MISSISSIPPI RIVER BARGE ARRIVALS AND UNLOADINGS A Queuing Simulation Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD Port of New Orleans

Two Courses of Action Considered COA Number 1 COA Number 2 DOCK CREW OF 6 DOCK CREW OF 12 DOCK CREW OF 6 DOCK CREW OF 12 COURSE OF ACTION NUMBER ONE COURSE OF ACTION NUMBER TWO

Two Relevant Variables Daily Evening Barge Arrivals Unloadings VARIABLENUMBERONEVARIABLENUMBERTWO Port of New Orleans

Evaluation Criteria 1.Average Number of Barges Unloaded Each evening. 2.Average Number of Barges Delayed Each evening.

Simulation Execution Simulate a daily barge arrival.  Simulate a daily barge arrival.

Simulation Execution Simulate a daily barge arrival.  Simulate a daily barge arrival.  Simulate a daily barge unloading.

Simulation Execution Simulate a daily barge arrival.  Simulate a daily barge arrival.  Simulate a daily barge unloading.  Determine how many, if any, barges remain unloaded at the end of the evening. remain unloaded at the end of the evening.

Simulation Execution Simulate a daily barge arrival.  Simulate a daily barge arrival.  Simulate a daily barge unloading.  Determine how many, if any, barges remain unloaded at the end of the evening. remain unloaded at the end of the evening.  Unloaded barges become the beginning balance for the following evening. balance for the following evening.

Overnight Barge Arrivals SPREADSHEET NUMBER OF ARRIVALS PROBABILITYCUMULATIVE PROBABILITY RANDOM NUMBER INTERVAL

Crew of 6 Unloading Rates SPREADSHEET DAILY UNLOADING RATE PROBABILITY CUMULATIVE PROBABILITY RANDOM NUMBER INTERVAL

Random Number Strings TO GENERATE DAILY ARRIVALS

Random Number Strings TO GENERATE DAILY ARRIVALS TO GENERATE DAILY UNLOADINGS

Random Number Strings Day 1 st 2 nd 3 rd Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 4 th 5 th 6 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 4 th 5 th 6 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 4 th 5 th 6 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 7 th 8 th 9 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 7 th 8 th 9 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 7 th 8 th 9 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 10 th 11 th 12 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 10 th 11 th 12 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 10 th 11 th 12 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 13 th 14 th 15 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 13 th 14 th 15 th Random Number for Daily Arrival Random Number for Daily Unloading

Random Number Strings Day 13 th 14 th 15 th Random Number for Daily Arrival Random Number for Daily Unloading

Simulation Execution EVENING NUMBERDELAYEDPREVIOUSEVENING ARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED 1 st - a - a nd b 0 b 3 rd a – a – WE CAN BEGIN WITH NO DELAYS OR SOME DELAYS FROM THE PREVIOUS EVENING. OVER THE LENGTH OF THE SIMULATION, THE INITIAL BALANCE AVERAGES OUT. b - b - THREE BARGES COULD HAVE BEEN UNLOADED BUT SINCE THERE WERE NO ARRIVALS AND NO BACKLOG, ZERO UNLOADINGS RESULTED. c- THE PROGRAM WOULD HAVE UNLOADED ANY NUMBER OF BARGES UP TO, AND INCLUDING THREE (3), HAD THERE BEEN A POSITIVE BALANCE FOR TOTAL TO BE UNLOADED !,c

Simulation Execution EVENING NUMBERDELAYEDPREVIOUSEVENING ARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADED UNLOADINGRANDOMNUMBER NUMBERUNLOADED 4 th th th

Simulation Execution EVENING NUMBERDELAYEDPREVIOUSEVENING ARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED 7 th th th c,d C – THREE BARGES COULD HAVE BEEN UNLOADED BUT SINCE THERE WERE NO ARRIVALS AND NO BACKLOGS, ZERO UNLOADINGS RESULTED. D - THE PROGRAM WOULD HAVE UNLOADED UP TO, AND INCLUDING THREE (3) BARGES, HAD THERE BEEN A POSITIVE BALANCE FOR UNLOADINGS !

Simulation Execution EVENING NUMBERDELAYEDPREVIOUSEVENING ARRIVAL RANDOM NUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED 13 th th d 3d 3d 3d 15 th d – FOUR BARGES COULD HAVE BEEN UNLOADED BUT SINCE ONLY THREE WERE IN THE QUEUE, THE NUMBER UNLOADED IS RECORDED AS “3”.

