Introduction to Management Science, 10e (Taylor)
Chapter 9 Multicriteria Decision Making

1) The different objectives in a goal programming problem are referred to as goals.
Answer: TRUE
Diff: 1 Page Ref: 400
Main Heading: Goal Programming
Key words: goal programming

2) All goal constraints are inequalities that include deviational variables.
Answer: FALSE
Diff: 1 Page Ref: 400
Main Heading: Goal Programming
Key words: goal constraints

3) A negative deviational variable is the amount by which a goal level is exceeded.
Answer: FALSE
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: goal constraints, deviational variable

4) At least one or both deviational variables in a goal constraint must equal 0.
Answer: TRUE
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: deviational variable, goal constraints

5) The objective function in a goal programming model seeks to minimize the deviation from goals in the order of the goal priorities.
Answer: TRUE
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: goal prog problem formulation, objective function for goal prog

6) In goal programming, terms are summed in the objective function in order to make consistent decisions.
Answer: FALSE
Diff: 2 Page Ref: 402
Main Heading: Goal Programming
Key words: goal prog problem formulation, objective function for goal prog

7) Goal constraints can include all deviational variables.
Answer: TRUE
Diff: 1 Page Ref: 402
Main Heading: Goal Programming
Key words: deviational variable, goal constraints

8) In goal programming, problems cannot have two or more goals at the same priority level.
Answer: FALSE
Diff: 1 Page Ref: 402
Main Heading: Goal Programming
Key words: goal prog problem formulation, objective function for goal prog
9) Goal programming provides a method for simultaneously striving to achieve several objectives.
Answer: TRUE
Diff: 2 Page Ref: 402
Main Heading: Goal Programming
Key words: goal prog problem formulation, objective function for goal prog

10) A requirement for the solution procedure for the goal programming problem is that all goals must be achieved.
Answer: FALSE
Diff: 2 Page Ref: 402
Main Heading: Goal Programming
Key words: goal programming problem solution procedure

11) One goal is never achieved at the expense of another higher-priority goal.
Answer: TRUE
Diff: 1 Page Ref: 405
Main Heading: Graphical Interpretation of Goal Programming
Key words: graphical solution to a goal prog problem, goal achievement

12) A goal can be achieved at the expense of another lower-priority goal.
Answer: TRUE
Diff: 1 Page Ref: 405
Main Heading: Graphical Interpretation of Goal Programming
Key words: graphical solution to a goal prog problem, goal achievement

13) Goal programming solutions do not always achieve all goals.
Answer: TRUE
Diff: 1 Page Ref: 405
Main Heading: Graphical Interpretation of Goal Programming
Key words: graphical solution to a goal prog problem, goal achievement

14) In a goal programming model, the terms in the objective function are summed to determine the maximum profit or minimum cost.
Answer: FALSE
Diff: 1 Page Ref: 402
Main Heading: Graphical Interpretation of Goal Programming
Key words: goal prog model, objective function of the goal prog model

15) Objective function terms are not summed in goal programming because not all goals are achievable.
Answer: FALSE
Diff: 1 Page Ref: 402
Main Heading: Graphical Interpretation of Goal Programming
Key words: goal programming

16) Goal programming violates the divisibility property of linear programming.
Answer: FALSE
Diff: 1 Page Ref: 402
Main Heading: Graphical Interpretation of Goal Programming
Key words: goal programming
17) In a pairwise comparison, 2 alternatives are compared according to a criterion and one is preferred.
Answer: TRUE
Diff: 1 Page Ref: 414
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process, pairwise comparison

18) A preference scale assigns numerical values to different levels of preference.
Answer: TRUE
Diff: 2 Page Ref: 415
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process, preference scale

19) On a preference scale for pairwise comparisons, the number "1" indicates that two objects are equally preferred.
Answer: TRUE
Diff: 2 Page Ref: 415
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process, pairwise comps, preference scale

20) A pairwise comparison matrix summarizes the pairwise comparisons for a criterion.
Answer: TRUE
Diff: 2 Page Ref: 415
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process, pairwise comparison matrix

21) In synthesization, decision alternatives are prioritized within each criterion.
Answer: TRUE
Diff: 2 Page Ref: 416
Main Heading: The Analytical Hierarchy Process
Key words: synthesization

22) A consistency index measures the degree of inconsistency in pairwise comparisons.
Answer: TRUE
Diff: 1 Page Ref: 421
Main Heading: The Analytical Hierarchy Process
Key words: consistency index

