Applied Mathematics Unit 2SBA
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The document describes research to optimize the time and cost efficiency of assembling desktop computers for Delta's Electronics. A critical path analysis determined the minimum time to assemble a computer is 77 minutes. A Hungarian algorithm was used to allocate parts purchases across 5 stores to minimize total costs, determining the optimal allocation that results in a total cost of $2341. The analysis provides Delta's Electronics with ways to improve the assembly process time and reduce costs.
Applied Mathematics Unit 2SBA
- 1. TIME AND COST EFFICIENCY OF COMPUTER ASSEMBLY BUSINESS AppliedMathematics Josh De Freitas Upper Six II SchoolBased Assessment HillviewCollege
- 2. 1 | P a g e Contents Introduction...................................................................................................................................2 Method of Data Collection ..............................................................................................................3 Critical Path Analysis.......................................................................................................................4 Hungarian Algorithm.......................................................................................................................8 Discussion ....................................................................................................................................13 Limitations ...................................................................................................................................14 Recommendations........................................................................................................................15 Conclusion....................................................................................................................................16
- 3. 2 | P a g e Introduction Delta’s Electronics is a popular computer store in the community. They specializein 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 assemblyof 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 assemblea 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.
- 4. 3 | P a g e 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.
- 5. 4 | P a g e 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 Activityduration Precededby EarliestStartTime (EST) LatestStart Time (LST) Each processof the computerassemblyisrepresentedbyaletterandits respective durationtime in minutesinthe table below. Description of Activity Task Preceded by Duration (minutes) Install Powersupplyoncase A - 10 Install motherboard B A 11 Place processoronboard C B 9 Attach heatsink D B, C 13 Install R.A.M.chips E B 10 Install harddrive F D, E 13 Install graphicscard G B 12 Connectsata cablestopowersupply H F, G, E 10 Assemble case withfansandscrews I H 11
- 6. 5 | P a g e 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
- 7. 6 | P a g e
- 8. 7 | P a g e Table 1 showing activity tasks and their earliest start times and latest start times and float times. Activity Task Earliest Start Time Latest StartTime 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.
- 9. 8 | P a g e 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.
- 10. 9 | P a g e 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 PowerSupply $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
- 11. 10 | P a g e The minima fromeach row is subtracted fromeach row PARTS STORE 1 STORE 2 STORE 3 STORE 4 STORE 5 Subtracting row minimum PowerSupply $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) Sata cables+ Case + Fans+ Screws $3 $6 $3 $0 $75 (-197) The minima fromeach column is subtracted fromeach column PARTS STORE 1 STORE 2 STORE 3 STORE 4 STORE 5 PowerSupply $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 Sata cables+ Case + Fans+ Screws $3 $6 $3 $0 $75 Subtracting column maximum -0 (-22) -0 -0 -0
- 12. 11 | P a g e Covering all zeros with minimum number of lines. PARTS STORE 1 STORE 2 STORE 3 STORE 4 STORE 5 PowerSupply $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 Sata cables+ Case + Fans+ Screws $3 $6 $3 $0 $75 The number of lines match number of columns therefore the zeros cover an optimal assignmentwhich correspond to the optimal assignmentof the cost matrix. The optimal cost for parts would be $2341 PARTS STORE 1 STORE 2 STORE 3 STORE 4 STORE 5 PowerSupply $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
- 13. 12 | P a g e 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 costwould be: $2341
- 14. 13 | P a g e 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 criticalpath 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.
- 15. 14 | P a g e Limitations There were manylimitationsthatmaybe consideredinthe researchconducted.Firstlythe various storeswhere partscan be obtainedare subjecttoprice changes andmay vary accordingly.Secondly,the cost of transport and fuel tothe differentstoresmaybe more that othersbecause theirlocationmaybe closeror furtherthanDelta’sElectronics.Thirdly,partsmaybe faultyandcostsmay vary unexpectedly to account forthis.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.
- 16. 15 | P a g e Recommendations The methodusedinconductingthisresearchmayhavenot beenidealandrecommendationscanbe made to improve this. More tests could be done to further maximize efficiency and account for human error. The tasksinthe critical pathwere simplifiedanda more detailedanalysiscouldbe done toachieve more accurate results in time efficiency.
- 17. 16 | P a g e 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.
- 18. 17 | P a g e Bibliography CPM- Critical PathMethod.(n.d.).Retrievedfromhttp://www.netmba.com/operations/project/cpm/ Critical PathMethod (CPM).(n.d.).RetrievedfromUniversityof SouthCarolina: http://hspm.sph.sc.edu/Courses/J716/CPM/CPM.html Howto use Hungarian Algorithm.(n.d.).RetrievedfromWikiHow:http://www.wikihow.com/Use-the- Hungarian-Algorithm Hungarian Algorithm .(n.d.).Retrievedfromhttp://hungarianalgorithm.com/