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Simulation Modeling for Subway using Arena Simulation Software

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- 1. By: Jasmine Sachdeva M No.:M10669285 Simulation Project in Arena Optimization of Subway Outlet at UC Campus Contents Objective .......................................................................................................................................2 Current Process..............................................................................................................................2 Problem and Counter Proposal.......................................................................................................2 Data Collection...............................................................................................................................2 Fitting Data....................................................................................................................................3 Model Assumptions........................................................................................................................5 Model............................................................................................................................................5 Model Results................................................................................................................................6 Model 2.........................................................................................................................................8 Output Analyzer.............................................................................................................................9 Process Analyzer..........................................................................................................................10 Conclusion:..................................................................................................................................11
- 2. By: Jasmine Sachdeva M No.:M10669285 Objective To improve the effectiveness,productivityandsalesof Subway byminimizingwaitingtime and maximizingthe speedof service. Thiscan be done byunderstandinghow the customerwaittimesvariesindifferentstagesfrom the time theyenterthe queue till the time theyreceivetheirorder. Current Process CustomersenterSubway,waitinthe queue orgoto the firststage where theyselectthe size and type of bread,meat,and cheese.Thendependingif the customerchose tobake or notbake theirbread,the customergoesthroughthe secondstage whichisthe oven. The customerthen movestothe next stage toadd veggies,meatandcondiments.Once the sandwichismade, the customermovestothe billingcounter afterchoosingadditionalchipsand/or drinks.Afterthis, the customermay or may notgo to the soda machine toget theirdrinks. Each stage hastwo resources exceptatthe billingcounter. Problem andCounter Proposal Duringlunchhours i.e.fromabout10:00 AMto 2:00PM, there’sa longerqueue atthe order counteras well asthe billingcounterwhichleadsto unsatisfiedcustomersand a chance of people decidingnottogo eatat a Subwaybecause of the longwaitingtime. Staffingthe rightnumberof employeesatthe righttime andhavingthe rightpersoninthe right place couldsolve the problem. The restaurantcan have an additional resource atthe ordercounterorbilling counter,whichcan make a significant difference in terms of waiting times and consequently customer satisfaction levels. Data Collection PermissionhadbeentakenfromSubwaytocollectthe data observe interarrival andprocessingtime.The time intervals were manually recorded for the following processes to get a rough estimate of entire system Inter-arrival time of customers coming on a day Processtime forchoosingbreadandcheese
- 3. By: Jasmine Sachdeva M No.:M10669285 Processtime forchoosingvegetablesandsauces Processtime forbilling Fitting Data Arena’sInputAnalyzer tool wasusedto fitthe probabilitydistributiontothe data. a. CustomerInter-arrival times Followingisthe schedule of customersgenerallyobservedinaday. 10 AMto 2 PMand 7 PMto 9 PMhave beenobservedasthe peakrushhours. 9 - 10 AM 10-11 AM 11AM- 12 PM 12 - 1 PM 1- 2 PM 2 - 3 PM 3 - 4 PM 4 - 5 PM 5 - 6 PM 6 - 7 PM 7 - 8 PM 8 - 9 PM 9 - 10 PM 22 42 47 48 50 9 19 11 27 9 47 36 10 b. Processtime for Choosingbread and cheese Distribution Summary Distribution: Beta Expression: 0.33 * BETA(1.41, 1.64) Square Error: 0.004607 Chi Square Test Number of intervals = 16 Degrees of freedom = 13 Test Statistic = 17.4 Correspondingp-value = 0.196 Kolmogorov-SmirnovTest Test Statistic = 0.0481 Correspondingp-value > 0.15 Data Summary Number of Data Points = 350 Min Data Value = 0.5 Max Data Value = 1.2 Sample Mean = 0.829 Sample StdDev = 0.208 Histogram Summary HistogramRange = 0.43 to 1.27 Number of Intervals = 18
