# AD605 Practice Week 08 Soln(2)

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BOSTON UNIVERSITY METROPOLITAN COLLEGE DEPARTMENT OF ADMINISTRATIVE SCIENCES AD 605 Operations Management Week 8: Practice Problems Solutions 1. Calculate the demand forecast per week (in hours) and the demand CV for a production manager who is expected to work 50 hours per week. Each week, the manager: (a) attends 10 daily meetings that each average 80 minutes each with a CV of 35%, (b) troubleshoots 21 problems that each averages 43 minutes each with a CV of 45%; (c) creates next week's schedule that averages 5.4 hours minutes each with a CV of 20%, and (d) works on 2 projects with product design that each average 1.75 hours with a CV of 50%. 𝜇 = 37.2 ℎ???? 𝜎 = 2.7 ℎ???? ?𝑉 = 7.1% 2. Calculate the demand forecast per month (in hours) and the demand CV for a human resource professional. Each month, they: (a) review 600 resumes each average 1.5 minutes each with a CV of 20%, (b) arrange for and interview 37 candidates that each averages 3.5 hours with a CV of 25%; and (c) meets with internal customers 30 times that each average 45 minutes with a CV of 40%. 𝜇 = 167.0 ℎ???? 𝜎 = 5.6 ℎ???? ?𝑉 = 3.3% 3. Determine the planned capacity and capacity buffer percentage for the following situation , where the "service level" (percentage of required hours that the resource will be available) is set at 99%. The weekly demand for a technician at a cable company is forecasted as follows: (a) 15 installations each averaging 2.3 hours with a CV of 55%; (b) 10 troubleshooting calls each averaging 45 minutes with a CV of 80%; and (c) 5 staff meetings each averaging 35 minutes with a CV of 25%. 1) 𝜇 = 44.9 ℎ???? 𝜎 = 5.3 ℎ???? ?𝑉 = 11.7% 2) 𝑆𝐿 = 0.99 3) ?(?) = 0.085 ? = 0.989 4) ?𝑎?𝑎?𝑖?𝑦 ?????? = 5.2 ℎ???? 𝑃?𝑎???? ?𝑎?𝑎?𝑖?𝑦 = 50.1 ℎ???? 5) ?𝑎?𝑎?𝑖?𝑦 ?????? 𝑃??????𝑎?? = 10.4% 4. Determine the planned capacity and capacity buffer percentage for the following situation, where the "service level" (percentage of required hours that the resource will be available) is set at 9 8%. The daily demand for a call center agent is forecasted as follows: (a) 80 calls each averaging 5.2 minutes with a CV of 90%; and (b) 1 report generation for the client firm averaging 1 hours with a CV of 65%. 1) 𝜇 = 476.0 ?𝑖????? 𝜎 = 57.2 ?𝑖????? ?𝑉 = 12.0% 2) 𝑆𝐿 = 0.98 3) ?(?) = 0.166 ? = 0.610 4) ?𝑎?𝑎?𝑖?𝑦 ?????? = 34.9 ?𝑖????? 𝑃?𝑎???? ?𝑎?𝑎?𝑖?𝑦 = 510.9 ?𝑖????? 5) ?𝑎?𝑎?𝑖?𝑦 ?????? 𝑃??????𝑎?? = 6.8% 5. Answer Discussion Question 1 in Chapter 8. Answer given in back of book 6. Answer Discussion Question 2 in Chapter 8. Answer given in back of book
7. Answer Discussion Question 3 in Chapter 8. Answer given in back of book 8. Consider a facility that provides services of investment customers on a walk-in basis. Data have shown that during the 10:00 - 3:00 timeframe, an average of 86 customers arrived and were served. One receptionist speaks to every customer to determine their needs; this takes an average of 3 minutes. Thirty-two percent of customers seek investment advice (they are each served by one of 3 investment advisors, who each averages 18 minutes to service a customer). Sixty-eight percent of customers seek to complete a simple transaction (e.g., deposit a check). These transactions are handled by 2 service agents, who each averages 7.5 minutes to service a customer. Do the following: a. Calculate the capacity of the receptionist (customers/hour). Service Time (minutes/customer): 3 Capacity for Resource Unit (customers/hour): 20 Number of Servers = 1 Capacity for Resource Pool (customers/hour) = 20 b. Calculate the resource utilization of the receptionist. Service Time (minutes/customer): 3 Capacity for Resource Unit (customers/hour): 20 Number of Servers = 1 Capacity for Resource Pool (customers/hour) = 20 Demand (customers/hour) = 17.2 (86 customers/5 hours) Utilization = 0.86 or 86% c. Calculate the resource utilization of the service agents. Service Time (minutes/customer): 7.5 Capacity for Resource Unit (customers/hour): 8 Number of Servers = 2 Capacity for Resource Pool (customers/hour) = 16 Demand (customers/hour) = 11.7 (17.2 × 0.68) Utilization = 0.731 or 73.1% 9. An amusement park serves many customers. During weekends, the park is opened from 10:00 AM to 8:00 PM. The average number of customers is 1800 per day. Each customer buys a ticket from one of eight cashiers, who each take an average of 2.5 minutes to serve a customer. Sixty-five percent of customers go on the roller coaster. This roller coaster serves 24 customers at a time and takes 12 minutes to complete the ride, including getting customers on and off. Do the following: a. Calculate the capacity of the cashiers (customers/hour). Service Time (minutes/customer) = 2.5 Capacity for Resource Unit (customers/hour): 24 Number of Servers = 8 Capacity for Resource Pool (customers/hour) = 192 b. Calculate the resource utilization of the cashiers. Capacity for Resource Pool (customers/hour) = 192 Demand (customers/hour) = 180 (1800 customers/10 hours) Utilization = 0.9375 or 93.75% c. Calculate the resource utilization of the roller coaster. Service Time (minutes/customer) = 12 Capacity for Resource Unit (customers/hour): 5 Number of Servers = 24 Capacity for Resource Pool (customers/hour) = 120 Demand (customers/hour) = 117 (0.65 x 180 customers/hour) Utilization = 0.975 or 97.5%
10. Ten workers are present in a painting process for metal parts. Each painter completes one part every 7.5 minutes. During each 8-hour shift, 600 parts are painted. Do the following: a. Calculate the utilization of the painters. Service Time per Worker (min/part): 7.5 Capacity for Resource Unit (parts/hour): 8 Number of Workers = 10 Capacity for Resource Pool (parts/hour) = 80 Demand (parts/hour) = 75 (600 parts/8 hours) Worker Utilization = 0.9375 or 93.75% b. Demand has increased to 760 parts per shift. How many painters are needed to have a maximum 95% utilization? Service Time per Worker (min/part): 7.5 Capacity for Resource Unit (parts/hour): 8 Demand (parts/hour) = 95 (760 parts/8 hours) [By trial and error]: Number of Painters = 10 Capacity for Resource Pool (parts/hour) = 80 Worker Utilization = 1.1875 or 119% Number of Painters = 11 Capacity for Resource Pool (parts/hour) = 88 Worker Utilization = 1.0795 or 108% Number of Painters = 12 Capacity for Resource Pool (parts/hour) = 96 Worker Utilization = 0.9896 or 99.0% Number of Painters = 13 Capacity for Resource Pool (parts/hour) = 104 Worker Utilization = 0.9135 or 91.4% [By math]: Number of Painters = n Capacity for Resource Pool (chairs/hour) = 8n Worker Utilization = 95/8n < 0.95 ......... n>12.5 ............... n=13 Workers