fruit computer company · web viewfruit computer company is ready to make its annual purchase of...

11/15/2011

98 Problem 2

Table of Contents

1. Problem Statement……………………………………………………………Pg. 3

2. Problem Summary…………………………………………………………….Pg. 3

3. Problem Formulation…………………………………………………………Pg. 4

i) Initial Constraints………………………………………………………….Pg. 5

ii) Constraints with Deviational Variables………………………………….Pg. 6

iii) Assumptions & Example…………………………………………………..Pg. 6

iv) Objective Function………………………………………………………...Pg. 7

4. WinQSB for Linear Programming…………………………………………...Pg. 8

5. Report to Manager for Linear Programming……………………………….Pg. 9

6. WinQSB for Preemptive Goal Programming…….………………………....Pg. 10

7. Report to Manager for Preemptive Goal Programming…………………....Pg. 13

8. Sensitivity Analysis…………………………………………………………..…Pg. 14

i) Scenario 2………………………………………………………………..….Pg. 15

ii) Report to Manager 2…………………………………………………..…..Pg. 17

iii) Scenario 3…………………………………………………………….….....Pg. 19

iv) Report to Manager 3………………………………………………..……..Pg. 20

v) Scenario 4…………………………………….…………………….……....Pg. 21

vi) Report to Manager 4……………………………………………………….Pg. 22

vii)Scenario 5…………………………………………………….……………..Pg. 23

viii) Report to Manger 5…………………………………………………….Pg. 26

9. Sensitivity Analysis Summery for Goal Programming……………...………Pg. 27

Problem Statement:

Fruit Computer Company is ready to make its annual purchase of computer chips. Fruit can purchase chips (in lots of 100) from three suppliers. Each chip is rated as being of excellent, good, or mediocre quality. During the coming year, Fruit will need 5,000 excellent chips, 3,000 good chips, and 1,000 mediocre chips. The characteristics of the chips purchased from each supplier are shown in Table 1 (see Problem Summary).

Each year, Fruit has budgeted $28,000 to spend on chips. If Fruit does not obtain enough chips of a given quality, then the company may special-order additional chips at $10 per excellent chip, $6 per good chip, and $4 per mediocre chip. Fruit assesses a penalty of $1 for each dollar by which the amount paid to supplier 1-3 exceeds the annual budget. Formulate and solve a linear program to help Fruit minimize the penalty associated with meeting the annual chip requirements. Also use preemptive goal programming to determine a purchasing strategy. Let the budget constraint have the highest priority, followed in order by the restrictions on excellent, good, and mediocre chips. Table 2 (see Problem Summary) will summarize the problem.

Parisay’s comments are in red.

Problem Summary:

As stated earlier, Table 1 is a compilation of the given data about how many types of chips are in one lot from each supplier, as well as how much each supplier charges for a single lot. Additionally, Table 2 includes the rest of the information that was given to solve the problem (Fruit’s desired amount of each chip, penalty cost, etc.)

Table 1

Characteristics of a Lot of 100 Chips

Supplier Excellent Good MediocrePrice Per

100 Chips ($)1 60 20 20 4002 50 35 15 3003 40 20 40 250

Team 9, Pg. 2

Table 2Characteristics of a Lot of 100

Chips

Supplier Excellent Good Mediocre

Price Per 100 Chips

($)

Price Per One Chip

($)Supplier 1 60 20 20 400 4.00Supplier 2 50 35 15 300 3.00Supplier 3 40 20 40 250 2.50

Total ≥ 5,000 ≥ 3,000 ≥ 1,000 ≤ $28,000

Price Per Special Order Per One Chip (Penalty

Cost) $10/chip $6/chip $4/chip

$1 for every

dollar over budget

Problem Formulation:

With a budget of $28,000 Fruit must determine how many lots should be ordered from each Supplier in order to meet their desired goal for each type of chip, while at the same time attempting to avoid going over budget and being forced to special-order additional chips to meet their demand.

