Archives: Solution Manual

Data Table Calculations set to Manual. Press F9 to recalculate. 25 Dry 276 276 $270.00 25 $7,711.25 26 Dry 315 300 $300.00 26 $7,395.00 27 Dry 284 284 $280.00 27 $7,726.25 28 Dry 292 292 $290.00 28 $7,688.75 29 Dry 326 300 $300.00 29 $7,567.50 30 Dry 289 289 $286.25 30 $7,220.00 31 $7,446.25 32 $7,811.25 33 $7,430.00 34 $7,707.50 35

Data Table Calculations set to Manual. Press F9 to recalculate. 25 Minor $74 27 $23,841 26 Minor $106 28 $15,863 27 Minor $102 29 $16,369 28 Minor $115 30 $15,241 29 Minor $110 31 $19,963 30 Minor $137 32 $20,454 Number of projects: 40 to 55 No. of jobs: 48 Run Profit Probability of minor 0.65 1 $15,955 Minor

P10-33 Data Table Calculations set to Manual. Press F9 to recalculate. Month Begin Inv Units Rec Avail Inv Demand Demand Filled End Inv Stock out End Inv + Order Place order? Lead time Arrive on day Inv cost Stockout cost Order cost Value Proba- bility RN intvl LL Run Avg stockout Cost per month 35 4.04 $31,371 36 3.08 $24,417 37 4.13 $32,004 38 3.54 $27,704 39 4.58 $35,192 40 3.88 $30,204 41 2.83 $22,600 42 4.13 $31,921 43 4.33 $33,375 44 2.33

Data Table Calculations set to Manual. Press F9 to recalculate. Custo- mer # Time between arrivals Arrival time Start service Service time End service Wait time Arrive within 1 hour? RN intvl LL Time Proba- bility Run Wait time 0 0 0 0 0 0 0 1 1 294.0 1 1 1 1 5 6 0 12 78.0 2 2 3 6 5 11 3 10.00 1 0.20 3 133.0 18

P10-31 Calculations set to Manual. Press F9 to recalculate. Pati- ent Room 1 Room 2 Room 3 Room 4 Room 5 Room 6 Roo m 7 Roo m 8 Room 9 Room 10 Room 11 Room 12 Room 13 Room 14 Room 15 Num. x-ray To Prob RN intvl LL Run P(multi x-ray) 4 Initial Out Out Out Out Out Out Out Out Out Out Out Out Out Out 0 Op 0.15 0.45 4

Problem 10-30 Data Table (Calculations set to Manual. Press F9 to recalculate). Maximum res accepted = 9 RN intvl LL Value Probability Run Profit Demand = 7 1 $174 Actual res accepted = 7 2$24 Number no shows = 0 0.00 5 0.05 3 $582 18 $582 19 $324 Fixed Cost $450 22 $840 23 $195 Aircraft capacity 6 24

Data Table Calculations set to Manual. Press F9 to recalculate. Day Begin Inv Units Rec Avail Inv Dem- and Demand Filled End Inv Stockout End Inv + Order Place order? Lead time Arrive on day Inv cost Stock out cost Order cost Lead time Proba- bility RN intvl LL Run Total cost % stoc- kout 1100 0100 18 18 82 082 0 0 0 $16.40 $0 $0 1 0.10 0.00 1 $7,131.40 8.23% 45 5 0

Data Table Calculations set to Manual. Press F9 to recalculate. Day Begin Inv Units Rec Avail Inv Dem- and Dem- and filled End Inv Stock out End Inv + Order Place order? Lead time Arrive on day Inv cost Stockout cost Order cost Run Total cost % stoc- kout 1300 0300 38 38 262 0262 0 0 0 $131.00 $0 $0 Minimum demand 30 1 $19,818.50 16.62% 41 50 050 41 41 9 0

Data Table Calculations set to Manual. Press F9 to recalculate. Day Begin Inv Units Rec Avail Inv Dem- and Dem- and filled End Inv Stock out End Inv + Order Place order? Lead time Arrive on day Inv cost Stockout cost Order cost Run Total cost % stoc- kout 1300 0300 49 49 251 0251 0 0 0 $125.50 $0 $0 Minimum demand 30 1 $17,537.00 14.38% 38 23 023 36 23 013 300