Simulation Summary EVENING NUMBERDELAYEDPREVIOUSEVENING ARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED 13 th th th TOTAL DELAYS = 20 AVERAGE = 1.33 TOTAL ARRIVALS = 41 AVERAGE = 2.73 TOTAL UNLOADINGS = 39 AVERAGE = 2.60

Overnight Barge Arrivals SPREADSHEET FOR CREW OF 12 NUMBER OF ARRIVALS PROBABILITYCUMULATIVE PROBABILITY RANDOM NUMBER INTERVAL

Crew of 12 Unloading Rates SPREADSHEET DAILY UNLOADING RATE PROBABILITY CUMULATIVE PROBABILITY RANDOM NUMBER INTERVAL

Random Number Strings CREW OF 12 SIMULATION TO GENERATE DAILY ARRIVALS

Random Number Strings CREW OF 12 SIMULATION TO GENERATE DAILY ARRIVALS TO GENERATE DAILY UNLOADINGS

Simulation Execution CREW OF TWELVE 1 st nd rd th EVENING DELAYEDPREVIOUSEVENINGARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED

Simulation Execution CREW OF TWELVE 5 th th th th EVENING DELAYEDPREVIOUSEVENINGARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED

Simulation Execution CREW OF TWELVE 12 th th th th EVENING DELAYEDPREVIOUSEVENINGARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED TOTAL DELAYS = 6 AVERAGE = 0.4 TOTAL ARRIVALS = 31 AVERAGE = 2.07 TOTAL UNLOADINGS = 31 AVERAGE = 2.07

ScoreboardBarges Crew of 6 Crew of 12 AVERAGE DAILY DELAYS AVERAGE DAILY UNLOADINGS ARRIVALS

Possible Relevant Variables  Winds  Currents  Fog  Temperature  River Ice  Seasonal Barge Traffic  Competing Docks  Precipitation  Absentee Rates  Barge Sizes  Additional Crew Staffing Options  Local Economy Effect on Barge Traffic on Barge Traffic  Crew Training BARGE SIMULATION

Repeating Random Number Strings Used for generating arrival and unloading rates for both crew staffing options if you want to isolate and observe the impact of each staffing option on the dock-river system. ANY DIFFERENCES FOUND IN THE UNLOADING RATES WOULD BE DIRECTLY ATTRIBUTABLE TO THE CREW SIZE ITSELF, SINCE ALL OTHER ELEMENTS OF THE SIMULATION HAD BEEN HELD CONSTANT!

Non-Repeating Random Number Strings Used for generating arrival and unloading rates for both crew staffing options if you want to test for consistent results of the impact of each staffing option on the dock-river system. TO YIELD VALID CONCLUSIONS HOWEVER, YOU MUST INSURE THAT THE SIMULATION HAS RUN OVER A SUFFICIENTLY LONG PERIOD OF TIME IN ORDER TO ALLOW THE NUMBERS TO “SETTLE DOWN” TO THEIR LONG-TERM AVERAGES.

Barge Simulation Postscript  If the data were also analyzed in terms of barge delay opportunity costs, extra crew hiring costs, idle time costs, insurance, and barge traffic po- tential, a better quality staffing decision might have been attained.  The simulation should also have been executed under other crew size options. THIS DATE IS AVAILABLE FROM HUMAN RESOURCES, MARKETING, ACCOUNTING, AND FINANCE.

QM for WINDOWS COMMENTS   This program cannot simultaneously accommodate two or more relevant variables.  Every simulation is custom-built, and therefore presents too many design options for assimilation into a general-purpose software program.  An alternative would be to run each relevant varia- ble separately, insert the simulated outcomes on a spreadsheet, and then manually calculate the out- comes of the variables’ interactions. THIS APPROACH IS FEASIBLE FOR ONLY THE MOST ELEMENTAL SIMULATIONS

Example EVENING NUMBERDELAYEDPREVIOUSEVENING ARRIVALRANDOMNUMBERBARGEARRIVALNUMBERTOTAL TO BE UNLOADEDUNLOADINGRANDOMNUMBER NUMBERUNLOADED 1 st nd rd SIMULATED VIA QM for WINDOWS or QM EXCEL SIMULATED VIA QM for WINDOWS or QM EXCEL NOT REQUIRED NOT REQUIRED MANUALLYENTERED

These simulated barge arrivals would be inserted on our manual spreadsheet

These simulated barge unloadings would be inserted on our manual spreadsheet

Average Daily Delays ( 20/15 days ) = 1.33 Barges Average Daily Arrivals ( 41/15 days ) = 2.73 Barges Average Daily Unloadings ( 39 / 15 days ) = 2.60 Barges

Template and Sample Data

Template And Sample Data

Template and Sample Data

Template and Sample Data

Inventory Policy Simulation Establishing an inventory control doctrine for an item having variable daily demand and variable reorder lead time. The goal is to minimize the ordering, holding, and stockout costs involved. a more realistic business application

Electric Drill Demand Daily Demand Frequency ( days ) ProbabilityCumulative Probability Random No. Interval ∑= 300 ∑= st relevant variable