Decision Variables

Let Xi : number of lots provided by Supplieri (where i = 1, 2, and 3)

Deviational Variables:

The deviational variables were added because it is unknown whether the cost-minimizing solution will under-satisfy or over-satisfy the given goals. Thus, the following deviational variables will be formed:

Si- : amount that goali is under (goal is not achieved and where i = 1, 2, and 3)

Team 9, Pg. 3

Si+ : amount that goali is over (goal has been passed and where i = 1, 2, and 3)

Initial Constraints:

Using the amount of chips of each type that must be ordered and the budget, the constraints were formed. The first constraint was formed using the total amount of excellent chips that were ordered from all three suppliers and how many were desired; in this case it was 60 from Supplier 1, 50 from Supplier 2, 40 from Supplier 3, and a desired amount of 5,000. Similarly, the second and third constraints were formed the same way; the second constraint had 20 from Supplier 1, 35 from Supplier 2, and 20 from Supplier 3 with a desired amount of 3,000. The third constraint was formed the same way, with 20 from Supplier 1, 15 from Supplier 2, 40 from Supplier 3, and a minimum order of 1,000.

1) The total number of excellent chips ordered from all three suppliers, with a desired quantity of 5,000 excellent chips:

60X1 + 50X2 + 40X3 ≥ 5,000

2) The total number of good chips ordered from all three suppliers, with a desired quantity of 3,000 good chips:

20X1 + 35X2 + 20X3 ≥ 3,000

3) The total number of mediocre chips ordered from all three suppliers, with a desired quantity of 1,000 mediocre chips:

20X1 + 15X2 + 40X3 ≥ 1,000

Due to the fact that Fruit is operating on a budget, a fourth constraint was created by taking the sum of the product of how much each supplier sold a lot for. Also, due to the fact that a supplier could not demand Fruit to ship chips to them, a constraint had to be formed to keep Fruit as a receiver.

4) Fruit has a budget of $28,000 with Supplier 1, Supplier 2, and Supplier 3 charging $400, $300, and $250 per lot respectively:

400X1 + 300X2 + 250X3 ≤ 28,000

5) Fruit does not ship any chips, it only receives:

Xi, Si-, Si

+ ≥ 0

Team 9, Pg. 4

In summary, the following five constraints were formed:

1) 60X1 + 50X2 + 40X3 ≥ 5,000

2) 20X1 + 35X2 + 20X3 ≥ 3,000

3) 20X1 + 15X2 + 40X3 ≥ 1,000

4) 400X1 + 300X2 + 250X3 ≤ 28,000

5) Xj, Si-, Si

+ ≥ 0

Constraints with Deviational Variables:

When the constraints were formed, it was noticed that with the first four constraints were flexible. Flexible refers to the fact that the cost-minimizing solution may either under-satisfy or over-satisfy the goal and it will still be used. Thus, the deviational variables S i

- and Si+ (where i =

1, 2, 3, and 4) will be used.

1) 60X1 + 50X2 + 40X3 +S1- – S1

+ = 5,000

2) 20X1 + 35X2 + 20X3 +S2- – S2

+ = 3,000

3) 20X1 + 15X2 + 40X3 + S3- – S3

+ = 1,000

4) 400X1 + 300X2 +250X3 + S4- –S4

+ = 28,000

Assumption and Explanation

In reality most of the time a companies’ budget is fixed; that is to say, that there is no additional money to be used. If that is the case and the budget is a constraint, it is not flexible. Because there is no possible way to go above the budget, deviational variables cannot be added.

For this problem, the budget is not fixed. We can assume that Fruit Computer Company’s annual budget is not fixed at $28,000 and there is additional money available to be used if penalty costs are incurred and if special-orders need to be placed. Thus, deviational variables can be added to the budget constraint.

To further explain the concepts of deviational variables in this problem, refer to the following example:

Team 9, Pg. 5

Example:

After inputting the objective function (refer to Objective Function below) into the computer program WinQSB, several values will be generated. Using the priorities given in the Problem Statement and the deviational variables that we defined will mean that S3

- and S3+ are the

deviational variables for the third goal. Thus, if the output defines a value for S3- to be 5, then it

means that the goal has not been reached and it is below by 5 units. On the other hand, if the output had defined a value for S3

+ to be 5, it would mean that the goal had been exceeded by 5 units. The former option is undesirable because the goal needs to be met, while the latter option is desirable because not only has the goal been met, but it has been exceeded.

