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Simulation Project in ARENA

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Simulation Project in ARENA

  1. 1. BANA 7030: Simulation Modeling and Method-Individual Project Report “On my honor, I have neither given nor received unauthorized aid in completing this academic work.” - Aditya Nakate (M10947951) A. Topic: Conducted a simulation study on ‘Canes’ restaurant near Calhoun street. This restaurant gets flooded with customers at night, especially on weekends and there are long queues outside the restaurant. Customers’waiting timeisquite highon thesetimings,alsosomecustomersleavethe queues withouttakingservice due tothe longwaitingtimes.Inthisstudy, Iwasplanningto see if addingaserver at the peak timings would help reduce customer waiting time significantly and therebyhelp restaurant serve more customers and make more profit. But after my conversation with the manager of the restaurant, I came to know that adding one more server justto reduce customers’ waiting time is not a beneficial option for the restaurant as they will need to pay the additional server. But after the close observation of the system,Irealized thatsome customersdecide theirorderafterarrivingatthe counter, mainly due to unavailability of menu (Though menu is available on the screen it is very inconvenient to read it from a distance).Also, those customers whocome in groupsdiscusstheirorder after reachingto an ordercounter, whichconsumesalot of time andothercustomershave to spendmore time waitingin queue. In this study, I have analyzed two scenarios: 1) ‘Original’scenario:Where some percentageof customersdecide theirordersafterarrivingatthe counter 2) ‘Whatif’ scenario: Where customers have already decided their orders I checked if there is a significant difference in the metrics like average waitingtime,average number of customers waiting in a queue etc. between these two scenarios. B. Model design and Data collection: In this restaurant, there isone serverfor takingorders fromthe customers,one serverfor deliveringthe food andfourserversworkinthe kitchen. Outof these fourservers,threeserversworkon the individual fooditems forthe combo,forexample,one serverwill workonpreparingfingers,one will work on preparingfriesetc. Andone serverwill justproduce a combofrom all the individual fooditems. Following data was collected on this system: 1. Interarrival time of the customers 2. Service Time at the order counter 3. Time required for food preparation and delivery 4. Number of customers who decide their order after arriving at the order counter B. Part (1). Interarrival time distribution: Data for interarrival times(inminutes) wascollectedforthree days(one houroneachday) between8:30 to 10:30 PMas this is the peak time for the restaurant.
  2. 2. Following is the data for the same: Day 1 Day 2 Day 3 0.47 2.11 4.16 2.61 0.37 2.35 0.03 4.70 0.38 5.17 2.89 0.11 0.01 1.12 0.87 1.41 1.08 2.77 3.53 0.23 0.33 0.23 4.29 0.92 1.26 0.24 1.78 0.48 0.22 3.26 2.50 0.01 1.35 0.16 0.04 1.81 1.90 0.64 6.52 0.61 1.64 0.66 5.35 1.08 5.97 0.94 0.82 1.39 4.98 1.37 0.07 1.30 1.69 0.09 4.78 0.65 4.21 0.47 0.70 1.56 1.92 2.33 0.11 1.55 0.03 1.37 1.88 4.99 1.81 2.02 0.12 0.65 0.54 2.11 0.24 1.47 0.56 1.47 1.29 0.19 2.40 1.00 0.39 0.98 0.08 0.14 0.73 3.18 0.40 0.65 2.01 1.07 1.22 0.31 0.74 0.23 8.93 1.04 4.71 0.43 Using Input Analyzer interarrival distribution was decided for the data: Fig. 1 Figure 1 shows the fit for the data. Let us check the statistics for different distributions. Squared errors after fitting different distributions:
  3. 3. Above table showsthatExponential andErlangdistributionshave the smallestsquarederror.Nowletus look at the p values for both: Erlang distribution: Exponential distribution: As we can see inabove tables,p-valuesforboththe distributionsandboththe testsisgreaterthan 0.05, whichmeansthatwe fail torejectthe null hypothesisandwe canuse one of the twodistributionsforour study. But as p-value for exponential distributionis greater than p-value for erlang distribution, we will choose exponential distribution: EXPO (1.62) B. Part (2). Service time distribution for Order placement counter: Data was collectedseparatelyforthe customerswhohadalreadydecidedtheirorders(before arrivingat the ordercounter) andcustomerswhodecidedtheirorderafterarrivingatthe counter.Forconvenience, this data was collected on separate days (i.e. not on the same days when interarrival time data was collected): B. Part (2a). Service Time data for customers who had already decided their order: Service Time (min) 1.38 1.20 1.25 1.23 1.47 1.29 1.30 1.45 1.48 1.19 1.00 1.33 1.18 1.35 1.41 1.11 1.42 1.42 1.18 1.21 1.43 1.64 1.32 1.51 0.91 1.16 1.04
