MBAX 6843 Supply Chain & Operations Analytics - Homework 2: Sales & Operations Planning + Waiting Line Analysis
MBAX 6843 Supply Chain & Operations Analytics
Homework 2: Sales & Operations Planning + Waiting Line Analysis
- (A production problem) The Mantell Company makes softballs and baseballs. In order to make each type of ball, leather, nylon, wood chips and machine time and labor are needed. The requirements for each item and the resources available are show in the following table:
| Item | Softball | Baseball | Available |
|---|---|---|---|
| Leather | 6 ounces | 4 ounces | 6000 ounces |
| Nylon | 8 yards | 3 yards | 5000 yards |
| Wood Chips | 10 ounces | 2 ounces | 5000 ounces |
| Labor | 3 minutes | 2 minutes | 3600 minutes |
| Machine | 1 minute | 1 minute | 2000 minutes |
Softballs sell for $17 each, and baseball sell for $15 each. Formulate & solve a linear programming model that can be used to determine the number of each type of ball to produce in order to maximize revenue. • How many variables do we need in this model? • Not considering the non-negativeity constraints, how many constraints do we have in this model? • What is the maximum profit of your production plan?
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Please see “S. Ne. D” tab in “HW02” Excel File.
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Please see “UCFL” tab in “HW02” Excel File.
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Please see “FCFL” tab in “HW02” Excel File.
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An open mic night at a local café is popular on Wednesday nights. Between 8-10 p.m., a performer arrives on average every 3.5 minutes. The performers sign up on a first come, first serve basis and each performer is asked to keep their songs short. Most performers abide by this, and the average performance time is 3 minutes. Assume Poisson arrivals and exponential perform times. a) What is the utilization of the performance stage? b) What is the average time (in minutes) a performer waits to get on stage? c) On average how many performers are in the café?
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Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy, who works eight hours per day. Assume Poisson arrivals and exponential service times. a) What percentage of time is Judy idle? b) How much time, on average, does a student spend waiting in line? And in the whole system? Answer in minutes. c) How long is the (waiting) line on average? d) What is the probability that an arriving student (just before entering the Administrative Service Office) will find at least two other students waiting in line?
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(Following question 6) Suppose the school considers using a process standardization approach to improve the performance of this office, and you are asked to judge the performance of this new approach. Under the process standardization approach, the service time of Judy can be considered as deterministic instead of exponentially distributed. However, the downside of process standardization is that the service time becomes larger, to 12 minutes per student. a) What is the average waiting time in the queue and the average total time in the system after process standardization? Answer in minutes. b) Would you recommend this standardization approach?
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(Following question 6,7) Now consider an alternative process standardization approach which is not as extreme as the one in question 9. Under this alternative process standardization approach, on average, Judy can serve 5.5 students every hour, and the standard deviation of the service time is 6.5 minutes. Solve this problem using G/G/1 queue. Note that the arrival process is not changed. a) What is the average waiting time in the queue and the average total time in the system after process standardization? Answer in minutes. b) Would you recommend this standardization approach compared with the original system?