It should be noted that the assignment of the terms “undesirable” and “desirable” are not always affiliated with S3

- and S3+ respectively. The assignment is based off of the constraint.

Objective Function:

Recall that the objective is to minimize the penalty cost, and that the penalty cost for special-ordering additional chips cost $10, $6, and $4 for excellent, good, and mediocre. There is also a penalty cost of $1 for every dollar that the budget is exceeded by. The costs are then treated as a penalty cost, which would result in the following objective function:

Objective Function: Min Z = 10S1- +6S2

- + 4 S3- + 1 S4

+

Refer to Table 3 (below) for a summary of the equations that were formed.

Table 3

Summary of All EquationsType Description Equation

Objective Function Minimize Penalty Cost Min Z = 10S1- +6S2

- + 4 S3- + 1 S4

+

Constraint Excellent Chips Ordered 60X1 + 50X2 + 40X3 +S1- – S1

+ = 5,000

Constraint Good Chips Ordered 20X1 + 35X2 + 20X3 +S2- – S2

+ = 3,000

Constraint Mediocre Chips Ordered 20X1 + 15X2 + 40X3 + S3- – S3

+ = 1,000

Constraint Annual Budget 400X1 + 300X2 +250X3 + S4- –S4

+ = 28,000

Team 9, Pg. 6

WinQSB for Linear Programming

WinQSB Input for Linear Programming

WinQSB Output for Linear Programming

Team 9, Pg. 7

It should be noted that when dealing with the problem as a Linear Program, the priority levels that were given were not taken into account.

Report to Manager (LP)

Dear Manager,

The team was tasked with minimizing the penalty cost that Fruit Computer Company would incur while fulfilling their orders; in order to efficiently determine that value, the computer program WinQSB was utilized. By assuming that fulfilling the demands for the three types of chips and staying within the annual budget are NOT all equally important (note the penalty costs) , the results from Figure 2 can be interpreted as such:

This paragraph as worded is not quite right. You need to start with the next paragraph and the solution will result in fulfilling this requirement. In order to achieve the lowest penalty cost, Fruit will have to ensure that the desired quantity of 5,000 excellent chips is met. Fruit should focus on achieving the desired number of excellent chips because if there are not 5,000 excellent chips, special-orders will have to be placed to achieve that quantity. Special-orders for excellent chips will cost Fruit $10 per chip. The other two chips have a lower cost for special-orders; they will cost $6 and $4 for good and mediocre chips, respectively. Thus, to achieve the lowest possible penalty cost, Fruit should place their attention towards satisfying the 5,000 unit requirement for excellent chips.

Thus, the most effective way to do so will be to purchase 100 lots of chips from Supplier 2. Doing so will give the company 5,000 excellent chips, meaning that the desired quantity of excellent chips has been met. However, this method of ordering will give the company 3,500 good chips and 1,500 mediocre chips; both of those values are 500 chips above the desired quantity. Despite being over the desired quantity, there is no penalty cost for exceeding the desired quantity; therefore, this overstocking is acceptable.

Supplier 2 charges $300 for each lot; purchasing 100 lots will cost Fruit $30,000. The annual budget that the company has allocated towards purchasing is only $28,000. Thus, the budget will have to be raised to $30,000 to accommodate all chip demands.

While this paragraph is a good analysis it should not be in report to the manager as it makes too many details that may create confusion. It should be noted that all the lots purchased should be from Supplier 2. The reason is that even though Supplier 3 charges less ($50 less per lot), there are less excellent chips in their lot than Supplier 2’s lot. Thus, in order to satisfy the quantity of excellent chips, 125 lots would have to be purchased from Supplier 3. At $250 per lot, Fruit would have to spend $31,250; that cost is $1,250 more than the cost of purchasing solely from Supplier 2.

Team 9, Pg. 8

While this paragraph is a good analysis it should not be in report to the manager as it makes too many details that may create confusion. Despite the fact that Supplier 1 offers more excellent chips per lot, their lot price of $400 is too expensive. In order to facilitate the company’s demand for excellent chips, 83 lots will have to be purchased. However, that would only give the company 4,980 excellent chips; thus, the remaining 20 chips would have to be special-ordered. The special-orders would incur the company a penalty cost of $200 dollars, raising the total price of ordering from Supplier 1 to be $33,400. That cost is $3,400 higher than ordering from just Supplier 2.

