Operation Research-1

Assignment – A

 

Q1: Explain how and why operation research methods have been valuable in aiding executives’ decisions.

Q2: Develop a multi – item deterministic inventory model for determining economic order quantity when

(i) the production is assumed to be instantaneous

(ii) the shortage is not allowed

Q3: Define the following

a) Pure strategy

b) Mixed Strategy

c) Saddle point

d) Pay-off matrix

Q4: Define simplex method of linear programming with an example.

 

Q5: What do you understand by the transportation problem? What is the basic assumption behind the transportation problem? Describe any method of solving transportation problem.

 

Assignment – B

 

Q1: What do you understand by queue? Give some important application of queuing theory.

Q2: Describe a method to obtain an initial feasible solution for a transportation problem.

Q3:

(1) The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend? Which targets will be exceeded? How much will the blend cost?

	Type A	Type B
Shade Tolerance	1	1
Traffic Resistance	2	1
Drought Resistance	2	5

(2) : Lakewood Fashions must decide how many lots of assorted ski wear to order for its three stores. Information on pricing, sales, and inventory costs has led to the following payoff table, in thousands.

		Demand
Order Size	Low	Medium	High
1 lot	12	15	15
2 lots	9	25	35
3 lots	6	35	60

a.	What decision should be made by the optimist?
b.	What decision should be made by the conservative?
c.	What decision should be made using minimax regret?

 

Assignment – C

(Q1 to Q15, please answer in TRUE or FALSE)

 

1. The process of decision making is more limited than that of problem solving.

2. The terms ‘stochastic’ and ‘deterministic’ have the same meaning in quantitative analysis.

3. The volume that results in marginal revenue equaling marginal cost is called the break-even point.

4. Problem solving encompasses both the identification of a problem and the action to resolve it.

5. The decision making process includes implementation and evaluation of the decision.

6. The most successful quantitative analysis will separate the analyst from the managerial team until after the problem is fully structured.

7. The value of any model is that it enables the user to make inferences about the real situation.

8. Uncontrollable inputs are the decision variables for a model.

9. The feasible solution is the best solution possible for a mathematical model.

10. A company seeks to maximize profit subject to limited availability of man-hours. Man-hours is a controllable input.

11. Frederick Taylor is credited with forming the first MS/OR interdisciplinary teams in the 1940’s.

12. To find the choice that provides the highest profit and the fewest employees, apply a single-criterion decision process.

13. The most critical component in determining the success or failure of any quantitative approach to decision making is problem definition.

14. The first step in the decision making process is to identify the problem.

15. All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem.

 

16. Which of the following is a valid objective function for a linear programming problem?

a.	Max 5xy
b.	Min 4x + 3y + (2/3)z
c.	Max 5x2 + 6y2
d.	Min (x1 + x2)/x3

 

17. A negative dual price for a constraint in a minimization problem means

a.	as the right-hand side increases, the objective function value will increase.
b.	as the right-hand side decreases, the objective function value will increase.
c.	as the right-hand side increases, the objective function value will decrease.
d.	as the right-hand side decreases, the objective function value will decrease.

 

18. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

a.	at least 1.
b.	0.
c.	an infinite number.
d.	at least 2.

 

 

 

19. A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD ? 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?

a.	the objective function coefficient of HD is 10.
b.	the dual price for the HD constraint is 10.
c.	the objective function coefficient of HD is ?10.
d.	the dual price for the HD constraint is ?10.

 

20 . For a two-person, zero-sum, mixed-strategy game, it is necessary to solve the LP for only one of the players to learn the optimal strategies for both players.

a.	1.
b.	the number of operating units.
c.	100.
d.	any arbitrary value.

 

21. For a two-person, zero-sum, mixed-strategy game, each player selects its strategy according to

a.	what strategy the other player used last.
b.	a fixed rotation of strategies.
c.	a probability distribution.
d.	the outcome of the previous game.

 

22. The assignment problem constraint x₃₁ + x₃₂ + x₃₃ + x₃₄ ? 2 means

a.	agent 3 can be assigned to 2 tasks.
b.	agent 2 can be assigned to 3 tasks.
c.	a mixture of agents 1, 2, 3, and 4 will be assigned to tasks.
d.	there is no feasible solution.

