11/15/2011
Operations Research I IE 416
Extra Credit Assignment
Problem #2 P.199
GROUP 9
Jin woo Choi
Philip Liu
Nallely Tagle
Fruit Computer Company
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 $1 for
each dollar by which the amount paid to supplier 1-3 exceeds the annual budget. Formulate and
solve a linear program to help Fruit minimize the penalty associated with meeting the annual
chip requirements. Also use preemptive goal programming to determine a purchasing strategy.
Let the budget constraint have the highest priority, followed in order by the restrictions on
excellent, good, and mediocre chips. Table 2 (see Problem Summary) will summarize the
problem.
Parisay’s comments are in red.
Problem Summary:
As stated earlier, Table 1 is a compilation of the given data about how many types of
chips are in one lot from each supplier, as well as how much each supplier charges for a single
lot. Additionally, Table 2 includes the rest of the information that was given to solve the
problem (Fruit’s desired amount of each chip, penalty cost, etc.)
Table 1
Characteristics of a Lot of 100 Chips
Supplier
1
2
3
Excellent
60
50
40
Good
20
35
20
Mediocre
20
15
40
Price Per 100
Chips ($)
400
300
250
Team 9, Pg. 3
Table 2
Characteristics of a Lot of 100 Chips
Supplier
Supplier 1
Supplier 2
Supplier 3
Total
Price Per Special Order
Per One Chip (Penalty
Cost)
Excellent
60
50
40
≥ 5,000
$10/chip
Good
20
35
20
≥ 3,000
$6/chip
Mediocre
20
15
40
≥ 1,000
Price Per 100
Chips ($)
400
300
250
≤ $28,000
$4/chip
Price Per
One Chip
($)
4.00
3.00
2.50
$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)
Si+ : amount that goali is over (goal has been passed and where i = 1, 2, and 3)
Team 9, Pg. 4
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. 5
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. 6
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 S 3- 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 Equations
Type
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. 7
WinQSB for Linear Programming
WinQSB Input for Linear Programming
WinQSB Output for Linear Programming
Team 9, Pg. 8
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 specialorders; 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. 9
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.
Information
Quantity of excellent chips
Quantity of good chips
Quantity of mediocre chips
Annual Budget
Total Penalty Cost
Fruit's Requirements
≥ 5,000
≥ 3,000
≥ 1,000
≤ $28,000
Table 4
Deviation from Requirements
Goal is met
Goal exceeded by 500
Goal exceeded by 500
Goal exceeded by $2,000
Penalty Cost
$0.00
$0.00
$0.00
$2,000.00
$2,000.00
Table 5
Information
Purchase from Supplier
Quantity of Lots Purchased
Quantity of Each Chip Obtained
Total Cost
Results
Supplier 2
100 lots at $300 per lot
5,000 excellent chips, 3,500 good chips, and 1,500 mediocre chips
(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 6
Priority
First Priority
Goals
The budget of $28,000 is not exceeded
Team 9, Pg. 10
Second Priority
Third Priority
Fourth Priority
At least 5,000 excellent chips are purchased
At least 3,000 good chips are purchased
At least 1,000 mediocre chips are purchased
WinQSB Input for Preemptive Goal Programming
Team 9, Pg. 11
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. 12
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. 13
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
$24,000. Thus, the total amount of funds that Fruit will have to allocate towards purchasing
costs will not exceed the amount that was allocated towards it.
This purchase order will result in 4,600 excellent chips, 3,000 good chips, and 1,400
mediocre chips. The goal for good chips will be met, while the goal for mediocre chips shall be
exceeded by 400 chips. However, the goal of excellent chips shall fall short by 400 chips. Due
to the fact that the budget was considered to be the most important goal, nothing should be done
to attempt to meet the goal set for excellent chips.
Refer to Tables 7 and 8 (below) for a tabular summary of the results:
Table 7
Quantity of
Quantity of good
excellent chips
chips
600
200
Supplier
1
Quantity of
Lots
10
2
3
80
0
4,000
0
2,800
0
1,200
0
Total
N/A
4,600
3,000
1,400
Quantity of excellent
chips
Table 8
Quantity of good
chips
Quantity of mediocre
Chips
200
Cost ($)
$4,000.00
$24,000.0
0
$0.00
$28,000.0
0
Quantity of mediocre
chips
Cost
($)
Team 9, Pg. 14
Goal
Deviation from
Requirements
5,000
Goal is not met by 400
chips
3,000
Goal is met
1,000
Goal is exceeded by
400 chips
$0.00
$0.00
Sensitivity Analysis
Sensitivity 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:
Table 9
Priority
First Priority
Second Priority
Third Priority
Fourth Priority
Goals
At least 5,000 excellent chips are purchased
At least 3,000 good chips are purchased
At least 1,000 mediocre chips are purchased
The budget of $28,000 is not exceeded
WinQSB Input for Preemptive Goal Programming (Scenario 2)
Team 9, Pg. 15
WinQSB Output for Preemptive Goal Programming (Scenario 2)
Team 9, Pg. 16
Report to Manager (2)
Team 9, Pg. 17
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).
