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Example 3.5 The Dump Truck Problem 8823005 張偉珉 8823033 歐冠麟

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Problem schematic Loder queue Weighing queue Scale Loading Figure 3.7. Dump truck problem

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Loading TimeProbability Cumulative Probability Random-Digit Assignment 50.30 1-3 100.500.804-8 150.201.009-0 Table 3.3. Distribution of Loading Time for the Dump Trucks Weighing Time Probability Cumulative Probability Random-Digit Assignment 120.70 1-7 160.301.008-0 Table 3.4. Distribution of Weighing Time for the Dump Trucks Distribution of time

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Travel TimeProbability Cumulative Probability Random-Digit Assignment 400.40 1-4 600.400.705-7 800.200.908-9 1000.101.000 Table 3.5. Distribution of Travel Time for the Dump Trucks Loading Time1055 1510 Weighing Time12 161216 Travel Time6010040 80 Table 3.5. Activity times

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Model components System state [LQ(t), L(t), WQ(t), W(t)] –LQ(t) = number of trucks in loader queue at time t –L(t) = number of trucks (0..2) being loaded at time t –WQ(t) = number of trucks in weigh queue at time t –W(t) = number of trucks (0..1) being weighed at time t Event notices –(ALQ, t, DTi), dump truck i arrives at loader queue at time t –(EL, t, DTi), dump truck i ends loading at time t –(EW, t, DTi), dump truck i ends weighing at time t Entities The six dump trucks (DT1, …, DT6) Lists Loader queue, Weigh queue Activities Loading time, weighing time, travel time Delays Delay at loader queue, and delay at scale

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Dump Truck Operation ClockSystem StateLists Future Event List Cumulative Statistics tLQ(t)L(t)WQ(t)W(t) Loader Queue Weigh Queue BLBL BSBS 03201DT4(EL.5.DT3)00 DT5(EL.10.DT2) DT6(EW.12.DT1) 52211DT5DT3(EL.10.DT2)105 DT6(EL.5 + 5.DT4) (EW.12.DT1) 101221DT6DT3(EL10.DT4)2010 DT2(EW.12.DT1) (EL.10 + 10.DT5) 100231DT3(EL.12.DT1)2010 DT2(EL.20.DT5) DT4(EL.10 + 15.DT6) 120221DT2(EL.20.DT5)2412 DT4(EW.12 + 12.DT3) (EL.25.DT6) (ALQ.12 + 60.DT1) Table 3.6. Simulation Table for Dump Truck Operation

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Dump Truck Operation ClockSystem StateLists Future Event List Cumulative Statistics tLQ(t)L(t)WQ(t)W(t) Loader Queue Weigh Queue BLBL BSBS 200131DT2(EW.24.DT3)4020 DT4(EL.25.DT6) DT5(ALQ.72.DT1) 240121DT4(EL.25.DT3)4424 DT5(EW.24 + 12.DT2) (ALQ.72.DT1) (ALQ.24 + 100.DT3) 250031DT4(EL.36.DT2)4525 DT5(ALQ.72.DT1) DT6(ALQ.124.DT3) 360021DT5(EW.36 + 16.DT4)4536 DT6(ALQ.72.DT1) (ALQ.36 + 40.DT2) (ALQ.124.DT3) Table 3.6. Continued

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Dump Truck Operation ClockSystem StateLists Future Event List Cumulative Statistics tLQ(t)L(t)WQ(t)W(t) Loader Queue Weigh Queue BLBL BSBS 520010DT6(EW.52 + 12.DT5)4552 (ALQ.72.DT1) (ALQ.76.DT2) (ALQ.52 + 40.DT4) (ALQ.124.DT3) 640001(ALQ.72.DT1)4564 (ALQ.76.DT2) (EW.64 + 16.DT6) (ALQ.92.DT4) (ALQ.124.DT3) (ALQ.64 + 80.DT5) Table 3.6. Continued

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Dump Truck Operation ClockSystem StateLists Future Event List Cumulative Statistics tLQ(t)L(t)WQ(t)W(t) Loader Queue Weigh Queue BLBL BSBS 720101(ALQ.76.DT2)4572 (EW.80.DT6) (EL.72 + 10.DT1) (ALQ.92.DT4) (ALQ.124.DT3) (ALQ.144.DT5) 760201(EW.80.DT6)4976 (EL.82.DT1) (EL.76 + 10.DT2) (ALQ.92.DT4) (ALQ.124.DT3) (ALQ.144.DT5) Table 3.6. Continued

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Conclusion Cumulative Statistics –B L = total busy time of both loaders from time 0 to time i –B S = total busy time of the scale from time 0 to time i Estimated Utilizations –Average loader utilization = = 0.32 –Average scale utilization = = 1.00

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