Please refer to the following Tables (Tables 4 and 5) for a tabular summary of the results that were gathered from the output.

Table 4

Information Fruit's Requirements Deviation from RequirementsPenalty

CostQuantity of excellent chips ≥ 5,000 Goal is met $0.00

Quantity of good chips ≥ 3,000 Goal exceeded by 500 $0.00Quantity of mediocre chips ≥ 1,000 Goal exceeded by 500 $0.00

Annual Budget ≤ $28,000 Goal exceeded by $2,000 $2,000.00Total Penalty Cost $2,000.00

Table 5Information Results

Purchase from Supplier Supplier 2Quantity of Lots Purchased 100 lots at $300 per lot

Quantity of Each Chip Obtained 5,000 excellent chips, 3,500 good chips, and 1,500 mediocre chipsTotal Cost (100 lots) * ($300/lot) = $30,000

Goal Programming

Preemptive Goal Programming

Recall that in the Problem Statement there were priority levels assigned to the different goals. The priority levels are shown in Table 6. Now that this problem will be solved from a Goal Programming perspective, the priority levels will be used to solve the equation, unlike how the Linear Programming ignored the priority levels.

Table 6Priority Goals

Team 9, Pg. 9

First Priority The budget of $28,000 is not exceededSecond Priority At least 5,000 excellent chips are purchasedThird Priority At least 3,000 good chips are purchased

Fourth Priority At least 1,000 mediocre chips are purchased

WinQSB Input for Preemptive Goal Programming

Team 9, Pg. 10

WinQSB Output for Preemptive Goal Programming

This paragraph is completely wrong! You cannot reject a solution obtained based on the problem. There is no penalty cost involved in this section of the problem. Note: This scenario is rejected because the goal is to minimize the penalty cost. The output that was given shows that Fruit Computer Company will not meet their desired amount of 5,000 excellent chips by 381.82 and will exceed their desired amount of mediocre chips by 1,200. Thus, Fruit will be

Team 9, Pg. 11

forced to special-order 382 excellent chips; at a price of $10 per excellent chip, the penalty cost for special-ordering excellent chips would be $3,820 penalty cost.

WinQSB Output for Preemptive Goal Programming (Scenario 1) It is not clear how you have got this output?

Report to Manager (1) needs major modifications

Dear Manager,

Team 9, Pg. 12

The team was tasked with minimizing the penalty cost (there is not penalty cost here. This section should change.) that Fruit Computer Company would incur while fulfilling their orders; in order to efficiently determine that value, the computer program WinQSB was used to run a preemptive goal program. The team was also informed that some goals of the company had priority over one another. Maintaining the budget of $28,000 was the highest priority, while meeting the company’s demand for excellent, good, and mediocre chips followed in decreasing priority. The priority levels were summarized in tabular form (see above, Table 6). With that in mind, the results from the output in Figure 5 (where is this figure, you do not have any figure number!) can be interpreted as such:

Fruit will be able to achieve only three of the specified four goals. The budget will be maintained and the desired quantity of good and mediocre chips will be met. However, the remaining goal regarding excellent chips will not be met.

In order to create the results that were just described, 10 lots should be purchased from Supplier 1; with a cost of $400 per lot, the company will pay $4,000. An additional 80 lots should be purchased from Supplier 2 at a cost of $300 per lot, which will result in a cost of $24,000. Thus, the total amount of funds that Fruit will have to allocate towards purchasing costs will not exceed the amount that was allocated towards it.

This purchase order will result in 4,600 excellent chips, 3,000 good chips, and 1,400 mediocre chips. The goal for good chips will be met, while the goal for mediocre chips shall be exceeded by 400 chips. However, the goal of excellent chips shall fall short by 400 chips. Due to the fact that the budget was considered to be the most important goal, nothing should be done to attempt to meet the goal set for excellent chips.

