Report- Hard Copy
ASSIGNMENT METHOD
The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. It consists of finding a maximum weight matching in a weighted bipartite graph. In its most general form, the problem is as follows:

There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one agent to each task in such a way that the total cost of the assignment is minimized. If the numbers of agents and tasks are equal and the total cost of the assignment for all tasks is equal to the sum of the costs for each agent (or the sum of the costs for each task, which is the same thing in this case), then the problem is called the linear assignment problem. Commonly, when speaking of the assignment problem without any additional qualification, then the linear assignment problem is meant. Example:

A machine shop currently has three jobs A,B,C to be done on three machines W,X,Y. Any one of the jobs can be processed completely on any one of the machines, and the assignment of jobs to machines must be on a one-on-one basis. Find the job assignments that will minimize the total costs. The cost for each job-machine assignment are given on table. | |Machines | |Jobs |W |X |Y | |A |P250 |P310 |P350 | |B |150 |200 |240 | |C...

...JET Copies Case Problem page 1
Assignment #1: JET Copies Case Problem
By: Jenna Kiragis
QuantitativeMethods 540
7/29/2012
JET Copies Case Problem page 2
In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown.
Lost revenue of Jet Copies due to breakdown can be done by generating random numbers from different probability distributions according the given probability law.
1. Simulation for the repair time.
|Repair Time (days) |Probability |
|1 |0.2 |
|2 |0.45 |
|3 |0.25 |
|4 |0.1 |
The generated random number 0.2 take repair time...

...computational steps of the simplex method for solving linear programming problems. How would you identify whether an optimal solution to a problem obtained using simplex algorithm is unique or not?
a) What is the difference between a feasible solution, a basic feasible solution, and an optimal solution of a linear programming problem?
b) What is the difference between simplex solution procedure for a `maximization’ and a `minimization’ problem?
c) Using the concept of net contribution, provide an intuitive explanation of why the criterion for optimality for maximization problem is different from that of minimization problems.
Outline the steps involved in the simplex algorithm for solving a linear programming maximization problem. Also define the technical terms used therein.
3. ``Linear programming is one of the most frequently and successfully employed Operations Research techniques to managerial and business decisions.’’ Elucidate this statement with some examples.
…2…
…2…
4. Describe the transporation problem and give its mathematical model. Explain, by taking an illustration, the North-West Corner Rule, the Least Cost Method and the Vogel’s Approximation Method to obtain the initial feasible solution to a transportation problem.
Discuss the various methods of finding initial feasible solution of a transportation problem and state the advantages, disadvantages, and areas of...

...Quantitative Research MethodsQuantitative means quantity which implies that there is something that can be counted. Quantitative research has been defined in many ways. It is the kind of research that involves the tallying, manipulation or systematic aggregation of quantities of data (Henning, 1986)
John W. Creswell defined quantitative research as an inquiry into a social or human problem based on testing a theory composed a theory composed of variables, measured with numbers, and analysed with statistical procedures in order to determine whether the predictive generalisations of the theory holds true. (Creswell, 2003)
On the other hand, another author defined quantitative research as the collection of numerical data in order to explain, predict and/or control phenomena of interest. Quantitative research is explaining phenomena by collecting numerical data that are analysed using mathematically based methods (Aliaga & Gunderson, 2000)
Quantitative research can also be said to be a research based on traditional scientific methods, which generates numerical data and usually seeks to establish causal relationships (or association) between two or more variables, using statistical methods to test the strength and significance of the relationships (A dictionary of Nursing, 2008)
Simply put, quantitative...

...Sub: QuantitativeTechniques in Management
1) Answer any Sixteen
1. What is a linear programming problem? Discuss the scope and role of
linear programming in solving management problems. Discuss and
describe the role of linear programming in managerial decision-making
bringing out limitations, if any.
2. Explain the concept and computational steps of the simplex method for
solving linear programming problems. How would you identify whether an
optimal solution to a problem obtained using simplex algorithm is unique
or not?
a) What is the difference between a feasible solution, a basic feasible
solution, and an optimal solution of a linear programming problem?
b) What is the difference between simplex solution procedure for a
`maximization’ and a `minimization’ problem?
c) Using the concept of net contribution, provide an intuitive
explanation of why the criterion for optimality for maximization
problem is different from that of minimization problems.
Outline the steps involved in the simplex algorithm for solving a linear
programming maximization problem. Also define the technical terms used
therein.
3. ``Linear programming is one of the most frequently and successfully
employed Operations Research techniques to managerial and business
decisions.’’ Elucidate this statement with some examples.
…2…
…2…
4. Describe the transporation problem and give its mathematical model.
Explain, by taking an...

