Assignment 4 Logistics

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School

Southern Alberta Institute of Technology *

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Course

310

Subject

Economics

Date

Apr 3, 2024

Type

docx

Pages

4

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Cla ssi fica tio n: Ge ner al 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.
Cla ssi fica tio n: Ge ner al 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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