Data Table (Calculations set to Manual. Press F9 to recalculate). Day Begin Inv Units Rec Avail Inv Dem and Demand Filled End Inv Stock out End Inv + Order Place order? Lead time Arrive on day Inv cost Stockout cost Order cost Demand Probability RN intvl LL Run Total cost % stoc- kout 1150 0150 50 50 100 0100 1 5 7 $75.00 $0 $75 20 0.08 0.00 1 $45,585.00 4.85% 46 140

Data Table (Calculations set to Manual. Press F9 to recalculate). Day Begin Inv Units Rec Avail Inv Dem and Demand Filled End Inv Stock out End Inv + Order Place order? Lead time Arrive on day Inv cost Stockout cost Order cost Demand Probability RN intvl LL Run Total cost % stoc- kout 1150 0150 60 60 90 090 1 4 6 $67.50 $0 $75 20 0.08 0.00 1 $81,630.00 10.43% 49 40

Data Table Calculations set to Manual. Press F9 to recalculate. Week Begin Inv Units Rec Avail Inv Dem- and Demand Filled End Inv Stockout End Inv + Order Place order? Lead time Arrive on week Inv cost Stockout cost Order cost Lead time Proba- bility RN intvl LL Run Total cost % stoc- kout 1140 0140 13 13 127 0127 0 0 0 $2,540 $0 $0 10.15 0.00 1$145,560 4.72% 35 180 0180 10 10

P10-23 Data Table Calculations set to Manual. Press F9 to recalculate. Patient Sched appt time Actual arrive Sched time needed Act time needed Start service Finish service Run Finish service Ada 0 0 20 16 016 Minutes Probability RN intvl LL 1177 Bro 15 25 15 12 25 37 -20 0.20 0.00 2 169 Factor Probability RN intvl LL 9175 33 162 34 175 35 171 36 171 37

P10-22 Data Table Calculations set to Manual. Press F9 to recalculate. Stude nt Sched appt time Actual arrive Sched time needed Act time needed Start service Finish service Run Finish service 1 0 -10 20 20 020 Minutes Probability RN intvl LL 1215 Based on 200 replications: 18 205 Finish service at: 221.68 19 230 20 215 21 200 22 225 23 220 24 210 25 220 26 220 27 210 33 205 34 215 35

P10-21 Data Table Calculations set to Manual. Press F9 to recalculate. Run Total time Cost/hr Total time Cost/hr # Time (Hrs) # Time (Hrs) Hours Probability RN intvl LL 1800 $14.50 2,470 $10.69 130 1130 10 0.05 0 2 750 $15.47 2,440 $10.82 36 910 $12.75 2,400 $11.00 37 700 $16.57 2,280 $11.58 38 770 $15.06 2,340

Data Table (Calculations set to Manual. Press F9 to recalculate). Day Demand Revenue Cost Profit Run Profit 129 $435.00 $120.00 $315.00 Mean = 30 1 $7,515.00 43 $7,560.00 44 $7,290.00 45 $7,395.00 46 $7,185.00 47 $7,275.00 48 $7,320.00 49 $7,725.00 50 $6,825.00 34 $7,545.00 35 $7,635.00 36 $7,080.00 37 $7,350.00 38 $7,455.00 39 $7,080.00 40 $7,380.00 41 $7,185.00 42 $7,275.00 Demand Distribution Problem 10-20 225 $375.00 $120.00 $255.00 Std dev = 6 2

Data Table Calculations set to Manual. Press F9 to recalculate. Day Demand Today Revenue Cost Next-Day Revenue Profit Demand Probability RN intvl LL Run Profit 42 $32,625.00 43 $33,750.00 44 $27,375.00 45 $30,000.00 46 $31,875.00 47 $31,500.00 48 $27,375.00 49 $32,625.00 50 $33,750.00 51 $29,250.00 52 $32,250.00 53 $33,375.00 54 $30,000.00 55 $32,250.00 56 $29,625.00 57 $31,500.00 58 $28,500.00 59 $32,250.00 130 $3,000.00 $1,500.00 $0.00 $1,500.00 15 0.08 0.00 1 $33,375.00 28 $31,125.00 29 $31,500.00 30 $30,000.00 31