Electric Drill Reorder Lead Time LEAD TIME ( DAYS ) Frequency ( ORDERS )Probability Cumulative Probability RN Interval ∑ = 50 ∑ = nd relevant variable

The Simulation The 1 st inventory policy to be simulated: Q = 10 units R = 5 units Regardless of the simulated lead time period, an order will not arrive the next morning but at the beginning of the following working day Order 10 drills at a time when the shelf stock falls to five drills or less at the end of the business day

NO NO YES NO NO-- DAY UNITS RECEIVED BEGINNING INVENTORYRANDOMNUMBER DEMAND ENDINGINVENTORYLOSTSALES ORDER?RANDOM NUMBER LEAD TIME a – 1 st order is placed b – generates 1 st lead time c – next random number in series d – no order placed because of outstanding order from previous day a bc d The Simulation

YES NO NO NO YES141 DAY UNITSRECEIVEDBEGINNINGINVENTORYRANDOMNUMBER DEMAND ENDINGINVENTORYLOSTSALES ORDER ? RANDOM NUMBER LEAD TIME f – order placed at end of 6 th day arrives f The Simulation ∑ = units ending inventory number of lost sales number of orders placed SUMMARY STATISTICS

Simulation Results AVERAGE ENDING INVENTORY 41 units / 10 days = 4.1 units per day AVERAGE LOST SALES 2 sales lost / 10 days =.2 unit per day AVERAGE NUMBER OF ORDERS PLACED 3 orders / 10 days =.3 order per day

Simulation Costs Daily Order Cost $10.00 per order x.3 daily orders = $3.00 Daily Holding Cost $.03 per unit per day x 4.1 units per day = $.12 Daily Stockout Cost $8.00 per lost sale x.2 daily lost sales = $1.60 Total Daily Cost = $4.72 ( TOTAL ANNUAL COSTS = $ )

Simulation Postscript  We must now compare this potential inventory control doctrine to others.  Perhaps we might evaluate every pair of values for Q ( 6 to 20 units ) and R ( 3 to 10 units ) : After simulating all reasonable combinations of Q and R, we select the pair yielding the lowest total inventory cost

Fast Food Drive-Through Simulation ARRIVAL RN for TIME between ARRIVALS TIME BETWEEN ARRIVALS TIME RN for SERVICE TIME SERVICE TIME WaitingTime CUSTOMER LEAVES 1 st 14 1 min. 11: min. 011:04 2 nd 74 3 min. 11: min. 011:06 3 rd 27 2 min. 11: :08 4 th 03 1 min. 11: :09 ( ASSUME THE DRIVE-THROUGH OPENS AT 11:00 AM )

Generator Breakdown Simulation

Generator Breakdown Simulation TIME BETWEEN RECORDED MACHINE FAILURES (hours) PROBABILITYCUMULATIVEPROBABILITYRANDOM NUMBER INTERVAL ½ ½ ½ ∑1.00

Generator Breakdown Simulation REPAIR TIME REQUIRED ( HOURS ) PROBABILITYCUMULATIVEPROBABILITYRANDOMNUMBERINTERVAL Total1.00 a – MAINTENANCE TIME IS ROUNDED TO HOURLY TIME BLOCKS a

: : : : : : : : : : : :00 3 BREAKDOWNNUMBER TIME BETWEEN BREAKDOWNS RANDOM NO. TIMEBETWEENBREAKDOWNS TIME OF BREAKDOWN TIMEMECHANIC FREE TO BEGIN THIS REPAIR REPAIR TIME RANDOM NO. REPAIR TIME REQUIRED TIME REPAIR ENDS NO. HRS. MACHINEDOWN

:0004: : :0006: : :3008: : BREAKDOWNNUMBER TIME BETWEEN BREAKDOWNS RANDOM NO. TIMEBETWEENBREAKDOWNS TIME OF BREAKDOWN TIMEMECHANIC FREE TO BEGIN THIS REPAIR REPAIR TIME RANDOM NO. REPAIR TIME REQUIRED TIME REPAIR ENDS TOTAL NO. HRS. MACHINESDOWN 44 Generator Breakdown Simulation

Simulation Results Simulation of fifteen (15) generator breakdowns spanned 34 hours of operation. The clock began at 00:00 hours of day 1 and ran until the final repair at 10:00 hours of day 2. THE TOTAL NUMBER OF HOURS THAT GENERATORS WERE OUT OF SERVICE IS COMPUTED TO BE 44 HOURS

Simulation Costs Service Maintenance Cost 34 hours x $30.00 per hour = $1, Simulated Machine Breakdown Cost 44 hours x $75.00 lost per down hour = $3, Total Simulated Maintenance Cost $4,320.00