...Decision Science Management:
Please show all your work with the problems in steps but NOT just answers.
22. Reiser Sports Products wants to determine the number of All-Pro (A) and College (C) footballs to produce in order to maximize profit over the next four-week planning horizon. Constraints affecting the production quantities are the production capacities in three departments: cutting and dyeing; sewing; and inspection and packaging. For the four-week planning period, 340 hours of cutting and dyeing time, 420 hours of sewing time, and 200 hours of inspection and packaging time are available. All-Pro footballs provide of $5 per unit and College footballs provide a profit of $4 per unit. The linear programming model with production times expressed in minutes is as follows:
Max 5A + 4C
s.t.
12A + 6C 20,400 Cutting and dyeing
9A + 15C 25,200 Sewing
6A + 6C 12,000 Inspection and packaging
A, C 0
A portion of the graphical solution to the Reiser problem is shown in Figure 2.23
a. Shade the feasible region for this problem.
b. Determine the coordinates of each extreme point and the corresponding profit. Which extreme point generates the highest profit?
c. Draw the profit line corresponding to a profit of $4000. Move the profit line as far from the origin as you can in order to determine which extreme point will provide the optimal solution. Compare your answer with the...

...known values
For example, deciding how many sections of a course to
offer during a semester can be modeled as a deterministic
model since the costs and benefits of offering each section
are known. The most commonly used deterministic
modeling technique is Linear Programming
Probabilistic (also called stochastic) models
assume that some input data are not known with
certainty
That is, these models assume that the values of
some important variables will not be known before
decisions are made
For Example this type of model is the decision of
whether to start a new business venture. As we seen
with high variability in the stock market during the
past several years the success of such venture is
unsure.
Quantitative factors are typically identifiable
and measurable, making their inclusion in the
model relatively easy.
In contrast, qualitative factors measure such
things as perceptions, feelings, and opinions.
Although some qualitative factors do have scales
of measures (for example, we can classify
opinions of the President’s performance as good,
fair, or poor), in general, they are difficult to
quantify and measure
Spreadsheet packages are capable of handling many decision
modeling techniques
Some advantages of using spreadsheets for decision modeling
are:
spreadsheets are capable of quickly calculating results for a
given set of input values
spreadsheets are effective tools...

...QuantitativeMethods
BITS Pilani
Pilani Campus
Course handout
BITS Pilani
Pilani Campus
Session-1
Instructor Details
Dr. Remica Aggarwal 1214 C ; FD-1 Department of Management Email: remica_or@rediffmail.com
Mobile: 09772054839
BITS Pilani, Pilani Campus
Course Details
• • • • • • •
Management Science Use of QM/QA Modelling Techniques Data Analysis Techniques MS Excel QM for Windows Test
BITS Pilani, Pilani Campus
QuantitativeMethods
• • • • • • • Operations Research Statistics Management Science Data IT & QM Business intelligence Theory Vs. Use?
BITS Pilani, Pilani Campus
Operational Research
...is concerned with scientifically deciding how best to design and operate man-machine systems under conditions requiring allocation of scarce resources
BITS Pilani, Pilani Campus
Definition of OR
–T.L. Saaty:
A collection of tools and techniques which provide bad answers to problems ………………………….…………….. which otherwise have ………………… worse answers
BITS Pilani, Pilani Campus
Evolution of OR
• History –U.S. Navy –Naval Research Forum –P.M.S. Blackett –Naval Research Logistics • Need – civilian applications • OR – Blend of art and science
BITS Pilani, Pilani Campus
Application Areas
• • • • • • • • Allocation (product-mix) Scheduling & Sequencing Routing Replacement Inventory Queueing Search Competitive
BITS Pilani,...