23) A preference scale assigns numerical values to different levels of preferences.
Answer: TRUE
Diff: 2 Page Ref: 414
Main Heading: The Analytical Hierarchy Process
Key words: preference scale

24) In a given AHP problem, the consistency index is .15, and the random index is .90. In this instance, there are probably serious inconsistencies and therefore AHP result may not be meaningful.
Answer: TRUE
Diff: 2 Page Ref: 420
Main Heading: The Analytical Hierarchy Process
Key words: consistency index
25) Scoring model is more subjective than the Analytical Hierarchy Process.
Answer: TRUE
Diff: 2 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring model, analytical hierarchy process

26) Scoring models use consistency indexes to measure the degree of consistency between choices.
Answer: FALSE
Diff: 1 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring

27) In scoring models, the two alternatives with the highest scores are compared to make the final decision.
Answer: FALSE
Diff: 1 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring

28) At least one or both deviational variables in a goal constraint must equal __________.
Answer: zero
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: deviational variables, goal constraints

29) Consider the following constraint: 2x1 + 3x2 =60. Assume that we convert this constraint into a goal constraint and the value of x1 = 15 and the value of x2 = 15, then the values of d1+ and d1- are __________ and __________ respectively.
Answer: 15;0
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: deviational variables, goal constraints

30) A(n) __________ variable is the amount by which a goal level is underachieved.
Answer: negative deviational
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: deviational variables

31) A(n) __________ variable is the amount by which a goal level is exceeded.
Answer: positive deviational
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: deviational variables

32) A(n) __________ assigns numerical values to different levels of preferences.
Answer: preference scale
Diff: 2 Page Ref: 414
Main Heading: Analytical Hierarchy Process
Key words: preference scale
33) Deviation variables that occur in the objective function and the constraints of a goal programming model indicate the difference between all actual and __________ values.
Answer: target
Diff: 2 Page Ref: 400
Main Heading: Analytical Hierarchy Process
Key words: deviation variables, goal programming formulation

34) A(n) __________ measures the degree of inconsistency in pairwise comparisons.
Answer: consistency index
Diff: 2 Page Ref: 420
Main Heading: Analytical Hierarchy Process
Key words: consistency index

35) A __________ vector is the average of the values in each row of the normalized matrix in the AHP process.
Answer: preference
Diff: 1 Page Ref: 417
Main Heading: Analytical Hierarchy Process
Key words: preference vector, AHP

36) If the CI/RI ration is more than __________ then there are probably serious inconsistencies in the AHP results.
Answer: .10
Diff: 2 Page Ref: 422
Main Heading: Analytical Hierarchy Process
Key words: consistency, AHP

37) The analytic hierarchy process, scoring models, and goal programming are all considered to be __________ decision making techniques because they incorporate decisions based on more than 1 objective.
Answer: multiple criteria
Diff: 2 Page Ref: 400
Main Heading: Analytical Hierarchy Process
Key words: multiple criteria decision making

38) A(n) __________ model is a similar to AHP, but simpler and easier to understand.
Answer: scoring
Diff: 2 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring

39) In a facility location problem, if location A receives a score of 45 for the criteria, "traffic congestion", which has a weight of .30; a score of 50 for the criteria, "labor force", which has a weight of .45; and a score of 60 for "utilities", which has a weight of .25, the overall score for location A is: __________.
Answer: 51
Diff: 2 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring 40) The objective function formulation for a goal programming model is as follows: Min P1 d1-, P2 d2-, P3 d1+, P4 d3-
Which one of the variables would the program designers like to have as the second goal such that its deviation from zero is minimized?
Answer: d2-
Diff: 1 Page Ref: 401
Main Heading: Goal Programming
Key words: goal prog formulation, objective function for a goal prog problem

41) The objective function formulation for a goal programming model is as follows: Min P1d1-, P2 d2-, (4 P4 d3- + 6 P4 d2+)
At the priority level 4, which one of the deviational variables is more important?
Answer: A d2+
Diff: 1 Page Ref: 401
Main Heading: Goal Programming
Key words: goal prog formulation, objective function for a goal prog problem

Ashley's manufactures home furnishings for department stores. Planning is underway for the production of the following items during the next production period:

Quilts (X1) Blinds (X2) Pillows (X3)
Fabric required (yards) (d1) 7 4 9
Time required (hours) (d2) 1.5 2 0.5
Packaging material (ounces) (d3) 3 2 1
Profit (d4) 12 10 8

Ashley has 3000 yards of material in stock for this production period. Five hundred hours of production time are scheduled and 400 ounces of packaging material is available. Each of these quantities can be adjusted through overtime or extra purchases. Ashley's highest priority is to achieve a profit of $3200. Her second priority is to avoid additional purchases of packaging material. Third, she wants to use all of the scheduled production hours and fourth, minimize any fabric remaining from the 3000 yards. Note that the deviational variables associated with each item is given in the table.