Simulation Applications Applied Management Science for Decision Making, 1e © 2011 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD

Solved Problems Simulation Modeling Computer-Based Manual Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD

Simulation Modeling Lundberg’s Car Wash The number of cars arriving per hour at Lundberg’s Car Wash during the past 200 hours of operation is observed to be as follows: CarsArrivingFrequencyCarsArrivingFrequency=< =>90 650∑200

Simulation Modeling Lundberg’s Car Wash REQUIREMENT: 1.Set up a probability and cumulative probability distribution for the variable of car arrivals. 2.Establish random number intervals for the above variable. 3.Simulate fifteen (15) hours of car arrivals and compute the average number of arrivals per hour. 4. Compute the expected number of cars arriving using the expected value formula. Compare this with the results ob- tained in the simulation. Note: Select the random numbers needed from the 1 st column of Table 15.5, beginning with the digits “52”.

Simulation Modeling Lundberg’s Car Wash Number of Cars ProbabilityCumulativeProbability Random Number Interval 3 or less or more

Simulation Modeling Lundberg’s Car Wash HourRN Simulated Arrivals HourRNSimulatedArrivals ∑= /15 = 7.00 cars Average hourly arrivals

Simulation Modeling Lundberg’s Car Wash (.10 x 4) + (.15 x 5) + (.25 x 6) + (.30 x 7) + (.20 x 8) = 6.35 Expected Value Arrival Events Probabilities The average number of arrivals in the simulation was “ 7.00 “. If enough simulations were performed, the average number computed would approach the expected value.

Simulation Modeling Time Between Arrivals (minutes ) Probability Local Bank A local bank A local bank collected one month’s arrival and service rates at its single-teller at its single-tellerdrive-through station. These data are shown here:ServiceTime(minutes)Probability

Simulation Modeling Local Bank REQUIREMENT : 1.Simulate a one-hour time period from 1:00 P.M. to 2:00 P.M. for the single-teller drive-through station. FOR THE TIME BETWEEN CUSTOMER ARRIVALS, USE THE RN STRING: 52,37,82,69,98,96,33,50,88,90,50,27,45,81,66,74,30,59,67 FOR THE CUSTOMER SERVICE TIME, USE THE RN STRING: 60,60,80,53,69,37,06,63,57,02,94,52,69,33,32,30,48,88

Simulation Modeling Local Bank Time Between Arrivals Probability Random Number Interval

Simulation Modeling Local Bank Service Time Probability Random Number Interval

Simulation Modeling Local Bank RANDOM NUMBER TIME BETWEEN ARRIVALS ACTUAL TIME TIME SERVICE BEGINS RANDOM NUMBER SERVICE TIME SERVICECOMPLETE WAIT TIME (MINUTES) 5231:031:036031: :051:066031: :091:098051: :121:145331: :171:176941:210

Simulation Modeling Local Bank RANDOM NUMBER TIME BETWEEN ARRIVALS ACTUAL TIME TIME SERVICE BEGINS RANDOM NUMBER SERVICE TIME SERVICECOMPLETE WAIT TIME (MINUTES) 9651:221:223731: :241:250611: :271:276341: :311:315731: :351:350211:360

Simulation Modeling Local Bank RANDOM NUMBER TIME BETWEEN ARRIVALS ACTUAL TIME TIME SERVICE BEGINS RANDOM NUMBER SERVICE TIME SERVICECOMPLETE WAIT TIME (MINUTES) 5031:381:389461: :401:445231: :421:476941: :461:513331: :491:543231:575

Simulation Modeling Local Bank RANDOM NUMBER TIME BETWEEN ARRIVALS ACTUAL TIME TIME SERVICE BEGINS RANDOM NUMBER SERVICE TIME SERVICECOMPLETE WAIT TIME (MINUTES) 7431:521:573032: :542:004832: :572:038852: : TOTAL40

Simulation Modeling Local Bank Cost of Customer Waiting 40 minutes per hour X 7 hours per day X 200 days per year X $1.00 per minute = $56,000.00

Simulation Modeling Local Bank Total Costs Drive-Through Depreciation per year - $12, Salary and Benefits for one teller per year - $16, Customer Waiting Cost per year - $56, = $84,

Simulation Modeling Local Bank Total Costs for Two Drive-Throughs Drive-Through Depreciation per year - $20, Salary and Benefits for two tellers per year - $32, Customer Waiting Cost per year - $1, = $53,

Simulation Modeling Local Bank Cost Savings With Two Tellers $84, ( 1 drive-through ) - $53, ( 2 drive-throughs ) $30, The conclusion is to place two teller booths in use. It is critical to replicate this simulation for a much longer time period before drawing any firm conclusions, however.

Solved Problems Simulation Modeling Computer-Based Manual Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD