Operations Research I ie 416 Extra Credit Assignment


WinQSB Input for Preemptive Goal Programming (Scenario 4)



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WinQSB Input for Preemptive Goal Programming (Scenario 4)

WinQSB Output for Preemptive Goal Programming (Scenario 4)

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:

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







Supplier

Quantity of Lots

Quantity of excellent chips

Quantity of good chips

Quantity of mediocre Chips

Cost ($)

1

10

600

200

200

$4,000.00

2

80

4,000

2,800

1,200

$24,000.00

3

0

0

0

0

$0.00

Total

N/A

4,600

3,000

1,400

$28,000.00









Table 17










Quantity of excellent chips

Quantity of good chips

Quantity of mediocre chips

Cost ($)

Goal

5,000

3,000

1,000

$0.00

Deviation from Requirements

Goal is not met by 400 chips

Goal is met

Goal is exceeded by 400 chips

$0.00



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 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:



Table 18

Priority

Goals

First Priority

The budget of $28,000 is not exceeded

Second Priority

At least 1,000 mediocre chips are purchased

Third Priority

At least 3,000 good chips are purchased

Fourth Priority

At least 5,000 excellent chips are purchased

WinQSB Input for Preemptive Goal Programming (Scenario 5)



WinQSB Output for Preemptive Goal Programming (Scenario 5)



Report to Manager (5)

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







Supplier

Quantity of Lots

Quantity of excellent chips

Quantity of good chips

Quantity of mediocre Chips

Cost ($)

1

10

600

200

200

$4,000.00

2

80

4,000

2,800

1,200

$24,000.00

3

0

0

0

0

$0.00

Total

N/A

4,600

3,000

1,400

$28,000.00









Table 20










Quantity of excellent chips

Quantity of good chips

Quantity of mediocre chips

Cost ($)

Goal

5,000

3,000

1,000

$0.00

Deviation from Requirements

Goal is not met by 400 chips

Goal is met

Goal is exceeded by 400 chips

$0.00


Sensitivity Analysis Summary for Preemptive Goal Programming













Table 13





































Optimal Solution







Priority of Goals




Lots Purchased from Suppliers




Deviation




Highest

Second

Third

Lowest

1

2

3

Z1

Z2

Z3

Z4

Budget

Excellent

Good

Mediocre

10

80

0

0

-400

0

400

Excellent

Good

Mediocre

Budget

0

100

0

0

500

500

2000

Mediocre

Good

Excellent

Budget

10

80

0

400

0

-400

0

Good

Mediocre

Excellent

Budget

10

80

0

0

400

-400

0

Budget

Mediocre

Good

Excellent

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.

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