Operations Research I ie 416 Extra Credit Assignment

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.

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 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.

Dear Manager,

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.

Sensitivity analysis was performed for the equation by changing the priority levels of the goals. The following four alternatives were performed using sensitivity analysis.

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:

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).

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:

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.

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.

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):