# A territory with 3 tech reps number of machines 450 l

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A territory with 3 tech reps: Number of machines = 450 l = 9 m = 4 s = 3 r = l / s m = 0.75 to find = 0.1893
Comparison of W q with Territories of Different Sizes Number of Tech Reps Number of Machine s l m s r W q 1 150 3 4 1 0.7 5 0.75 workday (6 hours) 2 300 6 4 2 0.7 5 0.321 workday (2.57 hours) 3 450 9 4 3 0.7 5 0.189 workday (1.51 hours) 4 600 1 2 4 4 0.7 5 0.127 workday (1.02 hours) Conclusion: Diminishing returns –– First few consolidations are most effective
Some Managerial Insights Into Queueing Systems A high utilization factor (workload) leads to surprisingly poor performance. See MMs.xlsx (2 nd sheet) Decreasing variability of service times (without any change in mean) improves performance substantially . See MG1.xlsx (2 nd sheet) Multiple-server queueing systems can perform satisfactorily with somewhat higher utilization factors than can single-server queueing systems. For example, pooling servers by combining separate single- server queueing systems into one multiple-server queueing system greatly improves measures of performance. Applying priorities when selecting customers to begin service can greatly improve performance for high-priority customers .
Economic Analysis of Number of Servers to Provide In many cases, consequences of making customers wait can be expressed as a waiting cost . manager is interested in minimizing total cost. TC = Expected total cost per unit time SC = Expected service cost per unit time WC = Expected waiting cost per unit time objective is to choose number of servers so as to Minimize TC = SC + WC When each server costs same ( C s = cost of server per unit time), SC = C s s When waiting cost is proportional to amount of waiting ( C w = waiting cost per unit time for each customer), and assuming that the waiting cost is incurred while in the queue and while in service: WC = C w L However, if the waiting cost is incurred only while waiting to be served, then WC = C w
Acme Machine Shop l = 120 customers/hour m = 80 customers/hour Total cost of each server is \$20/hour, i.e., C s = \$20. While servers busy, their value is \$48/hour, i.e., C w = \$48. Choose s so as to Minimize TC = \$20 s + \$48 L . See MMs_Economic_Analysis.xlsx

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• Fall '19
• Normal Distribution, Probability theory, Exponential distribution, Poisson process, Queueing theory

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