29 100 $300.0 $200.0 $100.0 29 $4,356 30 175 $300.0 $200.0 $100.0 30 $4,975 31 125 $300.0 $200.0 $100.0 31 $4,638 32 75 $243.8 $200.0 $43.8 32 $4,525 33 150 $300.0 $200.0 $100.0 33 $4,919 34 125 $300.0 $200.0 $100.0 34 $4,581 35 75 $243.8 $200.0 $43.8 35 $4,469 36 125 $300.0 $200.0 $100.0 36 $4,356 37 100

P10-17 Data Table Calculations set to Manual. Press F9 to recalculate. Month Begin Bal Income Expense End Bal Run End bal P(neg bal) 1 $1,500 $950 $1,000 $1,450 Income Probability RN intvl LL 1$400 0.0000 2 $1,450 $900 $800 $1,550 $850 0.35 0 2 $400 0.0000 3 $1,550 $900 $900 $1,550 $900 0.25 0.35 3 $450

(Calculations set to Manual. Press F9 to recalculate). Month Demand 125 Demand Probability RN intvl LL 230 10 0.02 0.00 325 15 0.07 0.02 33 35 34 25 35 35 36 35 37 25 38 15 39 25 40 40 41 35 42 25 43 35 44 30 45 35 46 40 47 35 48 35 17 30 18 45 19 35 20 50 21 30 22 35 23 20 24 40 25 30 26 35 27 45 28 25 29

P10-14 Month Failures 1 4 Lwr Lmt Failures Probability 2 3 0 0 0.10 13 5 Expected failures/month 2.48 18 3 19 3 20 3 21 2 22 2 23 1 24 1 25 1 26 3 27 4 33 3 34 3 35 3 36 2 Page 1 14 3 15 3 16 1 17 4 28 1 29 4 30 4 31 1 32 1 Failure Distribution Problem 10-15 3 0 0.10 10.17 4 4 0.27 20.21 5 2 0.48 30.28 6

Data Table Calculations set to Manual. Press F9 to recalculate. Week Demand Profit Run Avg profit Prob >= 200 20 42 $2,100.00 20 $1,700.96 15.38% 21 30 $1,500.00 21 $1,704.81 3.85% 22 38 $1,900.00 22 $1,768.27 17.31% 23 31 $1,550.00 23 $1,730.77 13.46% 24 39 $1,950.00 24 $1,806.73 21.15% 25 32 $1,600.00 25 $1,786.54 23.08% 26 32 $1,600.00 26

techniques. Problems that require quick answers that cannot wait for a simulation model to be built are a second category. probabilistic) elements through random sampling. Monte Carlo steps: (1) set up probability distribution(s), (2) set up cumulative probabilities, (3)

Data Table Calculations set to Manual. Press F9 to recalculate. Production per day (tons) 100 Number of failures 1 Run Cost Days lost Profit per ton $12 RN intvl LL Failures Probability 1 $28,800 24 Average production days lost 26.5 0.970 6 0.010 6 N/A 8 $75,600 63 Average cost per month $31,842 0.980 7

CHAPTER 10 SIMULATION MODELING Internet Case Study: Buffalo Alkali and Plastics To analyze this problem, we develop two simulation models. The first model, which is shown in file Ch10 Internet Case Buffalo Alkali.XLS, sheet Current, assumes that repair

Biales Data Table Calculations set to Manual. Press F9 to recalculate. Trip No. of barrels Rev per barrel Run Profit 143 60 RN intvl LL Barrels Probability 1 -6220 243 60 0.00 28 0.12 2 -3970 748 60 7 -9330 843 60 8 -9100 938 60 RN intvl LL Revenue Probability 9 -2900 11 33 60 0.20 60 0.44 11 -9220 12 43 70 0.64