Refer to Tables 7 and 8 (below) for a tabular summary of the results:

Table 7

SupplierQuantity of

LotsQuantity of

excellent chipsQuantity of good

chipsQuantity of mediocre

Chips Cost ($)1 10 600 200 200 $4,000.00

2 80 4,000 2,800 1,200$24,000.0

03 0 0 0 0 $0.00

Total N/A 4,600 3,000 1,400$28,000.0

0

Table 8Quantity of excellent

chipsQuantity of good


chipsCost ($)

Team 9, Pg. 13

Goal 5,000 3,000 1,000 $0.00Deviation from Requirements

Goal is not met by 400 chips Goal is met

Goal is exceeded by 400 chips $0.00

Sensitivity AnalysisSensitivity analysis was performed for the equation by changing the priority levels of the

goals. The following four alternatives were performed using sensitivity analysis.

Scenario 2

The highest priority was assigned to ordering the desired quantity of excellent chips, with the following levels of priority being assigned to the quantity of good and mediocre chips, while the lowest priority was assigned to Fruit Computer Company’s annual budget. Refer to Table 9 (below) for the new priority levels:


First Priority At least 5,000 excellent chips are purchasedSecond Priority At least 3,000 good chips are purchasedThird Priority At least 1,000 mediocre chips are purchased

Fourth Priority The budget of $28,000 is not exceeded

WinQSB Input for Preemptive Goal Programming (Scenario 2)

Team 9, Pg. 14

WinQSB Output for Preemptive Goal Programming (Scenario 2)

Team 9, Pg. 15

Report to Manager (2)

Team 9, Pg. 16

Dear Manager, no need for report for each SA

Fruit Computer Company assigned the team with determining the minimum penalty cost that would be incurred from their shipment orders. To obtain that value, the computer program WinQSB was used to run a preemptive goal program. Additionally, the company had placed priority levels for their four goals; meeting the excellent chip goal held the highest priority, followed in decreasing order by meeting the goal of good and mediocre chips. The lowest priority level was assigned to maintaining the annual budget. The priority levels were summarized in tabular form (see above, Table 9). With that in mind, the results from the output in Figure 7 can be interpreted as such:

In order to meet as many goals as possible, 100 lots of chips from Supplier 2 should be purchased. Doing so will give the company 5,000 excellent chips, meaning that the desired quantity of excellent chips has been met. However, this method of ordering will give the company 3,500 good chips and 1,500 mediocre chips; both of those values are 500 chips above the desired quantity. Despite being over the desired quantity, there is no penalty cost for exceeding the desired quantity; therefore, this overstocking is acceptable.

Supplier 2 charges $300 for each lot; purchasing 100 lots will cost Fruit $30,000. The annual budget that the company has allocated towards purchasing is only $28,000. Thus, the budget has been exceeded by $2,000. The budget will have to be raised to $30,000 to accommodate all demands. However, because the budget had the lowest priority of all the other goals, it has been determined that additional funds can be allocated towards the annual fund.

The results were then compiled into tables (see Tables 10 and 11).

Table 10

Information Fruit's Requirements Deviation from RequirementsPenalty

CostQuantity of excellent chips ≥ 5,000 Goal is met $0.00

Quantity of good chips ≥ 3,000 Goal exceeded by 500 $0.00Quantity of mediocre chips ≥ 1,000 Goal exceeded by 500 $0.00

Annual Budget ≤ $28,000 Goal exceeded by $2,000 $2,000.00Total Penalty Cost $2,000.00

Table 11Information Results

Purchase from Supplier Supplier 2Quantity of Lots Purchased 100 lots at $300 per lot

Quantity of Each Chip Obtained 5,000 excellent chips, 3,500 good chips, and 1,500 mediocre chipsTotal Cost (100 lots) * ($300/lot) = $30,000

Scenario 3

Team 9, Pg. 17

Ordering the desired quantity of mediocre chips was assigned the highest priority level, while the following levels of priority were assigned to the quantity of good and excellent chips. The lowest priority was assigned to Fruit Computer Company’s annual budget. Refer to Table 12 (below) for a tabular representation:


First Priority At least 1,000 mediocre chips are purchasedSecond Priority At least 3,000 good chips are purchasedThird Priority At least 5,000 excellent chips are purchased



Team 9, Pg. 18


Report to Manager (3) no need for report for each SA

Dear Manager,

The team was ordered to determine the minimum penalty cost that Fruit Computer Company would incur while fulfilling their orders. To do so, the computer program WinQSB was used to run a preemptive goal program. It should be noted that the computer had assigned different priority levels for their four goals. The highest priority was assigned to satisfying the goal for mediocre chips, with the following levels of priority being assigned to satisfying the goals of good and excellent chips, while the lowest priority was assigned to Fruit Computer Company’s annual budget. The priority levels were summarized in tabular form (see above, Table 12). With that in mind, the results from the output in Figure 9 can be interpreted as such:

Fruit will be able to achieve only three of the specified four goals. The mediocre chip goal will be exceeded, but that is not a deterrent. The only goal that was not met was the excellent chip goal.

