applied mathematics unit 2sba

TIME AND COST EFFICIENCY

OF COMPUTER ASSEMBLY

BUSINESS Applied Mathematics

Josh De Freitas Upper Six I I

School Based Assessment Hillview College

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Contents Introduction ...................................................................................................................................2

Method of Data Collection ..............................................................................................................3

Critical Path Analysis .......................................................................................................................4

Hungarian Algorithm .......................................................................................................................8

Discussion .................................................................................................................................... 13

Limitations ................................................................................................................................... 14

Recommendations ........................................................................................................................ 15

Conclusion.................................................................................................................................... 16

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Introduction

Delta’s Electronics is a popular computer store in the community. They specialize in the assembly

of desktop computers from parts and this often requires trips to various computer parts retail

stores who often sell all the parts but for different prices. Due to the rise in demand for

computers and country-wide recession, Delta’s Electronics have decided to increase production

and minimize cost as well. Therefore they have enlisted the help of the researcher, whom is a

great acquaintance to help achieve this task.

This project plans to optimize the assembly of a desktop computer, and minimize the cost of parts

to be used to assemble such computers. One of the main objectives is to minimize the amount

of time taken to completely assemble a desktop computer by presenting the order of tasks which

must be completed. This will be achieved by investigating the various steps done in assembling a

computer. Another objective is to minimize the amount of money spent on parts to keep the business running in harsh economic times.

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Method of Data Collection

Data was collected through an interview with the employees who build the computers and the

employees who retrieve the parts necessary for assembling the computer. They were asked the

procedure in assembly and the costs for each part from the various stores. The information gave

insight into the process and the steps taken which were used in the critical path analysis. The

employees also stated the price, in 5 stores, for the parts, which include: motherboard,

processor, heat sink, power supply, sata cables, fans, case, and screws, RAM chips and hard drives. These prices were used to conduct the Hungarian algorithm.

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Critical Path Analysis

Critical Path analysis or Critical Path method is the string of activities that, if the

durations are added, is longer than any other path through the network. Therefore a delay in

one of the critical path activities will cause the entire project to be delayed. This is a very

important tool used by businesses and project managers to keep projects on track and prepare

for emergency or unplanned situations.

In this case the critical path would be found for the assembly of a computer tower with

the various computer parts provided.

With the aid of a precedence diagram, each node is replaced with a square divided into

small squares as represented below.

Activity Activity duration

Preceded by

Earliest Start Time (EST) Latest Start Time (LST)

Each process of the computer assembly is represented by a letter and its respective duration time in

minutes in the table below.

Description of Activity Task Preceded by Duration (minutes)

Install Power supply on case A - 10

Install motherboard B A 11 Place processor on board C B 9

Attach heat sink D B, C 13 Install R.A.M. chips E B 10

Install hard drive F D, E 13

Install graphics card G B 12 Connect sata cables to power supply H F, G, E 10

Assemble case with fans and screws I H 11

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An activity network diagram is necessary to form the critical path. An activity network algorithm

will be used to make such diagram.

A B CEG D F H

A A B B C C D D F F H H I I

B B C C D D F F H H I I

C C D D E E H H I I

D D E E F F I I

E E F F G G

F F G G H H

G G H H I I

H H I I

I I

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Table 1 showing activity tasks and their earliest start times and latest start times and float

times.

Activity Task Earliest Start Time Latest Start Time Float Time A 0 0 0

B 10 10 0 C 21 21 0

D 30 30 0 E 21 46 25

F 43 43 0 G 21 44 23

H 56 56 0

I 66 66 0

The Critical Path: Start A, B, C, D, F, H, I End

From the diagram it can be seen that the minimum time to assemble a computer to sell would be 77 minutes.

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Hungarian Algorithm

The Hungarian Algorithm is used to minimize costs of allocating resources. The steps for conducting a Hungarian algorithm is as follows:

1. Draw a cost matrix

2. Subtract the smallest number in each row from all the numbers in that row

3. Subtract the smallest number in each column from all the numbers in that column

4. Draw a horizontal or vertical lines to cover all the zeroes. If the minimum number of

such lines is equal to the number of columns then you have finished. The answer is given

by selecting one zero in each row and column. There may be more than one minimum

cost.

5. If there are less horizontal or vertical lines to cover all the zeroes than there are columns

then subtract the smallest uncovered number from all the uncovered numbers and add

it to where the lines cross. Start again from step 4.

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In this case, the Hungarian algorithm would be used to determine which of 5 stores would be

suitable to purchase each part/group of parts. To retrieve the parts there is one static proof

electronic-safe box that can only carry one part/ group and the work day and path only allows

for one trip to each store to get parts.

The table below shows the cost matrix.

PARTS STORE 1 STORE 2 STORE 3 STORE 4 STORE 5

Power Supply $228 $252 $200 $264 $295

Motherboard $600 $650 $725 $732 $700

Processor + Heat sink

$655 $622 $622 $600 $646

RAM + Hard drives

$783 $777 $783 $790 $722

Sata cables + Case + Fans + Screws

$200 $225 $200 $197 $272

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The minima from each row is subtracted from each row

PARTS STORE 1 STORE 2 STORE 3 STORE 4 STORE 5 Subtracting row minimum

Power Supply $28 $52 $0 $64 $95 (-200)

Motherboard $0 $50 $125 $132 $100 (-600) Processor + Heat sink

$55 $22 $22 $0 $46 (-600)

RAM + Hard drives

$61 $55 $61 $68 $0 (-722)


$3 $6 $3 $0 $75 (-197)

The minima from each column is subtracted from each column

PARTS STORE 1 STORE 2 STORE 3 STORE 4 STORE 5 Power Supply $28 $52 $0 $64 $95

Motherboard $0 $50 $125 $132 $100 Processor + Heat sink

$55 $0 $22 $0 $46

RAM + Hard drives

$61 $55 $61 $68 $0


$3 $6 $3 $0 $75

Subtracting column maximum

-0 (-22) -0 -0 -0

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Covering all zeros with minimum number of lines.


Power Supply $28 $52 $0 $64 $95 Motherboard $0 $50 $125 $132 $100


$55 $0 $22 $0 $46

RAM + Hard drives

$61 $55 $61 $68 $0


$3 $6 $3 $0 $75

The number of lines match number of columns therefore the zeros cover an

optimal assignment which correspond to the optimal assignment of the cost

matrix.

The optimal cost for parts would be $2341


Power Supply $228 $252 $200 $264 $295

Motherboard $600 $650 $725 $732 $700


$655 $622 $622 $600 $646

RAM + Hard drives

$783 $777 $783 $790 $722


$200 $225 $200 $197 $272

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Therefore the following allocation for parts would minimize cost

STORE 1: Motherboard

STORE 2: Processor + heat sink

STORE 3: Power supply

STORE 4: Sata cables +case + fans + screws

STORE 5: RAM + Hard drives

The minimum cost would be: $2341

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Discussion

In this research two tests were conducted to improve upon the time and cost efficiency of the

assembly of computers by Delta’s Electronics. The tests were a critical path analysis and a

Hungarian algorithm. The critical path analysis was used to determine the minimum time needed

for the completion of the assembly of the computer system in order to determine float times.

This is done so that individual tasks can be delayed without causing a delay to the project

completion. An activity network diagram was used to help conduct the critical path analysis .

The critical path for the assembly of the computer was found to be Start A, B, C, D, F, H, I End

Where each letter represents the specific task that is path of the critical path. Using this critical

path, from the activity network diagram was found that the minimum time to assemble a

computer to sell would be 77 minutes. Therefore efficiency of assembly can be improved upon

if the employees of Delta’s Electronics assemble the desktop computer within 77 minutes.

The second test that was conducted was the Hungarian algorithm. This was done to allocate

various parts necessary for the assembly of the computer to the different stores so that the

least amount of money is spent to buy each part. The cost matrix was tabulated and through

row and column elimination the following optimal assignment was found:

Therefore the following allocation for parts would minimize cost

STORE 1: Motherboard

STORE 2: Processor + heat sink

STORE 3: Power supply

STORE 4: Sata cables +case + fans + screws STORE 5: RAM + Hard drives

Therefore Delta’s Electronics would spend the least money by following the previous allocation

inn purchasing its parts from each store. The Hungarian algorithm also showing that the optimal cost for parts would be $2341.

From these results Delta’s Electronics can now assemble desktop computers in a time and cost

efficient way.

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Limitations

There were many limitations that may be considered in the research conducted. Firstly the various

stores where parts can be obtained are subject to price changes and may vary accordingly. Secondly, the

cost of transport and fuel to the different stores may be more that others because their location may be

closer or further than Delta’s Electronics. Thirdly, parts may be faulty and costs may vary unexpectedly

to account for this. Finally the real world events were not accounted for when taking the duration into consideration as these factors could affect duration and hence the critical path.

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Recommendations

The method used in conducting this research may have not been ideal and recommendations can be made

to improve this. More tests could be done to further maximize efficiency and account for human error.

The tasks in the critical path were simplified and a more detailed analysis could be done to achieve more

accurate results in time efficiency.

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Conclusion

In conclusion the critical path analysis conducted highlighted the crucial steps and the minimum

amount of time taken to assemble a desktop computer by Delta’s Electronics which means they

would be able to assemble computers more efficiently and save time. The Hungarian algorithm

in this research showed optical assignment for stores and parts to be purchased to minimize

costs. The Hungarian algorithm also showed the least amount of money necessary to assemble a

desktop computer. With this information, Delta’s Electronics would be able to save money in assembling the computers.

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Bibliography CPM- Critical Path Method. (n.d.). Retrieved from http://www.netmba.com/operations/project/cpm/

Critical Path Method (CPM). (n.d.). Retrieved from University of South Carolina: http://hspm.sph.sc.edu/Courses/J716/CPM/CPM.html

How to use Hungarian Algorithm. (n.d.). Retrieved from WikiHow: http://www.wikihow.com/Use-the-

Hungarian-Algorithm

Hungarian Algorithm . (n.d.). Retrieved from http://hungarianalgorithm.com/

applied mathematics unit 2sba

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