CHAPTER 10 SIMULATION MODELING Internet Case Study: Biales Waste Disposal, GmbH Each trip out of Italy costs DM 900 for shipment and another DM 120 for loading and unloading. If there are 25 trips, the annual cost to operate the Italy office is (DM 1,020 x 25

Data Table Calculations set to Manual. Press F9 to recalculate. Custo- mer # Time between calls Call arrival time Call start service Service time Call end service Wait time Agent idle time RN interval lower limit Time Proba- bility Run Avg wait time Max wait time Idle time % 0 0 0 0 0 0 0 0 18.8 28 6.7% 12 342 45 449 3 0 0.39 30.18 13

Abjar Transport Company Data Table Calculations set to Manual. Press F9 to recalculate simulation values. 29 820 30 820 31 514 32 822 33 10 26 34 923 35 821 36 719 37 821 38 11 29 39 821 40 924 41 718 42 923 Monthly freight volume to be handled: Run C Rigs NC Rigs 21 820 22 10 26 23 822 24 925 25 10 27 26 924 27 822 28

(b) The probability of getting a 5-inch nail is = 0.19. (c) The probability of getting a nail 3 inches or shorter is the probability of getting a nail 1 inch, 2 inches, or 3 inches in length (the events are mutually exclusive). The probability is thus P(1 or 2

exclusive events can be seen in flipping a coin. The outcome of any one trial can either be a head or a tail. Thus, the events of getting a head and a tail are mutually exclusive because only one of these events can occur on any one trial. This assumes,

Problem 9-39 Queuing Model M/M/s with a finite population Input Data Operating Characteristics Arrival rate per customer (l) 0.9090909 Average server utilization (r)0.7190 Probabilities 8.143153 Number of Units Probability Cumulative Probability Number waiting Arrival rate(n) Term 1 Sum term 1 Term 2 Sum term 2 Decum term 2 P0(s) 0 0.1400 0.1400 0 6.363636 1 1 2 2 6.143153 1 0.2821 0.4221 0 5.454545 2.015152 3.015152 2.015152

Problem 9-38 Queuing Model M/G/1 (General Service Times) Input Data Operating Characteristics Arrival rate (l)8Average server utilization (r)0.8000 Service rate (m)10 Average number of customers in the queue (Lq)1.7778 Standard deviation (s)0.0333 Average number of customers in the system (L) 2.5778 Average waiting time in the queue (Wq)0.2222 Average time in the system (W) 0.3222 Probability (% of

1 2 3 4 17 18 19 20 21 22 23 24 25 Desired waiting time of 6 seconds, or 0.1 minutes Probabilities Desired queue length of 8 cummuters Number of Units Probability Cumulative Probability 0 0.0502 0.0502 1 0.1406 0.1908 2 0.1968 0.3876 3 0.1837 0.5713 4 0.1286 0.6999 5 0.0900 0.7900 14 15 16 31 32 33 34 35 36 37 38 39 11 0.0106 0.9753 12 0.0074 0.9827 13 0.0052 0.9879 14 0.0036 0.9915 15 0.0025 0.9941 16 0.0018 0.9958 17 0.0012 0.9971 18 0.0009 0.9980 19 0.0006 0.9986 26 27 28 29 30 A B

Problem 9-36 Queuing Model M/M/s with a finite population Input Data Operating Characteristics Arrival rate per customer (l) 0.03 Average server utilization (r)0.6899 Service rate (m)0.2 Average number of customers in the queue (Lq)0.7105 Probabilities 3.225126 Number of Units Probability Cumulative Probability Number waiting Arrival rate(n) Term 1 Sum term 1 Term 2 Sum term 2 Decum term 2 P0(s) 0 0.3101 0.3101 0 0.18 1 1

Problem 9-35 Queuing Model M/M/s with a finite population Input Data Operating Characteristics Arrival rate per customer (l) 0.5 Average server utilization (r)0.6918 Service rate (m)4Average number of customers in the queue (Lq)0.7735 Probabilities 3.245018 Number of Units Probability Cumulative Probability Number waiting Arrival rate(n) Term 1 Sum term 1 Term 2 Sum term 2 Decum term 2 P0(s) 0 0.3082 0.3082 0 3.5 1 1 1

