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Example 3.5 The Dump Truck Problem 張偉珉 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 Table 3.3. Distribution of Loading Time for the Dump Trucks Weighing Time Probability Cumulative Probability Random-Digit Assignment 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 Table 3.5. Distribution of Travel Time for the Dump Trucks Loading Time Weighing Time Travel Time 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 DT4) (EW.12.DT1) DT6DT3(EL10.DT4)2010 DT2(EW.12.DT1) (EL DT5) DT3(EL.12.DT1)2010 DT2(EL.20.DT5) DT4(EL DT6) DT2(EL.20.DT5)2412 DT4(EW DT3) (EL.25.DT6) (ALQ 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 DT2(EW.24.DT3)4020 DT4(EL.25.DT6) DT5(ALQ.72.DT1) DT4(EL.25.DT3)4424 DT5(EW DT2) (ALQ.72.DT1) (ALQ DT3) DT4(EL.36.DT2)4525 DT5(ALQ.72.DT1) DT6(ALQ.124.DT3) DT5(EW DT4)4536 DT6(ALQ.72.DT1) (ALQ 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 DT6(EW DT5)4552 (ALQ.72.DT1) (ALQ.76.DT2) (ALQ DT4) (ALQ.124.DT3) (ALQ.72.DT1)4564 (ALQ.76.DT2) (EW DT6) (ALQ.92.DT4) (ALQ.124.DT3) (ALQ 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 (ALQ.76.DT2)4572 (EW.80.DT6) (EL DT1) (ALQ.92.DT4) (ALQ.124.DT3) (ALQ.144.DT5) (EW.80.DT6)4976 (EL.82.DT1) (EL 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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