4 would have an average duration of {(600,000) (3) + (400,000) (9)]}/ 1,000,000 = 5.4. Constraint 3. Because of the diversification requirements, at most 40% of the total amount invested can be invested in a single bond. Formulate an LP model to help Solodex tom achieve its objective. Table. 15

11. Eli Daisy produces the drug Rozac from four chemicals. Today they must produce 1,000 lb of drug. The three active ingredients in Rozac are A, B, and C. By weight, at least 8% of Rozac must consist of A, at least 4% of B, and at least 2% of C. The cost per pound of each chemical and the amount of each ingredient in1 lb of each chemical are given in table below. It is necessary that at least 100 lb of chemical 2 be used. Formulate an LP whose solution would determine the cheapest way of producing today’s batch of Rozac. Chemical| Cost per lb| A| B| C|

...ORIGINS OF OPERATIONS MANAGEMENT AND OPERATIONS RESEARCH
comparison of the origins of operations management and operations research reveals that both are an innovation of the 20th century. The origin of operations research was in England, circa 1937, and has its roots in scientific management, with its first significant applications to military operations in both World War I and World War II.Operations management had its origins in the early factory system, and was more associated with physical production in a factory environment and it too was strongly influenced by the scientific method. (Chase, Aquilano and Jacobs, 2001). Operations management however, by way of distinction, is more commonly applied to the management of organizational resources in terms of both effectiveness and efficiency and has equal application in the service sector as well as the manufacturing sector. Both OR and OM are mathematically oriented, utilize the scientific method, and produce information output for managerial decision making.
CONCEPTUAL/PHILOSOPHICAL BRIEF DISCUSSION
At the conceptual or philosophical level, OM and OR differ substantially. OM is mainly concerned with the managing of production resources critical to strategic growth and competitiveness of a company or organization. It entails the design, operation, control, and updating of...

...Homework Assignment 2 Solution
Question 1: (True / False) (20 Points)
Answer this question in a table with the question number and the selected answer (True or False) in separate columns as shown below.
Question Number
Answer
1
2
…
10
Grading
2 points each
1- The feasible solution space only contains points that satisfy all constraints.
2- Graphical solution to linear programming problems can handle problems that involve any number of decision variables.
3- The value of an objective function decreases as its iso-objective line is moved away from the origin.
4- If a single optimal solution exists to a graphical LP problem, it will exist at a corner point.
5- Using the enumeration approach, optimality is obtained by evaluating every coordinate (or point) in the feasible solution space.
6- A non-unique solution to a linear program indicates the existence of more than one optimal point with different values of the decision variables but the same value of the objective function.
7- An unbounded solution to a linear programing problem is usually due to omitting a constraint.
8- If a linear programming model has no feasible solution space, then the answer to that model is a unique optimal solution.
9- The constraint x1 >= 2 x2 is non linear.
10- In the general diet problem, the objective function is a maximization of profit obtained from selling the foods.
Answer
Question Number
Answer
1
T
2
F
3
F
4
T
5
F
6
T...

...OPERATIONS RESEARCH
INTRODUCTION
Operations Research is a unique discipline, one of its kinds, best of breeds, employing several highly developed and advanced analytical techniques which in turn aids in effective decision making. It is often regarded as a sub-field of mathematics. Operations research (OR) are not only deeply involved with making and taking effective decisions. It is also concerned with minimizing losses, optimization, simulations, forecasting and predicting within an organization.
According to Morse and Kimball, Operations Research is a scientific method of providing executive departments with quantitative basis for decisions regarding the operations under their control.
HISTORY
Operations Research, took birth as a new field of study in Britain in 1939 -40 at the start of World War II in the efforts of military planners, and it has developed and expanded execeedingly in the last five to six decades. After the war, the techniques were used in areas such as business, industry and society. Since then, operational research has extended into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, moving to a focus on the development of mathematical models that can be used to analyze and optimize complex systems, and has become an area of active academic and industrial research.1
Historical Origin...

...Operation research
Operational Research (OR) is the use of advanced analytical techniques to improve decision making. It is sometimes known as Operations Research, Management Science or Industrial Engineering. People with skills in OR hold jobs in decision support, business analytics, marketing analysis and logistics planning – as well as jobs with OR in the title.
Examples of OR
* Scheduling: of aircrews and the fleet for airlines, of vehicles in supply chains, of orders in a factory and of operating theatres in a hospital.
* Facility planning: computer simulations of airports for the rapid and safe processing of travellers, improving appointments systems for medical practice.
* Planning and forecasting: identifying possible future developments in telecommunications, deciding how much capacity is needed in a holiday business.
* Yield management: setting the prices of airline seats and hotel rooms to reflect changing demand and the risk of no shows.
* Credit scoring: deciding which customers offer the best prospects for credit companies.
* Marketing: evaluating the value of sale promotions, developing customer profiles and computing the life-time value of a customer.
* Defence and peace keeping: finding ways to deploy troops rapidly.
Classifications of Operation Research Models :
1. Classification by degree of abstraction. With then aforesaid liberty in the definition of a...

