problem set b solutions

problem set b solutions - BUSI 403 Problem Set B Fall 2008...

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Unformatted text preview: BUSI 403 Problem Set B Fall 2008 Due: 09/09/08 Problem 1 a. What is the capacity of each of the four resources in the DMV office (waiting room, control cashiers, test computer and road test administrator) in total number of customer‐arrivals per hour? Waiting room: The average time an arriving customer spends on a seat is 1 1 20 60 3 There are 9 seats in the waiting room. Thus, the capacity of waiting room is 1 9 27 1 3 The capacity of the waiting room is 27 customers per hour. Control cashiers: The average time an arriving customer spends with a cashier is: 15 5 3 40% 60% 60 60 20 With 2 control cashier in the office, they can handle 1 40 2 13.33 3 3 20 Thus, the capacity of the control cashiers is 13.33 customers per hour. Test computers: The average time an arriving customer spends at a computer is: 20 2 60% 60 10 With 2 computers in the office, they can handle 1 2 10 2 10 Thus, the capacity of the test computers is 10 customers per hour. Road test administrator: The average time an arriving customer spends with an administrator is: 6 30 60% 80% 60 25 With 4 administrators in the office, they can handle 1 BUSI 403 Problem Set B Fall 2008 Due: 09/09/08 1 100 6 10 4 8 16.67 6 25 Thus, the capacity of the road test administrators is 16.67 customers per hour. b. What is the system capacity in total number of customer‐arrivals per hour? Identify the bottleneck(s). The bottleneck is the test computers, and the system capacity is 10 customers per hour. c. The DMV office aims to serve 120 customers per day. Assume that the office opens 8 hours a day. How many additional staff should they hire to meet their objective?? The current daily system capacity is 80 And the current bottleneck is the test computers. Adding one more staff to the bottleneck resource increases the system capacity to 13.33 customers per hour, equivalently 13.33*8=106.67 customers per day, with the new bottleneck being the control cashiers. After adding one more staff to the control cashiers, the new system capacity becomes 15 customers per hour, equivalently 15*8=120 customers per day, with the test computers being the bottleneck. Therefore at least 2 more staff should be hired, 1 control cashier and 1 test computer, to achieve 120 daily capacity. 2 BUSI 403 Problem Set B Fall 2008 Due: 09/09/08 Problem 2 a. What is the system capacity in lbs of finished product per day? Where do the bottleneck(s) occur? At step A the local capacity is 2000 lbs/day. The local capacity is converted into lbs/day of finished product using the mix ratios: lbs 1 lbs 4 lbs / 7500 / of finished product 2000 5 day 3 Applying the mix ratios for the other steps in the same manner, we get the following table Step Capacity (lbs/day in local units) A B C D E F G 2000 1500 3000 4000 4500 1000 5000 Capacity (lbs/day finished product) 2000/(1/3*4/5)=7500 1500/(1/3*4/5)=5625 3000/(2/3*4/5)=5625 4000/(4/5)=5000 4500/1=4500 1000/(1/5)=5000 5000/1=5000 Total system capacity is 4500 lbs/day of finished product and step E is the system bottleneck. b. How much slack capacity is available in lbs/day at each step? Give two different slacks: measured in lbs of local product per day and in lbs of final product per day System slack: Step Capacity (lbs/day finished product) A B C D E F G Used Capacity System Slack (lbs/day finished product) (lbs/day finished product) 7500 5625 5625 5000 4500 5000 5000 4500 4500 4500 4500 4500 4500 4500 3 7500-4500=3000 5625-4500=1125 5625-4500=1125 5000-4500=500 4500-4500=0 5000-4500=500 5000-4500=500 BUSI 403 Problem Set B Fall 2008 Due: 09/09/08 Local slack Step System Slack (lbs/day finished product) A B C D E F G 3000 1125 1125 500 0 500 500 Local Slack (lbs/day local product) 3000*(1/3*4/5)=800 1125*(1/3*4/5)=300 1125*(2/3*4/5)=600 500*(4/5)=400 0 500*(1/5)=100 500*1=500 c. If the capacity at the current bottleneck is increased by 15%, how much additional system capacity in lbs of finished product per day can be gained? Where does (do) bottleneck(s) occur? After increasing capacity of E by 15%, its new capacity is 4500 *1.15 = 5175 lbs/day of finished product. Using part (a), we get the following table: Step Capacity (lbs/day in local units) Capacity (lbs/day finished product) A B C D E F G 2000 1500 3000 4000 5175 1000 5000 7500 5625 5625 5000 5175 5000 5000 The overall system capacity now increases to 5000 lbs/day, which is a gain of 500 lbs/day. The new bottlenecks will be D, F, and G, since they all have capacity of 5000 lbs/day in terms of finished product. 4 ...
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