Minnetonka Warehouse
Introduction
The queuing theory is among the most essential techniques in business logistics. This theory provides an excellent platform for determining the potential length of queues in warehouses, ports, and other points of loading and unloading. This theory is also immensely beneficial in making projections about the potential delay time in a queue (Branch, 97). Consequently, the queuing theory plays an instrumental role towards streamlining the efficiency of decisions within a supply chain. Extensive delays in queues form the basis of increased operational costs. This can hamper a company’s framework for profitability. Additionally, such delays can discourage potential partners from entering into an agreement with another firm in business logistics. The queuing theory is an essential aspect of strategic decision making in business logistics. The paper focuses on the different practical aspects of the queuing theory in line with the operations of Minnetonka Warehouse.
Question 1: Expected Number of Trucks Waiting in the Queue
Based on the calculations, a truck will wait in the queue longer when two workers are unloading. In contrast, the Minnetonka Warehouse will attain the highest speed of unloading when a team of five workers is used.
Team of two:
Based on the queuing theory:
p = Arrival rate / Service Rate
Average queue length = p / (1-p)
Arrival rate = 4 trucks per hour
Service rate = 5 trucks per hour
p = 4/5 or 0.8
Average queue length = 0.8 / (1-0.8)
Average queue length = 4 trucks
Team of three:
Based on the queuing theory:
p = Arrival rate / Service Rate
Average queue length = p / (1-p)
Arrival rate = 4 trucks per hour
Service rate = 8 trucks per hour
p = 4/8 or 0.5
Average queue length = 0.5 / (1-0.5)
Average queue length = 1 truck
Team of four:
Based on the queuing theory:
p = Arrival rate / Service Rate
Average queue length = p / (1-p)
Arrival rate = 4 trucks per hour
Service rate = 10 trucks per hour
p = 4/10 or 0.4
Average queue length = 0.4 / (1-0.4)
Average queue length = 0.67 trucks
Team of five:
Based on the queuing theory:
p = Arrival rate / Service Rate
Average queue length = p / (1-p)
Arrival rate = 4 trucks per hour
Service rate = 11 trucks per hour
p = 4/11 or 0.36
Average queue length = 0.36 / (1-0.36)
Average queue length = 0.56 trucks
Question 2: Expected Time in the Queue
Based on the calculations, a truck will spend more time on the queue when the warehouse uses a team of two. The expected time in the queue for trucks reduces as the warehouse employs more workers to unload. Consequently, a higher number of workers reduce the time spent on the queue by trucks.
Team of two:
Based on the queuing theory:
Waiting time = [p / (2 × service rate)] [1 – p]
p = 0.8
Service rate = 5 trucks per hour
Waiting time = (0.8/10) (1 – 0.8)
= 0.016 hours
Team of three:
Based on the queuing theory:
Waiting time = [p / (2 × service rate)] [1 – p]
p = 0.5
Service rate = 8 trucks per hour
Waiting time = (0.5/16) (1 – 0.5)
= 0.015 hours
Team of four:
Based on the queuing theory:
Waiting time = [p / (2 × service rate)] [1 – p]
p = 0.4
Service rate = 10 trucks per hour
Waiting time = (0.4/20) (1 – 0.4)
= 0.012 hours
Team of five:
Based on the queuing theory:
Waiting time = [p / (2 × service rate)] [1 – p]
p = 0.36
Service rate = 11 trucks per hour
Waiting time = (0.36/22) (1 – 0.36)
= 0.01hours
Question 3: Probability that a truck cannot be offloaded immediately
Team of two;
Probability of not being offloaded immediately = Arrival rate / Service rate
= 0.8
Team of three;
Probability of not being offloaded immediately = 4/8
= 0.5
Team of four;
Probability of not being offloaded immediately =4/10
= 0.4
Team of five;
Probability of not being offloaded immediately = 4/11
= 0.36
Question 4
While Wayne has the alternative of renting a forklift for the warehouse, the hourly cost is $38. Using manual labor, the warehouse incurs an hourly cost of $28 while using a team of two workers. A total cost of $42 is incurred per hour when the company uses three workers to unload the trucks. When a team of four workers is used, the hourly cost incurred by the company is $56 (Murphy & Wood, 194). For a team of five workers, the warehouse incurs $70 per hour.
At a rate of five minutes per truck, the warehouse can unload 12 trucks in every hour using the forklift. This illustrates that the forklift is not only cost effective but also has an excellent rate of output. In view of such attributes, Wayne should rent the forklift. In essence, the forklift will help in enhancing the performance of the warehouse in different ways. Firstly, the forklift will be crucial in terms of mitigation of delays at the warehouse. This is because of the high rates of unloading trucks. In the absence of delays, Wayne will attract new clients easily. In addition to attracting new clients, increased efficiency will help the warehouse in maintaining its current clients (Neise, 21). Another advantage of the forklift concerns the minimization of operational costs in the warehouse. At an hourly cost of $28, the warehouse will have an excellent platform for the alleviation of operational costs. This is an essential aspect of logistics management. It is always essential for the business to employ mechanisms which are characterized by efficiency and minimal costs (Morse, 120).
The risk posed by the forklift is considerably minimal compared to the risk associated with manual labor. For instance, the warehouse will not incur excessive costs from the perspective of overtime charges (Gross, 89). This will also contribute towards boosting operational efficiency in the warehouse. These attributes exemplify the rationale behind the use of the forklift at Minnetonka Warehouse.
Conclusion
The queuing theory is an essential aspect of strategic decision making in business logistics. Based on the calculations, the different team sizes have different implications on the speed of unloading. For instance, a team of two workers has minimal rates for unloading trucks. In contrast, a team of five workers is characterized by excellent rates. From the analysis, Wayne should rent a forklift for the warehouse. The forklift is highly effective both in terms of costs and speed. With an excellent rate of 12 trucks per hour, the forklift is also characterized by minimal costs of $28.
References
Branch, A. E. (2008). Global supply chain management and international logistics, New York, NY: Routledge
Gross, D. & Thompson, J. M. (2011). Fundamentals of queuing theory, Hoboken, NJ: John Wiley & Sons
Morse, P. M. (2004). Queues, inventories, and maintenance, Hoboken, NJ: John Wiley & Sons
Murphy, P. R. & Wood, D. P. (2010). Contemporary logistics, 10th Edition. Prentice Hall
Neise, P. (2009). Managing quality and delivery reliability, Munich: Herbert Publishing
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