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**Example 3.5 The Dump Truck Problem**

張偉珉 歐冠麟

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**Problem schematic Figure 3.7. Dump truck problem Loading Scale**

Loder queue Weighing queue

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**Distribution of time Loading Time Probability Cumulative Probability**

Table 3.3. Distribution of Loading Time for the Dump Trucks Loading Time Probability Cumulative Probability Random-Digit Assignment 5 0.30 1-3 10 0.50 0.80 4-8 15 0.20 1.00 9-0 Table 3.4. Distribution of Weighing Time for the Dump Trucks Weighing Time Probability Cumulative Probability Random-Digit Assignment 12 0.70 1-7 16 0.30 1.00 8-0

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**Distribution of time Travel Time Probability Cumulative Probability**

Table 3.5. Distribution of Travel Time for the Dump Trucks Travel Time Probability Cumulative Probability Random-Digit Assignment 40 0.40 1-4 60 0.70 5-7 80 0.20 0.90 8-9 100 0.10 1.00 Table 3.5. Activity times Loading Time 10 5 15 Weighing Time 12 16 Travel Time 60 100 40 80

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**Model components System state [LQ(t), L(t), WQ(t), W(t)] Event notices**

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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**Cumulative Statistics**

Dump Truck Operation Table 3.6. Simulation Table for Dump Truck Operation Clock System State Lists Future Event List Cumulative Statistics t LQ(t) L(t) WQ(t) W(t) Loader Queue Weigh Queue BL BS 3 2 1 DT4 (EL.5.DT3) DT5 (EL.10.DT2) DT6 (EW.12.DT1) 5 DT3 10 (EL DT4) (EL10.DT4) 20 DT2 (EL DT5) (EL.12.DT1) (EL.20.DT5) (EL DT6) 12 24 (EW DT3) (EL.25.DT6) (ALQ DT1)

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**Cumulative Statistics**

Dump Truck Operation Table 3.6. Continued Clock System State Lists Future Event List Cumulative Statistics t LQ(t) L(t) WQ(t) W(t) Loader Queue Weigh Queue BL BS 20 1 3 DT2 (EW.24.DT3) 40 DT4 (EL.25.DT6) DT5 (ALQ.72.DT1) 24 2 (EL.25.DT3) 44 (EW DT2) (ALQ DT3) 25 (EL.36.DT2) 45 DT6 (ALQ.124.DT3) 36 (EW DT4) (ALQ DT2)

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**Cumulative Statistics**

Dump Truck Operation Table 3.6. Continued Clock System State Lists Future Event List Cumulative Statistics t LQ(t) L(t) WQ(t) W(t) Loader Queue Weigh Queue BL BS 52 1 DT6 (EW DT5) 45 (ALQ.72.DT1) (ALQ.76.DT2) (ALQ DT4) (ALQ.124.DT3) 64 (EW DT6) (ALQ.92.DT4) (ALQ DT5)

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**Cumulative Statistics**

Dump Truck Operation Table 3.6. Continued Clock System State Lists Future Event List Cumulative Statistics t LQ(t) L(t) WQ(t) W(t) Loader Queue Weigh Queue BL BS 72 1 (ALQ.76.DT2) 45 (EW.80.DT6) (EL DT1) (ALQ.92.DT4) (ALQ.124.DT3) (ALQ.144.DT5) 76 2 49 (EL.82.DT1) (EL DT2)

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**Conclusion Cumulative Statistics Estimated Utilizations**

BL = total busy time of both loaders from time 0 to time i BS = 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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