Team 9, Pg. 19

In order to obtain the results that were just described, 10 lots should be purchased from Supplier 1; at a cost of $400 per lot, the company will pay $4,000. An additional 80 lots should be purchased from Supplier 2 at a cost of $300 per lot, which will result in a cost of $24,000. Thus, the total cost will be $28,000; thus, Fruit’s annual budget will not be exceeded.

This purchase order will result in 4,600 excellent chips, 3,000 good chips, and 1,400 mediocre chips. The good chips goal will be met, while the mediocre chips goal shall be exceeded by 400 chips. However, the excellent chips goal will fall short by 400 chips. Due to the fact that the two most important goals (achieving the desired quantity of mediocre and good chips) were met, achieving the second-lowest priority (achieving 5,000 excellent chips) was deemed to be an acceptable loss.

Please see the following tables (13 and 14) for a brief summary:

Table 13

SupplierQuantity of

LotsQuantity of



Chips Cost ($)1 10 600 200 200 $4,000.00

2 80 4,000 2,800 1,200$24,000.0

03 0 0 0 0 $0.00

Total N/A 4,600 3,000 1,400$28,000.0

0




chipsCost ($)




Team 9, Pg. 20

Scenario 4

For this Scenario, sensitivity analysis was performed by changing the priority levels. In this solution, the highest priority was assigned to ordering the desired quantity of good chips, with the following levels of priority being assigned to the quantity of mediocre and excellent chips, while the lowest priority is assigned to Fruit Computer Company’s annual budget. The tabular summary is shown below (Table 15):


First Priority At least 3,000 good chips are purchasedSecond Priority At least 1,000 mediocre chips are purchasedThird Priority At least 5,000 excellent chips are purchased



Team 9, Pg. 21


Report to Manager (4) no need for report for each SA

Dear Manager,

The team was given the objective of minimizing the penalty cost that Fruit Computer Company would incur while fulfilling their orders; in order to obtain that value, the computer program WinQSB was utilized. In this solution, the highest priority was assigned to ordering the desired quantity of good chips, with the following levels of priority being assigned to the quantity of mediocre and excellent chips, while the lowest priority is assigned to Fruit Computer Company’s annual budget. The priority levels were summarized in tabular form (see above, Table 15). With that in mind, the results from the output in Figure 11 can be interpreted as such:

Team 9, Pg. 22

The company will be able to achieve only three of the specified four goals. There will be enough good and mediocre chips to meet the goals. Additionally, the total amount spent on the shipments will not force the company to allocate additional funds to the annual budget. Unfortunately, there will not be enough excellent chips.

In order to receive the results that were just described, 10 lots should be purchased from Supplier 1 and 80 lots from Supplier 2. This will cost the company a total of $28,000, which is the exact amount of money that was designated for the purchasing cost.

This purchase order will result in a lack of excellent chips. To be exact, the excellent chip goal will not be met by 400 chips. However, there will be an additional 400 mediocre chips. The goals for good chips and annual budget will be met. Since the two most important goals (achieving the desired quantity of good and mediocre chips) were met, achieving the second-lowest priority (achieving 5,000 excellent chips) was not considered important enough to place special-orders for.