42) What is the objective function?
Answer: Min P1d4-, P2d3+, P3d2-, P4d1+
Diff: 3 Page Ref: 401
Main Heading: Goal Programming
Key words: goal prog formulation, objective function for a goal prog problem

43) What is the fabric constraint?
Answer: 7x1 + 4x2 + 9x3 + d1- - d1+ = 3000
Diff: 2 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal prog formulation, constraints for a goal prog problem
44) What is the profit constraint?
Answer: 12x1 + 10x2 + 8x3 + d4- - d4+ = 3200
Diff: 2 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal prog formulation, constraints for a goal prog problem

45) What is the production time constraint?
Answer: 1.5x1 + 2x2 + 0.5x3 + d2- - d2+ = 500
Diff: 2 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal prog formulation, objective function for a goal prog problem

46) What is the packaging material constraint?
Answer: 3x1 + 2x2 + 1x3 + d3- - d3+ = 400
Diff: 2 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal prog formulation, constraints for a goal prog problem

An investor has $80,000 to invest in three stocks, stock A costs $100, stock B costs$120 and stock C costs $80. Each stock A has a risk factor of 8, each stock B has a risk factor of 10 and each stock C has a risk factor of 7. The investor believes that the sum of the risk factors for all stocks purchase should not exceed 6,000. The projected annual growth rate for the three stocks are 9%, 13% and 8% respectively. The projected annual dividend income from these stocks are as follows: Stock A: $14/stock, Stock B: $15/stock and Stock C: $20/stock. The investor desires an annual dividend income of $10,000. The investor has established the following goals in order of their importance:
(1) The investor believes that the budget cannot be exceeded. (d1)
(2) The risk factor should not exceed the target amount of 6,000. (d2)
(3) The average annual growth rate in stock prices must be at least 10% (d3)
(4) The investor desires a dividend income of at least $10,000 (d4)

47) State the goal programming objective function.
Answer: Min P1d1+, P2d2+, P3d3-, P4d4-
Diff: 3 Page Ref: 401
Main Heading: Goal Programming
Key words: goal programming objective function

48) Write the budget constraint
Answer: 100A + 120B + 80C + d1- - d1+ = 80,000
Diff: 2 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal programming constraints

49) Write the risk factor constraint
Answer: 8A + 10B + 7C + d1- - d1+ = 6,000
Diff: 2 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal programming constraints
50) Centerville City council is in the process of developing city tax rates. The annual tax base for real estate property is $750 million and for general sales, $80 million. Annual local gas consumption is estimated at 12 million gallons. They have 3 goals, listed in order of priority:
1. Tax revenues must be at least $25 million to meet the city's financial commitments.
2. Sales tax cannot exceed 25% of all taxes collected.
3. Gasoline tax cannot exceed 8 cents per gallon.
Formulate as a goal programming problem.
Answer: Let xp = tax rate for property; xs = sales tax rate, and xg = gas tax in cents per gallon.
Min P1d1-, P2d2-, P3d3+
750 xp + 80 xs + .12 xg ≥ 25
80 xs ≤ .25(750 xp + 80 xs + .12 xg) xg ≤ 8
Simplify the second constraint: 187.5 xp - 60 xs +.03 xg ≥ 0. If this constraint is written as -187.5 xp + 60 xs -.03 xg = 0, then the objective function should be: Min P1d1-, P2d2+, P3d3+
Diff: 3 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal programming formulation

A production of 300 units of Twiddle Bugs, an educational toy for children, must be completed within 1 week by BugU Manufacturing. Two production lines are available, each for 30 hours during the week. Production line 1 can produce five units per hour and production line 2 can produce 4 units an hour. Line 1 costs $50 per hour to operate and line 2 costs $55 per hour. Overtime is available for line 1 at $15 per hour and for line 2 at $12 per hour. Management goals in decreasing order are: P1: Produce 300 units.
P2: Maximum allowable overtime of 6 hours for line 1.
P3: Cost of overtime must not exceed $750.
P4: Avoid the underutilization of either production line. Assign weights that are proportional to their production capability.
P5: Producing more than 300 units is 1 1/2 times as undesirable as producing under 300 units.

