Title:
Group Assignment
Prepared for:
Miss Wan Nurshazelin Wan Shahidan
Prepared by:
Syahida Bt Abd Aziz 2011253056
Haulah Bt Abd Aziz 2011203594
Nur Atiqah Bt Ibrahim 2011674814
Group: BMB3Ad
Due date: 20th December 2011
September 2011 – January 2012
Bachelor of Business Administration (Hons) Marketing
Faculty of Business Management
Universiti Teknologi MARA Perlis
02600, Perlis
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- Meaning of decision-making under uncertainty and decision-making under risk?
Under uncertainty decision making
When several states of nature exist and a manager cannot assess the outcome probability with confidence or when virtually no probability data are available, the environment is called decision making under uncertainty. Several criteria exist for making decisions under these conditions which are Maximax, Maximin, Creterion of realism, Equally likely and Minimax regret.
Under risk decision making
Decision making under risk is a decision situation in which several possible states of nature may occur, and the probabilities of these states of nature are known. The probabilities with the opportunity loss table are also being used to minimize the expected opportunity loss.
- Two characteristics of a good model:
Fitting the Textbook Models
One problem in developing quantitative models is that a manager’s perception of a problem won’t always match the textbook approach. Some managers view the total of holding cost and ordering cost are unimportant. Therefore, the analyst must completely understand the model process and can explain to the manager how the model does consider these other factors when estimating different type of inventory costs.
Understanding the Model
The second major concern involves the trade-off between the complexity of a model and ease of understanding. Managers simply will not use the results of a model they do not understand. One simplifying assumption in inventory modelling is that demand is known and constant. This means that probability distributions are not needed and it allows us to build simple, easy-to-understand models. One approach is for the quantitative analyst to start with simple model and make sure that it is completely understood.
- Two advantages of using mathematical models in problem-solving
Models can accurately represent reality
If properly formulated, a model can be extremely accurate. A valid model is one that is accurate and correctly represents the problem or system under investigation. The profit model is the example is accurate and valid for many business problems.
Models can save time and money in decision making and problem solving
It usually takes less time, effort, and expense to analyze a model. We can use a profit model to analyze the impact of a new marketing campaign on profits, revenues, and expenses. In most cases, using models is faster and less expensive than actually trying a new marketing campaign in a real business setting and observing the results.
4. State whether each of the following statement TRUE or FALSE.
a) In the project management, the variance of the project completion time is equal to the sum of the variances of all the activities in a project.
FALSE
b) The corner-point solution method is solving a linear programming problem will provide one, and only one, optimum.
TRUE
c) If the Economic Order Quantity assumptions are met and a company orders more than the economic order quantity, then total annual holding cost will be greater than the total annual ordering cost.
FALSE
d) Sequential decisions are best made using decision trees.
TRUE
e) Simulation models are designed to generate optimal solutions, which can then be applied to real-world situations.
FALSE
5. What is meant by arrival rate and service rate?
Arrival rate
Arrival rate is rates where the input source that arrive to customers for the service system. Example of arrival rate is when the number of customers or arrivals on hand at any given moment is just a small portion of potential arrivals. Arrivals are considered random when they are independent of one another and cannot be predicted exactly.
Service rate
Service rate is rates where the customers get the services in the service system. Service rate can be constant or random. If it is constant, it takes the same amount of time to take care of each customer.
6. Explain the terms slack variable and surplus variable
Slack variable
Slack variables represent unused resources which are these may be in the form of time on a machine, labour hours, money, warehouse space, or any number of such resources in various business problem. Slack variables are added to each less-than-or-equal-to constraint.
Surplus variable
Surplus variable tell us how much the solution exceeds the constraint amount. Because of its analogy to a slack variable, surplus is sometimes simply called negative slack. We subtract a surplus variable to form equality when dealing with a greater-than-or-equal-to constraint.
7. State whether each of the following statements is TRUE or FALSE.
a) A model is not a perfect duplicate of the real system but contains sufficient detail so that we can study the model.
TRUE
b) An analog model is a physical replica or representation of a real object.
FALSE
c) The most important step in operations research approach to decision making is properly defining the variables.