  4. 4. 1.33 1.06 1.26 1.09 1.03 1.27 1.38 1.26 Using Input Analyzer, service time distribution was decided for the data: Fig. 2 Figure 2 shows the fit for the data. Let us check the statistics for different distributions. Squared errors after fitting different distributions: Above table showsthat Normal distributionhas the smallestsquarederror. But,Normal distributioncan’t be usedforservice time distributionas itdoescreate negative valuesalso. Now letus look atthe pvalues for Weibull and Beta distribution:
  5. 5. Weibull distribution: Beta distribution: As we can see inabove tables,p-valuesforboththe distributions are lesserthan0.05 for chi-square test, which means that we reject the null hypothesis and we cannot use boththe distributionsfor our study. Now, let us look at the p-values for triangular distribution: As we can see p-values for both the testsare greater than 0.05 in case of triangular distribution. So, we will use triangular distribution to approximate the service time for the customers who have already decided their order (before arriving at the counter): TRIA(0.8, 1.3, 1.7)
  6. 6. B. Part (2b). Service Time data for customers who had not decided their order before reaching to the order counter: Service Time (min) 1.61 2.34 2.35 2.06 2.39 2.56 1.85 1.77 2.09 2.15 2.14 2.48 2.23 2.20 2.19 1.93 2.26 2.42 1.68 1.97 2.02 Using Input Analyzer, service time distribution was decided for the data: Fig. 3 Figure 3 shows the fit for the data. Let us check the statistics for different distributions. Squared errors after fitting different distributions:
  7. 7. Above table shows that Triangular distribution has the smallest squared error. Now, let us look at the p-values for triangular distribution: As we can see p-values for both the testsare greater than 0.05 in case of triangular distribution. So, we will use triangular distribution to approximate the service time for the customers who had not already decided their order (before arriving at the counter): TRIA (1.5, 2.2, 2.7) B. Part (3). Percentage of customers who decide their order after arriving at the order counter: This percentage was estimated on two facts: 1. Afterspendingaroundoneandhalfhourscollectingthedataforservice time atthe ordercounter, I could collect this data for 35 customers who had already decided their order and for 21 customers who decided their order after arriving at the counter. So,% of people whodidnotdecide theirorderbefore comingto the counter: (21/35+21): 37.5% 2. After talking to the server at order counter and manager I got the estimate of around 25-30%. So, I decided to conduct the analysis with 30%. B. Part (4). Service time distribution for food preparation and serving counter: In thiscase, all the individual itemsinthe comboare alreadypreparedby the three serverswhoare just workingon individual fooditems.The fourthserverjust needsto prepare combo out of these individual items,soservice time inthiscase isquite low.Basedonfew readingstakenforthe same,we will assume that it follows uniform distribution: UNIF (0.5,1)
  8. 8. Based on the collected data and the distributions estimated, following model was built in ARENA: Fig. 4 1. Create Module: Customers arrive at the rate of: EXPO (1.62) 2. Decide Module:Customersare dividedinthe groupof 70-30% (randomly,aswe have estimated that 70% of customers already decide their order and 30% do not 3. Two AssignModules:These assignmodulesare for assigningdifferentservice time distributions to the customers A. Customers who have already decided their order will have lesser service times: TRIA (0.8, 1.3, 1.7) B. Customers who have not already decided their order will have higher service times: TRIA (1.5, 2.2, 2.7) 4. Two Process Modules:Two processmodulesare for order placementandfoodpreparationand delivery process. Service time for food preparation and delivery: UNIF (0.5,1) C. Model verification and Primary Analysis: C. Part (1). Model Verification: 1. Single entity was released in the system and checked if it is following the expected path 2. Output values like waiting time and total time were quite high when service time was increased and interarrival time was decreased significantly 3. 100 replications were run on the model and performance metrics like wait time, total time, average number in queue and average number in system made sense C. Part (2). Primary Analysis: Modelsfor both the scenarios were run for 3 hours (as 8-11PM are the peak hours for the restaurant), 100 replications and following stats were obtained:
  9. 9. Average Max Average Original Scenario What-if scenario Original Scenario What-if scenario Numberof customersserved 105 109 122 131 Total Time insystem 7.91(min) 3.95 (min) 18.8(min) 7.38(min) Average numberof customersin system 4.98 2.47 12.99 5.26 Average waittime inordercounter queue 5.67(min) 1.94(min) 16.51(min) 5.26(min) Average numberwaitinginorder counterqueue 3.64 1.25 11.51 3.81 Comparison of metrics in graphs: Original Scenario: Fig. 5 What-if scenario: Fig. 6
  10. 10. Total customers in system and total customers waiting in queue vs time: Original scenario: Fig. 7 What-if scenario: Fig. 8
  11. 11. Checking the precision values for 100 replications: Metric Original Scenario Whatif scenario Outputperformance metric: Number seen Average length of stay Number seen Average length of stay Initial numberof replicatins(N0) 100 100 100 100 Initial mean 106.7 7.9114 108.65 3.95 Initial 95% half width(h0) 4.66 0.74 2.1 0.19 Initial relative precision 0.0437 0.0935 0.0193 0.0481 Intial %relative precision 4.3674 9.3536 1.9328 4.8101 Desiredrelativeprecision 0.09 0.09 0.09 0.09 Desiredhalf width(h) 9.603 0.7120 9.7785 0.3555 Approximate total nrequired 24 109 5 29 Approximate additional replications required -76 9 -95 -71 As we can see from above table, our output values are quite precise with 100 replications. From the above analysis, we see that performance metrics of what-if scenario are comparatively better than the original scenario. Now, let’s check these differences statistically and see if the difference is significant. D. Statistical Analysis: Statistical analysiswasconductedinARENA outputanalyzerand ARENA processanalyzerto check if the difference is significant. Twenty replications of each scenario were run to collect the data. 1. Analysis using ARENA output analyzer: Usingthe outputfromtwentyreplicationsof eachscenariotwosamplet-testwith95% confidenceinterval was run on the samples using output analyzer to check if the difference is significant:
  12. 12. As we can see from above output,the difference in all the metrics are significant withalpha value=0.05 level. This proves that alternate scenario is better than the original one. 2. Analysis using ARENA process analyzer:
  13. 13. Fig. 9 Fig. 10 Fig. 11
  14. 14. Fig. 12 Fig. 13 Above figuresalsogive the same conclusion, that the difference between all the metrics is significant.
  15. 15. E. Conclusion: From the ARENA process and output analyzer, we can conclude that in alternate scenario average wait time, average number of customers in queue, total time in system and average number of customers in system(WIP) has decreased compared to the original scenario and the number of customers served has increased and these differences are statistically significant. So, our alternate system is better than the original system and is more beneficial for both customers and restaurant. F. Recommendation: As we saw, in alternate scenario customer waiting time, total time in system has decreased significantly. Also, the average number of customers in system and in the queue at the time has alsocome down. If, restaurant can implement the alternate scenarioit will result in better customer experience and more profit for the restaurant. It is not difficult to implement this scenario, as it can be done in following ways: 1. Restaurant can put menu boards just besides the queue, so that customers don’t have any difficulty in reading it and can decide their menu while standing in a queue. 2. Also, it would be great if restaurant can keep that board updated in the current time per the availabilityof the food item, so that customers don’t have to rethink about their order while at the order counter These options are not very costly and will be very beneficial to customers as well as restaurant.

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