Problem 9-34 Queuing Model M/M/s with a finite population Input Data Operating Characteristics Arrival rate per customer (l) 0.7058824 Average server utilization (r)0.6635 Probabilities 2.971843 Number of Units Probability Cumulative Probability Number waiting Arrival rate(n) Term 1 Sum term 1 Term 2 Sum term 2 Decum term 2 P0(s) 0 0.3365 0.3365 0 3.529412 1 1 1 1 1.971843 1 0.2969 0.6334 0 2.823529 0.882353 1.882353 0.882353

Problem 9-33 Queuing Model M/M/s with a finite population Input Data Operating Characteristics Arrival rate per customer (l) 0.1 Average server utilization (r)0.5155 Service rate (m)1Average number of customers in the queue (Lq)0.3297 Probabilities 2.06392 Number of Units Probability Cumulative Probability Number waiting Arrival rate(n) Term 1 Sum term 1 Term 2 Sum term 2 Decum term 2 P0(s) 0 0.4845 0.4845 0 0.6 1 1 1

Queuing Model M/G/1 (General Service Times) Input Data Operating Characteristics Arrival rate (l)0.9 Average server utilization (r)0.9000 Problme 9-32 (m = 1) Service rate (m)1Average number of customers in the queue (Lq)5.0625 Standard deviation (s)0.5000 Average number of customers in the system (L) 5.9625 Average waiting time in the queue (Wq)5.6250 Average time in the system (W)

Problem 9-31 Queuing Model M/G/1 (General Service Times) Input Data Operating Characteristics Arrival rate (l)0.125 Average server utilization (r)0.6250 Service rate (m)0.2 Average number of customers in the queue (Lq)0.5417 Standard deviation (s)1.0000 Average number of customers in the system (L) 1.1667 Average waiting time in the queue (Wq)4.3333 Average time in the system (W) 9.3333 Probability (%

Queuing Model M/D/1 (Constant Service Times) Input Data Operating Characteristics Arrival rate (l)4Average server utilization (r)0.6667 Problem 9-30 Service rate (m)6Average number of customers in the queue (Lq)0.6667 Average number of customers in the system (L) 1.3333 Average waiting time in the queue (Wq)0.1667 Average time in the system (W) 0.3333 Probability (% of time) system is empty

Problem 9-29 Queuing Model M/G/1 (General Service Times) Input Data Operating Characteristics Arrival rate (l)1Average server utilization (r)0.3797 Service rate (m)2.633836 Average number of customers in the queue (Lq)0.1666 Standard deviation (s)0.2500 Average number of customers in the system (L) 0.5462 Average waiting time in the queue (Wq)0.1666 Average time in the system (W) 0.5462 Probability (% of

Problem 9-28 Queuing Model M/G/1 (General Service Times) Input Data Operating Characteristics Arrival rate (l)1Average server utilization (r)0.5000 Service rate (m)2Average number of customers in the queue (Lq)0.3125 Standard deviation (s)0.2500 Average number of customers in the system (L) 0.8125 Average waiting time in the queue (Wq)0.3125 Average time in the system (W) 0.8125 Probability (% of time)

1 2 3 4 5 6 7 8 9 17 18 32 33 34 35 36 37 38 39 40 12 0.0126 0.9732 13 0.0086 0.9818 14 0.0058 0.9876 15 0.0040 0.9916 16 0.0027 0.9943 17 0.0018 0.9961 18 0.0012 0.9973 19 0.0008 0.9982 20 0.0006 0.9988 21 22 23 24 25 26 27 28 1 0.0373 0.0452 2 0.0889 0.1340 3 0.1411 0.2751 4 0.1679 0.4430 5 0.1599 0.6030 6 0.1269 0.7299 7 0.0864 0.8163 8 0.0587 0.8750 19 20 29 30 31 A B C D E F G H I J Problem 9-27 Queuing Model M/M/s (Exponential Service Times) Input