TRUE
d) Even if a model is a perfect representation of the reality, improper input data will result in misleading results.
TRUE
8. Indicate if it is a single or multiple-server model, queue discipline, and is its calling population is infinite or finite.
ATM machine
It is a single model with one server. For queue discipline, it uses first-in, first out (FIFO) rule. The population in ATM machine is finite.
Cinema ticket counter
It is a multiple-server model. For queue discipline, it uses first-in, first-out (FIFO) rule. The population in cinema ticket counter is infinite.
9. State whether each of the following statements is TRUE or FALSE.
a) The transportation problem arises frequently in planning for the distribution of goods and services from several supply locations to only one demand location.
FALSE
b) The usual objective in a transportation problem is to minimize the cost of shipping goods from the origins to the destinations
TRUE
c) To determine the project completion time, we have to analyze the network and identify what is called the critical path for the network.
TRUE
d) The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors.
FALSE
10. State the assumptions of a simple queuing model.
1) Services time varies from one customer to the next and is independent of one another, but their average rate is known.
2) Services times occur according to the negative exponential probability distributions.
3) The average service rate is greater than the average arrival rate.
4) Arrivals are described by a Poisson probability distribution and come from an infinite or very large population.
11. State whether the following statements is TRUE or FALSE:
a) Decision-making under risk is a probabilistic decision situation.
TRUE
b) A typical linear programming problem involves maximizing an objective function while simultaneously optimizing resources constraint usage.
FALSE
c) Inventory is any stored resource that is used to satisfy a current or future need.
TRUE
d) The objective of queuing theory is to minimize customer dissatisfaction.
FALSE
12. Give THREE (3) advantages of using mathematical modelling in problem solving.
Represent reality
Models can accurately represent reality. If properly formulated, a model can be extremely accurate. A valid model is one that is accurate and correctly represents the problem or systems under investigation. The profit model in the example is accurate and valid for many business problems.
Formulate problems
Models can also help a decision maker formulate problems. In the profit model, for example, a decision maker can determine the important factors or contributors to revenues and expenses, such as sales, returns, selling expenses, production costs, transportation costs, and so on.
Save time and money
Models can save time and money in decision making and problem solving. It usually takes less time, effort and expense to analyze a model. We can use a profit model to analyze the impact of a new marketing campaign for profits, revenues and expenses. In most cases, using models is faster and less expensive than actually trying a new marketing campaign in a real business setting and observing the results.
13. State whether each of the following statements is TRUE or FALSE.
a) An optimal solution is a mathematically-best solution.
TRUE
b) In the EOQ model, the doubling of both the ordering and holding costs would result in no change in optimal order quantity.
FALSE
c) The variance of the project completion time is equal to the sum of the variances of all the activities.
FALSE
d) For a single server queuing system the average number of customers in the waiting line is less than the average number in the system.
TRUE
14. What are the two important decisions in inventory control?
1. How much to order
The decision-maker needs to specify how much they want to order.
2. When to order
They also need to know when they are supposed to order new orders to cover the ones that had been used.
15. State two (2) assumptions underlying the single channel queuing model.
1. Arrivals are served on first-in, first-out (FIFO) basis.
2. Every arrivals wait to be served regardless of the length of the line; that is, there is no balking or reneging.
16. List all the operations research approaches in decision making process.
1. Defining the problem
2. Developing a model
3. Acquiring input data
4. Developing a solution
5. Testing the solution
6. Analyzing the results
7. Implementing the results
17. Briefly describe all the following cases in solving linear programming problem.
Infeasibility
When there is no solution to LP problem that satisfies all of the constraints given, infeasibility will occur. Graphically, it means that no feasible solutions regions exist. This, by the way, is a frequent occurrence in real life, large-scale LP problem that involves hundreds of constraints.
Unbounded
When the profit in maximization problem can be infinitely large, the problem is unbounded and is missing one or more constraints. If we try to solve such problem graphically, we will note that the feasible region is open-ended.
Redundancy
The presence of redundant constraint is another common situation that occurs in large LP formulations. A redundant constraint is simply one that does not affect the feasible region. One constraint may be more binding or restrictive than another and thereby negate its needs to be considered.