51) What are the constraints for this problem?
Answer: Let x1 = hours of production time on line 1. x2 = hours of production time on line 2
5x1 + 4x2 = 300 x1≤ 30 x2 ≤ 30

P1: 5x1 + 4x2 + d1- - d1+ = 300
P2: x1 + d2- - d2+=34
P3: 50(x1 - 30) + 55(x2 - 30) + d2- - d2+ = 750 or 50x1 + 55x2 + d2- - d2+ = 3150
P4a: x1 + d4- - d4+= 30
P4b: x2 + d5- - d5+= 30

P5: See objective function

Objective function: Minimize P1A d1- + 1.5 P1B d1+ + P2 d2+ + P3 d3+ + 5P4A d4- + 4P4B d5-
Diff: 2 Page Ref: 400-402
Main Heading: Goal Programming
Key words: goal programming, constraints

52) What is the objective function?
Answer: Minimize P1A d1- + 1.5 P1B d1+ + P2 d2+ + P3 d3+ + 5P4A d4- + 4P4B d5-
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: goal programming, objective function

53) Assume that a decision maker using analytical hierarchy process generated the following pairwise comparison matrix. Calculate the normalized matrix.
Answer: normalized matrix:
Diff: 2 Page Ref: 416
Main Heading: The Analytical Hierarchy Process
Key words: pairwise comparison matrix, normalized matrix
54) Using the normalized matrix given below, calculate the row averages.

Answer: row average 1.00
Diff: 1 Page Ref: 416
Main Heading: The Analytical Hierarchy Process
Key words: normalized matrix, row average

55) Assume that a decision maker has to make a choice between three types of cars. Chevy, Honda, and Ford. Based on three criteria: comfort, MPG and style.

The row averages for criteria is summarized in the following column vector:

The preference matrix for the three types of cars is given as follows:

Compute the overall score for each decision alternative (car).
Answer: Chevy = .29
Honda = .48
Ford = .23
Diff: 2 Page Ref: 418
Main Heading: The Analytical Hierarchy Process
Key words: AHP, overall score 56) Assume that a plant manager has to decide where to locate its warehouse. The decision has been narrowed down to choices among the following three cities: Detroit, Michigan, Cleveland, Ohio and St. Louis Missouri. The following pairwise comparison matrix summarizes the preferences of the plant manager.

Detroit Cleveland St. Louis
Detroit 1 1/3 1/4
Cleveland 3 1 1/2
St. Louis 4 2 1

Determine the normalized matrix.
Answer: Detroit Cleveland St. Louis
Detroit .125 .10 .1429
Cleveland .375 .30 .2857
St. Louis .500 .60 .5714

Diff: 2 Page Ref: 416
Main Heading: The Analytical Hierarchy Process
Key words: pairwise comparison matrix, normalized matrix

57) Consider the following normalized matrix for Car Comfort that was computed using the analytical hierarchy process:

Car A Car B Car C
Car A 0.30 0.25 0.50
Car B 0.60 0.50 0.33
Car C 0.10 0.25 0.17

Which car is the most preferred based on comfort?
Answer: Row averages indicate a preference for Car B.
0.35
0.48
0.17

Diff: 2 Page Ref: 417
Main Heading: The Analytical Hierarchy Process
Key words: preference vector 58) The analytical hierarchy process was used to determine which car to purchase. Four criteria were used: price, miles per gallon, comfort, and durability. Consider the following normalized matrix and the preference vector for durability.

Multiplying the normalized matrix by the preference vector gives the following results:
2.17
2.26
1.69

Compute the consistency index.
Answer: 2.17 0.36 = 5.958
2.26 0.59 = 3.797
1.69 0.41 = 4.092 sum = 13.847 avg of sum = 4.616 CI = 0.808
Very inconsistent!
Diff: 3 Page Ref: 416
Main Heading: The Analytical Hierarchy Process
Key words: AHP, consistency 59) Three job applicants were rated on 4 criteria, resulting in the following preference vectors:

Applicant Criterion 1 Criterion 2 Criterion 3 Criterion 4
A .3085 .0792 .5986 .6192
B .2147 .4615 .0126 .3045
C .4768 .4593 .3888 .0763

The priorities of the criteria are:

Criterion Priority 1 .2178 2 .1915 3 .4123 4 .1784

Rank the 3 applicants.