 

23. The difference between the transportation and assignment problems is that

a.	total supply must equal total demand in the transportation problem
b.	the number of origins must equal the number of destinations in the transportation problem
c.	each supply and demand value is 1 in the assignment problem
d.	there are many differences between the transportation and assignment problems

 

24. Consider a shortest route problem in which a bank courier must travel between branches and the main operations center. When represented with a network,

a.	the branches are the arcs and the operations center is the node.
b.	the branches are the nodes and the operations center is the source.
c.	the branches and the operations center are all nodes and the streets are the arcs.
d.	the branches are the network and the operations center is the node.

 

25. Activities G, P, and R are the immediate predecessors for activity W. If the earliest finish times for the three are 12, 15, and 10, then the earliest start time for W

a.	is 10.
b.	is 12.
c.	is 15.
d.	cannot be determined.

 

26. For an activity with more than one immediate successor activity, its latest-finish time is equal to the

a.	largest latest-finish time among its immediate successors.
b.	smallest latest-finish time among its immediate successors.
c.	largest latest-start time among its immediate successors.
d.	smallest latest-start time among its immediate successors.

 

27. The economic production lot size model is appropriate when

a.	demand exceeds the production rate.
b.	there is a constant supply rate for every period, without pause.
c.	ordering cost is equivalent to the production setup cost.
d.	All of the alternatives are correct.

 

28. Annual purchase cost is included in the total cost in

a.	the EOQ model.
b.	the economic production lot size model.
c.	the quantity discount model.
d.	all inventory models.

 

29. Inventory position is defined as

a.	the amount of inventory on hand in excess of expected demand.
b.	the amount of inventory on hand.
c.	the amount of inventory on hand plus the amount of inventory on order.
d.	None of the alternatives is correct.

 

30. which of the following relationships is incorrect?

a.	As the order quantity increases, the number of orders placed annually decreases.
b.	As the order quantity increases, annual holding cost increases.
c.	As the order quantity increases, annual ordering cost increases.
d.	As the order quantity increases, average inventory increases.

 

31. In a waiting line situation, arrivals occur, on average, every 10 minutes, and 10 units can be received every hour. What are ? and ??

a.	? = 10, ? = 10
b.	? = 6, ? = 6
c.	? = 6, ? = 10
d.	? = 10, ? = 6

32. The arrival rate in queuing formulas is expressed as

a.	the mean time between arrivals.
b.	the minimum number of arrivals per time period.
c.	the mean number of arrivals per channel.
d.	the mean number of arrivals per time period.

 

33. For many waiting line situations, the arrivals occur randomly and independently of other arrivals and it has been found that a good description of the arrival pattern is provided by

a.	a normal probability distribution.
b.	an exponential probability distribution.
c.	a uniform probability distribution.
d.	a Poisson probability distribution.

 

 

34. Making a good decision

a.	requires probabilities for all states of nature.
b.	requires a clear understanding of decision alternatives, states of nature, and payoffs.
c.	implies that a desirable outcome will occur.
d.	All of the alternatives are true.

 

35. Algebraic methods such as the simplex method are used to solve

a.	nonlinear programming problems.
b.	any size linear programming problem.
c.	programming problems under uncertainty.
d.	graphical models.

 

36. A basic solution and a basic feasible solution

a.	are the same thing.
b.	differ in the number of variables allowed to be zero.
c.	describe interior points and exterior points, respectively.
d.	differ in their inclusion of nonnegativity restrictions.

 

37. In the simplex method, a tableau is optimal only if all the c_j ? z_j values are

a.	zero or negative.
b.	zero.
c.	negative and nonzero.
d.	positive and nonzero.

 

38. The stepping-stone method requires that one or more artificially occupied cells with a flow of zero be created in the transportation tableau when the number of occupied cells is fewer than

a.	m + n ? 2
b.	m + n ? 1
c.	m + n
d.	m + n + 1

 

39. Using the transportation simplex method, the optimal solution to the transportation problem has been found when

a.	there is a shipment in every cell.
b.	more than one stepping-stone path is available.
c.	there is a tie for outgoing cell.
d.	the net evaluation index for each unoccupied cell is ? 0.

 

40. When there is a tie between two or more variables for removal from the simplex tableau,

a.	post-optimality analysis is required.
b.	their dual prices will be equal.
c.	converting the pivot element will break the tie.
d.	a condition of degeneracy is present.