- 4. By: Jasmine Sachdeva M No.:M10669285 c. Toast It was observed that the toasting time for bread is uniform between 0.33 mins (20 secs) to 0.66 minutes (40 secs), depending on the type of bread and the meat chosen. UNIF (0.33, 0.66) d. Processtime for Choosingvegetables,saucesand condiments DistributionSummary Distribution:Gamma Expression: 0.11 + GAMM(.45, 4.23) Square Error:0.015364 Chi Square Test Number of intervals = 17 Degrees of freedom = 14 Test Statistic = 391 Correspondingp-value=0.496 Kolmogorov-Smirnov Test Test Statistic = 0.113 Correspondingp-value>0.01
- 5. By: Jasmine Sachdeva M No.:M10669285 Model Assumptions • The two resourceswhotake the orderandprepare the sandwich are equallyefficient andhave the same service time. • The time takento use the soda machine has not beenaddedin the model,since it doesn’taddto the queue time. The model has been simulated only till the billing counter. Model My arena model has 7 modules as given below: 1. Arrival Module:The customerarrivesatthe restaurantandjoinsxxaqueueatone of the counters based on the length of the queue 2. Seize ‘Sub Resource’: The customer goes to one of the resource who is idle and orders his sub. The same resource prepares the sub for a particular customer. 3. Delay Moduleto choosebread, meat and cheese: The customerchoose the type of bread,meat and the cheese and the Resource prepares the sub before toasting it. 4. DecisionModule forToast/NoToast decision: The customercan chooseto toastor not toasthis bread in oven. 5. Delay Module for Toasting bread in Oven: Bread is toasted in the oven. It takes 20 to 40 secs, depending on the type of bread, cheese and meat chosen 6. Delay Module to prepare the sub: The resource prepares the sub by adding vegetables, condiments and sauces. 7. Release ‘Sub Resource’: Once the sub is prepared, the resource is released to be seized by the next customer (or from the queue, if any). 8. Process Modulefor BillingCounter:Whenthe subis ready,customersfrombothcountersmove to a single billing counter. Once the customerfinalizesthe order,he/she canchoose to get a glass of soda/waterif it’spart of the order. If the customer decides to get a glass soda/water along with his order, he goes to the soda machine and gets his glass filled. (This part is not included in the model)
- 6. By: Jasmine Sachdeva M No.:M10669285 Following is the outlay of the Arena model. Model Results The model wasinitiallyrunfor50 replicationsandthe numberof replicationsrequiredforaprecisionof 9% was calculated. The model wasfinallyrunfor52 replicationsand the resultsobtainedare asshownbelow. A.
- 7. By: Jasmine Sachdeva M No.:M10669285 B. C. D. The waitingtime of customersinthe queue are 5.07 minsfor the billingqueue and2.58 for the Order queue. Due to extreme rushinpeakhours, eventhe average total time insystemis 11 minuteswhichis quite high.Therefore,itis proposed toincrease the resources.Thisisimplementedinthe secondmodel.
- 8. By: Jasmine Sachdeva M No.:M10669285 Model 2 In thismodel,The SubResource andBillingResourcehasbeenincreasedbyone unit. Thismodel isrun fora 52 replicationsandthe resultsare as givenbelow. A. B. C. D. To check the authenticityof these results,itisimportanttoanalyze themstatistically.Thiscanbe done by usingthe OUTPUT ANALYSERand PROCESS ANALYZER.
- 9. By: Jasmine Sachdeva M No.:M10669285 Output Analyzer The Statisticsto be checkedare: Total Time spentby the Customer inthe System, Average WaitTime in the BillingQueue and Average Wait Time in the Order Queue. All of these are outputstatisticsi.e.theirresultsgetstoredin.DATfilesspecifiedbyus.The Output Analyzercanbe employedtoperformT-Testsonthe samplestodetermine the hypothesis: H0: the meansof the two samplesof the statistic are same Ha: the meansof the two samplesof the statistic are not the same. We can use the filesfromboththe modelstocompare the Means of these Statistics. We rejectHo forall the three Responses,as we can’tsay that there isa statisticallysignificantdifference inthe means.
- 10. By: Jasmine Sachdeva M No.:M10669285 ProcessAnalyzer Followingare the resultsobtainedfromthe ProcessAnalyzer:
- 11. By: Jasmine Sachdeva M No.:M10669285 From thischart and the resultof the PAN we can say that, increasingbothresourcesbyone unitwould be a betterapproach. Conclusion: Aftergoingthroughall the results,chartsand graphswe can clearlysee that reducingbothresourcesby a unitwouldgreatlydecrease the waittime of customers,thereby decreasingthe total time of customers insystem. Therefore,we cansaythat, using the Secondmodel,i.e.byhiringanadditionalemployee we can improve the customerexperience bydecreasingthe waittime andhence furtherimprove the reputation of subway. So the final conclusioncomesouttobe that Model 2 isa validandbetterapproach. Hence two new employeescanbe hiredby the restaurant. References: 1. SimulationwithArena 2. Data collectedfromSubway,UC

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