# Example 3.5 The Dump Truck Problem

## Presentation on theme: "Example 3.5 The Dump Truck Problem"— Presentation transcript:

Example 3.5 The Dump Truck Problem

Loder queue Weighing queue

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

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

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

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)

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)

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)

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)

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