Exam 9: Multicriteria Decision Making

In scoring models, the two alternatives with the highest scores are compared to make the final decision.

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 3 4 2 1 2 1 2 2 Available\nobreakspaceHours 600 400 400 Management wants to achieve three 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. -The goal programming constraint for the first goal is:

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 3 4 2 1 2 1 2 2 Available\nobreakspaceHours 600 400 400 Management wants to achieve three 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. -Goal programming solutions achieve the ________ satisfactory solution possible.

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 6000. 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 6000. (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) -Write the risk factor constraint

The analytic hierarchy process

Pairwise comparisons are made among

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 four 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. -What are the constraints for this problem?

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. ~~~~~~~~~~~~~~~~~~~~~~~~~~{ \text { Durability Matrix } } ~~~~~~~~~ \text { Preference } \\ \begin{array} { l c c c c } & \text { Car A } & \text { Car B } & \text { Car C } & \text { Vector } \\ \hline \text { Car A } & 1 & 0.25 & 4 & 0.36 \\ \text { Car B } & 4 & 1 & 0.5 & 0.59 \\ \text { Car C } & 0.25 & 2.00 & 1.00 & 0.41 \\ \hline \end{array} Multiplying the normalized matrix by the preference vector gives the following results: 2.17 2.26 1.69 Compute the consistency index.

Consider the following constraint: 2x1 + 3x2 =60. Assume that we convert this constraint into a goal constraint with the value of x1 = 15 and the value of x2 = 15. Then the values of d1+ and d1- are ________ and ________, respectively.

In goal programming, problems cannot have two or more goals at the same priority level.

A pairwise comparison matrix summarizes the pairwise comparisons for a criterion.

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 one objective.

One goal is never achieved at the expense of another higher-priority goal.

A consistency index measures the degree of inconsistency in pairwise comparisons.

Goal programming provides a method for simultaneously striving to achieve several objectives.

If the CI/RI ratio is more than ________, then there are probably serious inconsistencies in the AHP results.

At least one or both deviational variables in a goal constraint must equal ________.

Goal constraints can include all deviational variables.

Ashley's manufactures home furnishings for department stores. Planning is underway for the production of the following items during the next production period: Quilts Blinds Pillows Fabric required (yards) 7 4 9 Time required (hours) 1.5 2 0.5 Packaging material (ounces) 3 2 1 Profit 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 are given in the table. -What is the fabric constraint?

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 3 4 2 1 2 1 2 2 Available\nobreakspaceHours 600 400 400 Management wants to achieve three 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. -In a pairwise comparison, ________ alternatives are compared according to a criterion and one is preferred.