...DEPARTMENT OF APPLIED MATHEMATICS BSc Honours in Operations Research and Applied Statistics SMO 1101 Introduction to Operations Research TUTORIAL QUESTIONS
1. List and discuss the six major steps in the quantitative modeling process. 2. What is the difference between a i. descriptive and a normative model? ii. discrete and a continuous variable? 3. Show that the set ℜ n is a convex set. 4. Is the linearity assumption, in LP models, realistic in applications? 5. Print-Rite assembles printers for personal computers. These printers are assembled at five different points along the production line. Each production line consists of five work teams with different levels of skill. Each team can be assigned to any of the five assembly points. The following table gives the time, in minutes, to perform the tasks at each assembly point for the individual teams. Assembly 2 26 24 26 24 26 Point 3 40 30 28 36 30 4 30 32 36 30 40 5 26 18 18 20 24
Team A B C D E
1 20 22 24 20 20
Formulate a linear programming model that will minimize the total assembly time for a printer. 6. Why is implementation a difficult aspect of the quantitative modeling process?
Caston Sigauke 2006
1
7. A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table below. Employee Requirements for Post Office Day 1 = Monday Day 2 = Tuesday Day 3 = Wednesday Day 4 = Thursday...

...Assignment on Operations Research Transportation Model
INTRODUCTION
Many practical problems in operations research can be broadly formulated as linear programming problems, for which the simplex this is a general method and cannot be used for specific types of problems like,
(i)transportation models,
(ii)transshipment models and
(iii) the assignment models.
The above models are also basically allocation models. We can adopt the simplex technique to solve them, but easier algorithms have been developed for solution of such problems. The following sections deal with the transportation problems and their streamlined procedures for solution.
TRANSPORTATION MODEL
In a transportation problem, we have certain origins, which may represent factories where we produce items and supply a required quantity of the products to a certain number of destinations. This must be done in such a way as to maximize the profit or minimize the cost. Thus we have the places of production as origins and the places of supply as destinations. Sometimes the origins and destinations are also termed as sources and sinks.
To illustrate a typical transportation model, suppose m factories supply certain items to n warehouses. Let factory i (i = 1, 2, …, m) produce ai units and the warehouse j (j = 1, 2, …, n) requires bj units. Suppose the
cost of transportation from factory i to...

...INTRODUCTION TO OPERATIONS RESEARCH (OR)
1.1 INTRODUCTION
Operation Research, an approach to decision making based on the scientific method, makes extensive use of quantitative approaches to decision making. In addition to operation research, two other widely known and accepted names are management sciences and decision science interchangeably.
The scientific management revolution of the early 1900s, initiated by Frederic W. Taylor, provided the foundation for the use of quantitative methods in management. But modern management science research is generally considered to have originated during the World War II period, when teams were formed to deal with strategic and tactical problems faced by the military. These teams, which often consisted of people with diverse specialities (e.g., mathematicians, engineers and behavioural scientists) were jointed together to solve a common problem through the utilization of the scientific method. After the war, many of these team members continued their research in the field of management science.
1.2 WHAT IS OPERATION RESEARCH?
Operation Research is the scientific approach to managerial decision making. This approach starts with data. These data are processed into information that is valuable to people making decisions. This processing and manipulating of raw data into meaningful information is the heart of the Operation Research. Computers...

...MBA SEMESTER II MB0048 –Operation Research- 4 Credits (Book ID: B1137) Assignment Set- 1 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions
1. a. Explain how and why Operation Research methods have been valuable in aiding executive decisions. [5 Marks] b. Discuss the usefulness of Operation Research in decision making process and the role of computers in this field. [5 Marks]
2. Explain how the linear programming technique can be helpful in decision-making in the areas of Marketing and Finance. [10 Marks]
3. a. How do you recognise optimality in the simplex method? b. Write the role of pivot element in simplex table?
[5 Marks] [5 Marks]
4. What is the significance of duality theory of linear programming? Describe the general rules for writing the dual of a linear programming problem. [10 Marks]
5. Use Two-Phase simplex method to solve: Minimize z= + + + ≥ 0, + ≤3 ≥4 ≥ 0 and is unrestricted. =5
[10 Marks]
Subject to constraints:
6. Use Branch and Bound method to solve the following L.P.P: Maximize z= 7 + 9 Subject to constraints: - + 3 ≤6 7 + ≤7 , ≥ 0 and are integers. ≤ 35
[10 Marks]
MBA SEMESTER II MB0048 –Operation Research- 4 Credits (Book ID: B1137) Assignment Set- 2 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions
1. What are the essential characteristics of Operation Research? Mention different phases in an...