Alternate optimal solutions
An LP problem may, an occasion, has two or more alternative optimal solutions. Graphically, this is the case when the objective function’s isoprofit or isocost line runs perfectly parallel to one of the problem’s constraints or in another word, when they have the same slope.
18. State whether each of the following statements is TRUE or FALSE.
a) The expected value of sample information (EVSI) is obtained by subtracting the expected monetary value (EMV) without sample information from the EMV with sample information.
TRUE
b) If the economic order quantity (EOQ) assumptions are met and a company orders more than EOQ, then the total annual holding cost will be less than the total annual ordering cost.
TRUE
c) A feasible solution to a linear programming (LP) problem must satisfy all of the problem’s constraints simultaneously.
TRUE
d) If the project completion time is normally distributed and the due date for the project is greater than the expected completion time, then the probability that the project will be finished by the due date is greater than 0.5.
TRUE
19. What is mean by balanced transportation problem? Briefly outline the initial procedure for dealing with unbalanced transportation problems.
Balanced transportation problems refer to total demand equal to total supply, while unbalanced problems states the different amount of demand and supply. Initial procedures for dealing with unbalanced transportation problems are:
Dummy
Through the usage of dummy in transportation problem, unbalanced can be prevented. If the number of demand is greater than its supply, addition of dummy supply can balanced the amount of demand and supply.
For example, suppose that, Des Moines factory supply 850 desks per month, but their demand is at 700. This will create unbalanced transportation problem. Through adding dummy demand of 150 desks, the unbalanced problem may be prevented.
20. Define the following terms:
a) Earliest start time
It refers to the earliest time an activity can begin without violation of immediate predecessor requirements.
b) Earliest finish time
It states the earliest time at which an activity can ends.
c) Latest start time
It refers as the latest time an activity can begin without delaying the entire project.
d) Latest start finish
It can be defined as the latest time an activity can end without delaying the entire projects or accumulating loss.
21. States the advantages and disadvantages of simulation.
Advantages of simulation are:
1. It is relatively straightforward and flexible.
2. Recent advances in software make some simulation models very easy to develop.
3. It can be used to analyze large and complex real-world situations that cannot be solved by conventional quantitative analysis model.
4. Simulation allows us to study the interactive effects of individual’s components or variables to determine which ones are important.
Disadvantages of simulation are:
1. Good simulation models for complex situations can be very expensive.
2. Simulation does not generate optimal solutions to problem as do other quantitative analysis techniques such as economic order quantity, linear programming or PERT.
3. Managers must generate all of the conditions and constraints for solutions that they want to examine.
4. Each simulation problem is unique. Its solutions and inferences are not usually transferable to other problems.
22. State whether each of the following statements is TRUE or FALSE.
a) Quantitative Analysis has been around since World War 2.
TRUE
b) The main purpose of quantitative models is to help automate the decision-making process.
TRUE
c) The expected value of sample information is lower than the expected value of perfect information.
TRUE
23. What is meant by operations research? Give an example of operation research application in your daily life.
Operations research is a scientific approach to management. It consists of quantitative analysis to modify the problems. One example of operation research application in my daily life is when I need a favour such as a small loan from friends. Before achieving the loan, I need to do the quantitative analysis approach from one step to another step accordingly.
24. Two major reasons for the growth in the use of the operations research since World War II.
Using a similar technique in managerial decision making and planning
During World War II, many new scientific and quantitative techniques were developed to assist the military. These new developments were so successful that after World War II many companies start to using similar techniques in managerial decision making and planning
Apply principle of scientific management
Today, many organizations employ a staff of operations research or management science personnel or consultants to apply the principles of scientific management to the problems and opportunities. There are several terms in the quantitative analysis which are management science, operations research, and quantitative analysis interchangeably.
25. State whether each of the following statements is TRUE or FALSE.
a) In a balanced transportation model, total supply is greater than total demand or total demand is greater than the total supply.
FALSE
b) The optimal solution to a maximization transportation problem has been found when all improvement indices are negative or zero.
TRUE
c) We can use MODI method to develop an initial solution.
FALSE
d) Multiple solutions are possible when one or more improvement indices in the final tableau are equal to zero.
FALSE
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