Answer: Applicant Score A .4396 B .1947 C .3658

Applicant A is ranked highest and applicant B, the lowest.
Diff: 3 Page Ref: 416-419
Main Heading: Analytical Hierarchy Process
Key words: analytical hierarchy process solution method, calc of overall scores

60) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Michigan, Cleveland, Ohio and St. Louis Missouri. The company has weighted each of these criteria in terms of its relative importance in the decision making process, and it has analyzed each potential warehouse location and graded them according to each criteria as shown in the following table.

Decision Criteria Weight Grades for Detroit Grades for Cleveland Grades for
St. Louis
Proximity to suppliers .45 80 70 60
Proximity to customers .35 75 90 80
Land and construction costs .20 60 50 85

Calculate the scores for each location and state where the warehouse should be located?
Answer: SDetroit = 74.25
SCleveland = 73
SSt.Louis = 72
Choose Detroit
Diff: 2 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring model
61) A business is trying to decide which restaurant to hold its annual awards banquet. Use the information below to determine the best choice.

Restaurant
Criteria Weight A B C
Appearance 0.15 40 65 60
Service 0.30 75 80 70
Atmosphere 0.15 60 40 70
Location 0.10 90 100 75
Quality of food 0.30 70 80 75

Answer: A score = 67.5, B score = 73.75, C score = 70.5. Select B
Diff: 2 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring

62) A positive deviational variable is the amount by which a goal level is
A) underachieved
B) exceeded
C) kept short off
D) none of the above
Answer: B
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: deviational variables, goal constraints

63) A __________ deviational variable is the amount by which a goal level is exceeded.
A) negative
B) positive
C) positive or negative
D) positive and negative
Answer: B
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: deviational variables, goal constraints

64) At least one or both deviational variables in a goal constraint must equal
A) 1
B) -1
C) 0
D) 2
E) none of the above
Answer: C
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: deviational variables, goal constraints
65) A decision with more than 1 objective
A) should be decomposed into a separate model for each objective
B) depends on the probability of satisfying each objective
C) requires the decision maker to put the objectives in some order of importance
D) cannot have an optimal solution
Answer: C
Diff: 1 Page Ref: 401
Main Heading: Goal Programming
Key words: objective function of a goal programming problem

66) Deviation variables
A) represent the actual value of the function part of a goal constraint.
B) are limited so that only one appears per constraint.
C) represent the difference between the target and actual values
D) must sum to one
E) equal the difference between actual and predicted values of the decision variables
Answer: C
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: deviational variables, goal programming model

67) The objective function min P1d1- , P2d2+
A) attempts to avoid being below target for the priority 1 goal
B) attempts to avoid being below target for the priority 2 goal
C) will not have any feasible solutions
D) will have a solution only if P1 > P2
E) none of the above
Answer: A
Diff: 1 Page Ref: 401
Main Heading: Goal Programming
Key words: goal programming formulation, goal constraints

68) The majority of the goal constraints are equalities that include __________ variables.
A) only deviational
B) deviational and decision
C) only decision
D) neither deviational nor decision variables
E) undeviational
Answer: B
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: goal programming formulation, goal constraints

69) A __________ deviational variable is the amount by which a goal level is underachieved.
A) negative
B) positive
C) positive or negative
D) positive and negative
Answer: A
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: goal programming formulation, goal constraints 70) The objective function in a goal programming model seeks to __________ the deviation from goals in the order of the goal priorities.
A) free
B) even out
C) maximize
D) minimize
Answer: D
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: goal prog formulation, objective function for a goal prog problem

71) Goal constraints can include __________ deviational variables.
A) no
B) some
C) all
D) multiple
Answer: C
Diff: 2 Page Ref: 402
Main Heading: Goal Programming
Key words: goal programming formulation, goal constraints

72) Deviational variables in a goal programming model constraint represent the
A) underachievement or overachievement of a goal level
B) resource constraint as defined by the linear model
C) probability of an optimal solution
D) probabilistic variables in the objective constraints
Answer: A
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: deviational variables, goal programming formulation