Information
Quantity of excellent chips
Quantity of good chips
Quantity of mediocre chips
Annual Budget
Total Penalty Cost
Fruit's Requirements
≥ 5,000
≥ 3,000
≥ 1,000
≤ $28,000
Table 10
Deviation from Requirements
Goal is met
Goal exceeded by 500
Goal exceeded by 500
Goal exceeded by $2,000
Penalty Cost
$0.00
$0.00
$0.00
$2,000.00
$2,000.00
Table 11
Information
Purchase from Supplier
Quantity of Lots Purchased
Quantity of Each Chip Obtained
Total Cost
Results
Supplier 2
100 lots at $300 per lot
5,000 excellent chips, 3,500 good chips, and 1,500 mediocre chips
(100 lots) * ($300/lot) = $30,000
Scenario 3
Team 9, Pg. 18
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:
Table 12
Priority
First Priority
Second Priority
Third Priority
Fourth Priority
Goals
At least 1,000 mediocre chips are purchased
At least 3,000 good chips are purchased
At least 5,000 excellent chips are purchased
The budget of $28,000 is not exceeded
WinQSB Input for Preemptive Goal Programming (Scenario 3)
Team 9, Pg. 19
WinQSB Output for Preemptive Goal Programming (Scenario 3)
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. 20
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 $28,000; thus, Fruit’s annual budget will not be exceeded.
This purchase order will result in 4,600 excellent chips, 3,000 good chips, and 1,400
mediocre chips. The good chips goal will be met, while the mediocre chips goal shall be
exceeded by 400 chips. However, the excellent chips goal will fall short by 400 chips. Due to
the fact that the two most important goals (achieving the desired quantity of mediocre and good
chips) were met, achieving the second-lowest priority (achieving 5,000 excellent chips) was
deemed to be an acceptable loss.
Please see the following tables (13 and 14) for a brief summary:
Table 13
Quantity of
Quantity of good
excellent chips
chips
600
200
Supplier
1
Quantity of
Lots
10
2
3
80
0
4,000
0
2,800
0
1,200
0
Total
N/A
4,600
3,000
1,400
Goal
Deviation from
Requirements
Quantity of excellent
chips
5,000
Goal is not met by 400
chips
Table 14
Quantity of good
chips
3,000
Goal is met
Quantity of mediocre
Chips
200
Cost ($)
$4,000.00
$24,000.0
0
$0.00
$28,000.0
0
Quantity of mediocre
chips
1,000
Goal is exceeded by
400 chips
Cost
($)
$0.00
$0.00
Team 9, Pg. 21
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):
Table 15
Priority
First Priority
Second Priority
Third Priority
Fourth Priority
Goals
At least 3,000 good chips are purchased
At least 1,000 mediocre chips are purchased
At least 5,000 excellent chips are purchased
The budget of $28,000 is not exceeded
WinQSB Input for Preemptive Goal Programming (Scenario 4)
Team 9, Pg. 22
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:
Team 9, Pg. 23
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 $28,000, which is
the exact amount of money that was designated for the purchasing cost.
This purchase order will result in a lack of excellent chips. To be exact, the excellent
chip goal will not be met by 400 chips. However, there will be an additional 400 mediocre
chips. The goals for good chips and annual budget will be met. Since the two most important
goals (achieving the desired quantity of good and mediocre chips) were met, achieving the
second-lowest priority (achieving 5,000 excellent chips) was not considered important enough to
place special-orders for.
Please see Tables 7 and 8:
Table 16
Quantity of
Quantity of good
excellent chips
chips
600
200
Supplier
1
Quantity of
Lots
10
2
3
80
0
4,000
0
2,800
0
1,200
0
Total
N/A
4,600
3,000
1,400
Goal
Deviation from
Requirements
Quantity of excellent
chips
5,000
Goal is not met by 400
chips
Table 17
Quantity of good
chips
3,000
Goal is met
Quantity of mediocre
Chips
200
Cost ($)
$4,000.00
$24,000.0
0
$0.00
$28,000.0
0
Quantity of mediocre
chips
1,000
Goal is exceeded by
400 chips
Cost
($)
$0.00
$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
Team 9, Pg. 24
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
First Priority
Second Priority
Third Priority
Fourth Priority
Goals
The budget of $28,000 is not exceeded
At least 1,000 mediocre chips are purchased
At least 3,000 good chips are purchased
At least 5,000 excellent chips are purchased
WinQSB Input for Preemptive Goal Programming (Scenario 5)
Team 9, Pg. 25
WinQSB Output for Preemptive Goal Programming (Scenario 5)
Team 9, Pg. 26
Report to Manager (5)
Team 9, Pg. 27
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 $28,000; that is the exact amount of money in Fruit’s
annual budget.
Refer to Tables 19 and 20 for a tabular summary of the results:
Table 19
Quantity of
Quantity of good
excellent chips
chips
600
200
Supplier
1
Quantity of
Lots
10
Quantity of mediocre
Chips
200
2
3
80
0
4,000
0
2,800
0
1,200
0
Total
N/A
4,600
3,000
1,400
Cost ($)
$4,000.00
$24,000.0
0
$0.00
$28,000.0
0
Team 9, Pg. 28
Goal
Deviation from
Requirements
Quantity of excellent
chips
5,000
Goal is not met by 400
chips
Table 20
Quantity of good
chips
3,000
Goal is met
Quantity of mediocre
chips
1,000
Goal is exceeded by
400 chips
Cost
($)
$0.00
$0.00
Team 9, Pg. 29
Sensitivity Analysis Summary for Preemptive Goal
Programming
Table 13
Optimal
Solution
Priority of Goals
Highest Second
Third
Excellen
Budget
t
Good
Excellen
Mediocr
t
Good
e
Mediocr
Excellen
e
Good
t
Mediocr Excellen
Good
e
t
Mediocr
Budget
e
Good
Lowest
Mediocr
e
Lots Purchased from
Suppliers
1
2
3
Z1
10
80
0
0
-400
0
Budget
0
100
0
500
500
Budget
10
80
0
0
40
0
400
200
0
0
-400
0
Budget
Excellen
t
10
80
0
0
400
-400
10
80
0
0
400
0
0
400
Deviation
Z2
Z3
Z4
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. 30