1 2 3 4 5 6 7 8 9 15 16 17 18 32 33 34 35 36 37 38 39 12 0.0000 1.0000 13 0.0000 1.0000 14 0.0000 1.0000 15 0.0000 1.0000 16 0.0000 1.0000 17 0.0000 1.0000 18 0.0000 1.0000 19 0.0000 1.0000 22 23 24 25 26 2 0.1535 0.9393 3 0.0435 0.9828 4 0.0123 0.9951 5 0.0035 0.9986 6 0.0010 0.9996 19 20 21 27 28 29 30 31 A B C D E F G H I J Problem 9-26 Queuing Model M/M/s (Exponential Service Times) Input Data Operating Characteristics Arrival rate (l)30 Average server utilization

Problem 9-25 Queuing Model M/G/1 (General Service Times) Input Data Operating Characteristics Arrival rate (l)10 Average server utilization (r)0.8333 Service rate (m)12 Average number of customers in the queue (Lq)2.2708 Standard deviation (s)0.0250 Average number of customers in the system (L) 3.1042 Average waiting time in the queue (Wq)0.2271 Average time in the system (W) 0.3104 Probability

1 2 3 4 5 21 22 23 24 25 26 27 28 29 30 1 0.2479 0.7022 2 0.1353 0.8375 3 0.0738 0.9113 4 0.0403 0.9516 5 0.0220 0.9736 6 0.0120 0.9856 7 0.0065 0.9921 8 0.0036 0.9957 9 0.0019 0.9977 10 0.0011 0.9987 minutes per customer 36 37 38 39 16 0.0000 1.0000 17 0.0000 1.0000 18 0.0000 1.0000 19 0.0000 1.0000 19 20 31 32 33 34 35 A B C D E F G H I J Problem 9-24 Queuing Model M/M/s (Exponential Service Times) Number of Units Probability Probability 0 0.4543

1 2 3 4 5 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Number of Units Probability Cumulative Probability 0 0.4118 0.4118 1 0.3431 0.7549 2 0.1430 0.8979 3 0.0596 0.9574 4 0.0248 0.9823 5 0.0103 0.9926 6 0.0043 0.9969 7 0.0018 0.9987 33 34 35 36 37 38 39 40 13 0.0000 1.0000 14 0.0000 1.0000 15 0.0000 1.0000 16 0.0000 1.0000 17 0.0000 1.0000 18 0.0000 1.0000 19 0.0000 1.0000 20 0.0000 1.0000 28 29 30 31 32 A B C D E F G H I J Problem 9-23 Queuing Model M/M/s (Exponential

1 2 3 4 5 6 7 8 17 18 20 00.1667 0.1667 22 20.1157 0.4213 24 40.0804 0.5981 26 60.0558 0.7209 28 80.0388 0.8062 33 34 35 36 37 38 39 40 13 0.0156 0.9221 14 0.0130 0.9351 15 0.0108 0.9459 16 0.0090 0.9549 17 0.0075 0.9624 18 0.0063 0.9687 19 0.0052 0.9739 20 0.0043 0.9783 19 21 23 25 27 29 30 31 32 A B C D E F G H I J Problem 9-22 (a) Queuing Model M/M/s (Exponential Service Times) Input Data Operating Characteristics Probabilities Number of Units Probability Cumulative Probability 10.1389 0.3056 30.0965 0.5177 50.0670 0.6651 70.0465 0.7674 90.0323 0.8385 10 0.0269

1 2 3 4 5 6 7 8 9 17 18 22 20.1764 0.3140 24 40.1633 0.6733 26 60.0726 0.8548 27 28 70.0484 0.9032 80.0323 0.9355 33 34 35 36 37 38 39 40 13 0.0042 0.9915 14 0.0028 0.9943 15 0.0019 0.9962 16 0.0013 0.9975 17 0.0008 0.9983 18 0.0006 0.9989 19 0.0004 0.9993 20 0.0002 0.9995 19 20 21 23 25 29 30 31 32 A B C D E F G H I J Queuing Model M/M/s (Exponential Service Times) Input Data Operating Characteristics Arrival rate (l)20 Average server utilization (r)0.6667 Probabilities Number of Units Probability Cumulative Probability 00.0318 0.0318 10.1058