73) Two or more goals at the same priority level can be assigned weights to indicate their relative
A) meaning
B) slack
C) difference
D) importance
Answer: D
Diff: 2 Page Ref: 403
Main Heading: Goal Programming
Key words: goal programming solution 74) A company has 3 goals, listed in order of importance.
1. Achieve a total profit of at least $240 million.
2. Maintain the current employment level of 3,000 employees
3. Invest no more than $70 million in capital.
What is the objective function for a goal program for this situation?
A) P1d1- , P2d2- , P3d3+
B) P1d1- , P2d2+ , P2d2- , P3d3-
C) P1d1- , P2d2- , P2d2- , P3d3+
D) P1d1+ , P2d2- , P2d2- , P3d3+
E) None of the above
Answer: C
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: goal programming, objective function

75) If the constraint 3x1 + 4x2 + (d1-) - (d1+) = 250 measures hours, then
A) 3x1 + 4x2 is equal to the actual time spent
B) if d1- is equal to 25, then 3x1 + 4x2 must equal 225.
C) overtime could be represented by d1+
D) all of the above are true.
Answer: D
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: goal programming constraints

76) A company has a goal to maintain the currently employment level, but places more importance on laying employees off than on hiring new employees. In other words, the company would rather hire than lay off employees. If the company assigns a "penalty weight" of 4 for the amount under the employment goal (goal 2) , and a weight of 2 for the amount over the employment goal, how would this be expressed in the objective function?
A) Min 4P2d2- + 2P2d2+
B) Min 2P2d2- + 4P2d2+
C) Max 4P2d2- + 2P2d2+
D) Min 4P2d2+ + 2P2d2-
E) None of the above
Answer: A
Diff: 2 Page Ref: 401
Main Heading: Goal Programming
Key words: goal programming, objective function 77) A company has a goal of calling on at least 400 customers a month (goal 1), but no fewer than 260 customers a month (goal 2). If X represents the number of customers contacted, which pair of constraints listed below is the appropriate representation in a goal programming problem?
A) X + d1- - d1+ = 400, X + d2- - d2+ = 260
B) X - d1- + d1+ = 400, X - d2- - d2+ = 260
C) X - d1- + d1+ = 400, X + d2- - d2+ = 260
D) X + d1- - d1+ = 400, X - d2- + d2+ = 260
Answer: A
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: goal programming, constraints

78) Consider the following constraint: 2x1 + 3x2 =60. Assume that we convert this constraint into a goal constraint and the value of x1 = 15 and the value of x2 = 15, then the values of d1+ and d1- are __________ and __________ respectively.
A) 0, 15
B) 15, 0
C) 20, 0
D) 0, 20
E) 15, 15
Answer: B
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: goal programming solution

79) One goal __________ achieved at the expense of another higher-priority goal.
A) is never
B) can sometimes be
C) is always
D) is under certain circumstances
Answer: A
Diff: 2 Page Ref: 405
Main Heading: Goal Programming
Key words: graphical solution of a goal programming problem

80) The objective function in all goal programming models is to __________ from the goal constraint levels.
A) maximize alternatives
B) minimize alternatives
C) minimize deviation
D) maximize deviation
Answer: C
Diff: 3 Page Ref: 400
Main Heading: Goal Programming
Key words: objective function of a goal programming problem
81) Goal programming solutions __________ achieve all goals.
A) always
B) don't always
C) sometimes
D) never
Answer: B
Diff: 1 Page Ref: 401
Main Heading: Goal Programming
Key words: solution of a goal programming problem

Riverside Industries makes two products and each product is processed in three departments. The time requirements for each product in each department are given below. The profit for each product is also provided as well as the available hours in each department.

Product Department A Department B Department C Profit
1 3 4 2 1
2 2 1 2 2
Available Hours 600 400 400

Management wants to achieve 3 goals. The first two goals are equal in priority.

Priority 1: Produce at least 125 units of product 1.
Priority 1: Produce at least 80 units of product 2.
Priority 2: Achieve a profit of at least 300.