Please see Tables 7 and 8:

Table 16

SupplierQuantity of

LotsQuantity of



Chips Cost ($)1 10 600 200 200 $4,000.00

2 80 4,000 2,800 1,200$24,000.0

03 0 0 0 0 $0.00

Total N/A 4,600 3,000 1,400$28,000.0

0




chipsCost ($)




Scenario 5

In this solution, the highest priority was assigned to meeting Fruit Computer Company’s annual budget, with the following levels of priority being assigned to the quantity of mediocre

Team 9, Pg. 23

and good chips, while the lowest priority is assigned to ordering the desired quantity of excellent chips. See Table 12 (below) for the tabular summary:


First Priority The budget of $28,000 is not exceededSecond Priority At least 1,000 mediocre chips are purchasedThird Priority At least 3,000 good chips are purchased

Fourth Priority At least 5,000 excellent chips are purchased


Team 9, Pg. 24


Team 9, Pg. 25

Report to Manager (5)

Team 9, Pg. 26

Dear Manager, no need for report for each SA

The team was tasked with minimizing the penalty cost that Fruit Computer Company would incur while fulfilling their orders; in order to efficiently determine that value, the computer program WinQSB was used to run a preemptive goal program. In this solution, the highest priority was assigned to maintaining the annual budget of $28,000. The following levels of priority in decreasing order were assigned to ordering the desired quantities of mediocre chips, then good chips, and finally excellent chips. The priority levels were summarized in tabular form (see above, Table 18). With that in mind, the results from the output in Figure 13 can be interpreted as such:

The company will be able to achieve only three of the specified four goals. The total amount that the company will have to spend will not go over $28,000, meaning that the budget goal was met. Additionally, the desired quantity of good and mediocre chips will be reached. Unfortunately, the desired quantity of 5,000 excellent chips will not be met. Due to the fact that the two most important goals (not going over the annual budget and achieving the desired quantity of mediocre chips) were met, satisfying the goal with the lowest priority (achieving 5,000 excellent chips) was ignored.

In order to get the results that were just described, 10 lots should be purchased from Supplier 1; with a cost of $400 per lot, the company will pay $4,000. An additional 80 lots should be purchased from Supplier 2 at a cost of $300 per lot, which will result in a cost of $24,000. Thus, the total cost will be $28,000; that is the exact amount of money in Fruit’s annual budget.

Refer to Tables 19 and 20 for a tabular summary of the results:

Table 19

SupplierQuantity of

LotsQuantity of



Chips Cost ($)1 10 600 200 200 $4,000.00

2 80 4,000 2,800 1,200$24,000.0

03 0 0 0 0 $0.00

Total N/A 4,600 3,000 1,400$28,000.0

0

Table 20

Team 9, Pg. 27

Quantity of excellent chips

Quantity of good chips

Quantity of mediocre chips

Cost ($)




Team 9, Pg. 28

Sensitivity Analysis Summary for Preemptive Goal Programming

Table 13Optimal Solution

Priority of GoalsLots Purchased from

Suppliers DeviationHighest Second Third Lowest 1 2 3 Z1 Z2 Z3 Z4

BudgetExcellen

t GoodMedioc

re 10 80 0 0 -400 0 400Excellen

t GoodMedioc

re Budget 0 100 0 0 500 500200

0Medioc

re GoodExcellen

t Budget 10 80 0400 0 -400 0

GoodMedioc

reExcellen

t Budget 10 80 0 0 400 -400 0

BudgetMedioc

re GoodExcellen

t 10 80 0 0 400 0-

400

It should be noted that under the Optimal Solution Deviation, the Z-values are associated with different goals for each row. Due to the fact that the priority levels change for each row, the Z-values are associated with different deviational variables. For example, in the first row, Z1 is associated with maintaining Fruit Computer Company’s annual budget of $28,000. In the second row, Z1 is associated with meeting Fruit’s demand of 5,000 excellent chips.

. By looking the summary of the sensitivity analysis that was performed (Table 13), despite the fact that the priority levels were assigned to different goals, four out of five times the result was the same. That is to say, 10 lots were purchased from Supplier 1 and 80 lots from Supplier 2. The result was a shortage of 400 excellent chips and a surplus of 400 mediocre chips. The other two goals were met exactly.

The one time that the result was different was when obtaining the desired number of excellent chips was given the highest priority. In all of the Scenarios that were viewed, this was the only case where the goal for excellent chips was satisfied. Additionally, the goals for both the good and mediocre chips were exceeded by 500 chips. Despite those goals being met, the annual budget was exceeded by $2,000.

Team 9, Pg. 29

fruit computer company · web viewfruit computer company is ready to make its annual purchase of...

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