Assignment 4 Logistics
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Assignment 4: Case Study - Minnetonka Warehouse
We’ll use queueing theory and the provided information to answer the questions related to the Minnetonka Warehouse case.
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Question 1: For each of the four work team sizes, calculate the expected number of trucks in the queue to be unloaded.
1.
Team of 2 workers (unloading rate: 5 trucks per hour or one every 12 minutes):
Arrival rate (λ) = 4 trucks per hour
Service rate (μ) = 5 trucks per hour Using the M/M/1 queue model:
Expected number of trucks in the queue (Lq) = (λ^2) / (μ * (μ - λ)) = (16) / (5 * (5
- 4)) = 16 trucks
2.
Team of 3 workers (unloading rate: 8 trucks per hour or one every 7.5 minutes):
Arrival rate (λ) = 4 trucks per hour
Service rate (μ) = 8 trucks per hour Using the M/M/1 queue model:
Expected number of trucks in the queue (Lq) = (λ^2) / (μ * (μ - λ)) = (16) / (8 * (8
- 4)) = 1 truck
3.
Team of 4 workers (unloading rate: 10 trucks per hour or one every 6 minutes):
Arrival rate (λ) = 4 trucks per hour
Service rate (μ) = 10 trucks per hour Using the M/M/1 queue model:
Expected number of trucks in the queue (Lq) = (λ^2) / (μ * (μ - λ)) = (16) / (10 * (10 - 4)) = 0.4 trucks
4.
Team of 5 workers (unloading rate: 11 trucks per hour or one every 4.45 minutes):
Arrival rate (λ) = 4 trucks per hour
Service rate (μ) = 11 trucks per hour Using the M/M/1 queue model:
Expected number of trucks in the queue (Lq) = (λ^2) / (μ * (μ - λ)) = (16) / (11 * (11 - 4)) = 0.206 trucks
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