82) The goal programming model for this problem has how many constraints?
A) 3
B) 4
C) 6
D) 7
Answer: C
Diff: 1 Page Ref: 402
Main Heading: Goal Programming
Key words: goal constraints

83) The goal programming constraint for the first goal is:
A) 3x1 + d1- - d1+ = 125
B) 3x1 - d1- + d1+ = 125
C) 1x1 + d1- - d1+ = 125
D) 1x1 - d1- + d1+ = 125
Answer: C
Diff: 1 Page Ref: 402
Main Heading: Goal Programming
Key words: goal constraints
84) The objective function for this goal program is:
A) Min P1d1- + P1d2-, P2d3-
B) Min P1d1+ + P1d2-, P2d3-
C) Min P1d1- + P1d2+, P2d3-
D) Min P1d1- + P1d2-, P2d3+
Answer: A
Diff: 1 Page Ref: 401
Main Heading: Goal Programming
Key words: goal constraints

85) If the second goal was to produce no more than 80 units of product two, the objective function would be:
A) Min P1d1- + P1d2-, P2d3-
B) Min P1d1+ + P1d2-, P2d3-
C) Min P1d1- + P1d2+, P2d3-
D) Min P1d1- + P1d2-, P2d3+
Answer: C
Diff: 1 Page Ref: 401
Main Heading: Goal Programming
Key words: goal constraints

86) Goal programming solutions achieve the __________ satisfactory solution possible.
A) best or most
B) worst or least
C) only
D) somewhat
Answer: A
Diff: 2 Page Ref: 400
Main Heading: Goal Programming
Key words: graphical solution of a goal programming problem

87) If choice A is strongly preferred to choice B and choice B is moderately preferred to choice C, and the decision maker says choice C is equally preferred to choice A, what conclusion can be drawn?
A) The decision maker is consistent.
B) The decision maker is inconsistent.
C) The pairwise comparison matrix is symmetric.
D) The decision maker has already synthesized.
Answer: D
Diff: 1 Page Ref: 416
Main Heading: Analytical Hierarchy Process
Key words: synthesization
88) In a pairwise comparison, __________ alternatives are compared according to a criterion and one is preferred.
A) 6
B) 4
C) 8
D) 2
Answer: D
Diff: 1 Page Ref: 414
Main Heading: The Analytical Hierarchy Process
Key words: a pairwise comparisons, Analytical Hierarchy Process

89) In synthesization, decision alternatives are prioritized __________ criteria/ion.
A) within some
B) among some
C) among all
D) within each
Answer: D
Diff: 2 Page Ref: 416
Main Heading: The Analytical Hierarchy Process
Key words: synthesization

90) Pairwise comparisons are made among
A) all alternatives for a particular criterion
B) all alternatives for all criteria
C) some alternatives for a particular criterion
D) some alternatives for all criteria
Answer: A
Diff: 2 Page Ref: 415
Main Heading: The Analytical Hierarchy Process
Key words: pairwise comparisons

91) In a pairwise comparison matrix the diagonal values will __________ equal __________.
A) sometimes, 1
B) always, 0
C) sometimes, 0
D) always, 1
E) none of the above
Answer: D
Diff: 2 Page Ref: 415
Main Heading: The Analytical Hierarchy Process
Key words: pairwise comparisons

92) The analytic hierarchy process
A) optimizes procedures with a single goal
B) requires no pairwise comparison
C) uses both qualitative and subjective assessment
D) does not require the input of a decision maker
Answer: C
Diff: 2 Page Ref: 413
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process
93) In determining the pair wise comparison matrix, if the decision maker rates the option A compared to option B as "4", then option B compared to option A __________.
A) would have to be also Answered by the decision maker
B) is also 4
C) 1/4
D) 2
E) would have to be computed by making various calculations based on other values in the pairwise comparison matrix
Answer: C
Diff: 2 Page Ref: 415
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process

94) The analytical hierarchy process is a method for __________ decision alternatives.
A) creating
B) ranking
C) changing
D) deleting
Answer: B
Diff: 1 Page Ref: 413
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process

95) Values with an acceptable consistency ratio are values
A) less than or equal to 0.1
B) greater than 0.5 but less than 0.6
C) less than 1 but greater than 0.5
D) greater than 0.2 but less than 0.5
Answer: A
Diff: 2 Page Ref: 422
Main Heading: The Analytical Hierarchy Process
Key words: graphical solution of a goal programming problem
96) Assume that a decision maker has to make a choice between three types of cars. Chevy, Honda, and Ford. Based on three criteria: comfort, MPG and style.

The row averages for criteria is summarized in the following column vector:

The preference matrix for the three types of cars is given as follows:

The first row of the following matrix represents Chevy, the second row represents Honda, and the third row represents Ford.

Compute the overall score for each decision alternative (car). Which choice does the decision maker prefer?
A) Chevy
B) Honda
C) Ford
D) Honda and Chevy are equally preferred
E) Ford and Chevy are equally preferred
Answer: B
Diff: 3 Page Ref: 418
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process solution method, calc of overall scores

97) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Michigan, Cleveland, Ohio and St. Louis Missouri. The following pairwise comparison matrix summarizes the preferences of the plant manager.

Detroit Cleveland St. Louis
Detroit 1 1/3 1/4
Cleveland 3 1 1/2
St. Louis 4 2 1

Which choice does the decision maker prefer?
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred
E) Detroit and St. Louis are equally preferred
Answer: B
Diff: 3 Page Ref: 418
Main Heading: The Analytical Hierarchy Process
Key words: pairwise comparison, normalized matrix
98) Three fast food restaurants on a college campus have been subjected to pairwise comparisons on the quality of their food. The matrix is

Pizza Mama's Papa's Freddie's
Mama's 1 3 8
Papa's 1 4
Freddie's 1

Which choice does the decision maker prefer?
A) Mama's
B) Papa's
C) Freddie's
D) Mama's and Papa's are equally preferred.
E) Cannot be determined from the information provided
Answer: A
Diff: 3 Page Ref: 418
Main Heading: The Analytical Hierarchy Process
Key words: pairwise comparison, normalized matrix

99) In the __________ process, the decision maker determines how well each alternative scores on a criterion using pairwise comparisons.
A) linear programming
B) simplex tableau
C) goal programming
D) analytical hierarchy
Answer: D
Diff: 2 Page Ref: 413
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process

100) In the analytical hierarchy process, a high consistency ratio is considered __________ consistent than a low consistency ratio.
A) less
B) more
C) none of the above
Answer: A
Diff: 2 Page Ref: 422
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process, consistency ratio

101) A required step in the analytic hierarchy process is to determine the
A) number of hierarchies to use
B) relative importance of a set of features based on a criterion
C) goals to be satisfied
D) expected value of the criteria
Answer: B
Diff: 2 Page Ref: 413
Main Heading: The Analytical Hierarchy Process
Key words: analytical hierarchy process 102) An art critic is evaluating four different interpretations "The Nutcracker". The pairwise comparison matrix for the criterion "originality of choreography" is given below.

Choreographer A B C D
A 1 1/3 3 4
B 3 1 5 2
C 1/3 1/5 1 6
D 1/4 1/2 1/6 1

Determine the priorities of the four choreographers relative to "originality".
A) A is preferred to B; B is preferred to C; and C is preferred to D.
B) B is preferred to A; A is preferred to D; and D is preferred to C.
C) B is preferred to A; A is preferred to C; and C is preferred to D.
D) C is preferred to A; A is preferred to D; and D is preferred to B.
Answer: C
Diff: 2 Page Ref: 414
Main Heading: The Analytical Hierarchy Process
Key words: pairwise comparisons

103) In synthesization, dividing each value in each column of the pairwise comparison matrix by the corresponding column sum, we obtain the __________ matrix.
A) pairwise
B) normalized
C) preference
D) criteria
E) criteria preference
Answer: B
Diff: 2 Page Ref: 416
Main Heading: The Analytical Hierarchy Process
Key words: synthesization, normalized matrix 104) Assume that a plant manager has to decide where to locate its warehouse The decision has been narrowed down to choices among the following three cities: Detroit, Michigan, Cleveland, Ohio and St. Louis Missouri. The company has weighted each of these criteria in terms of its relative importance in the decision making process, and it has analyzed each potential warehouse location and graded them according to each criteria as shown in the following table.

Decision Criteria Weight Grades for Detroit Grades for Cleveland Grades for
St. Louis
Proximity to suppliers .45 80 70 60
Proximity to customers .35 75 90 80
Land and construction costs .20 60 50 85

Calculate the scores for each location and state where the warehouse should be located?
A) Detroit
B) Cleveland
C) St. Louis
D) Cleveland and St. Louis are equally preferred
E) Detroit and St. Louis are equally preferred
Answer: B
Diff: 2 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring model

105) A business is trying to decide which restaurant to hold its annual awards banquet. Use the information below to determine the best choice.

Restaurant
Criteria Weight A B C
Appearance 0.15 40 65 60
Service 0.30 75 80 70
Atmosphere 0.15 60 40 70
Location 0.10 90 100 75
Quality of food 0.30 70 80 75

Where should the restaurant be located?
A) A
B) B
C) C
D) A and B equally preferred
E) B and C equally preferred
Answer: B
Diff: 2 Page Ref: 425
Main Heading: Scoring Model
Key words: scoring