SampleMidterm2Test2Solutions

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Operations Management Sample Midterm 2 Test 2 Solutions Please write your name: Instructions: 1. Write your name above on this Exam paper. 2. Answer all questions in the indicated spaces on this Exam paper. Use the back of the pre- ceding page if you need more space, and clearly indicate where your work can be found. 3. Please show all your work on this Exam paper. Your grade will depend on the clarity of your answers, the detailed reasoning that you used and the correctness of your work and answers. 4. If the answer to a sub-question depends on the answer to a previous one, you will get full credit if you give the right reasoning based on an incorrect previous response. Therefore do not skip sub-questions because you could not answer the previous ones. 5. The exam is closed book, closed notes. You may use calculators but no computer or mo- bile phone is allowed. 6. Total possible points = 100. 7. Exam duration: 1 hour and 15 minutes. 8. Stern Honor Code: “I will not lie, cheat or steal to gain an academic advantage, or toler- ate those who do”. Good Luck! Problem 1 2 3 4 5 Total Max 20 35 15 15 15 100 Points 1

1. (20 points total, 2 points each) True or False (write your answers below each statement). (a) When performing the greedy method of project crashing, it is possible to crash two or more activities on the same critical path in the same week. True. (b) The null hypothesis in statistical process control is that the process is in control. True. (c) Benchmarking improves quality by selecting best practices to use as a standard for performance. True. (d) In statistical process control, assuming that all else is held constant, if we decrease the up- per control limit on the R-chart and increase the lower control limit on the R-chart, then the probability of committing a Type I error decreases. False. This will make us more likely to say that the process is out of control and hence will increase the probability of committing a Type I error. (e) The critical path method finds the amount of time to complete the project. True. (f) When talking about quality, the 80-20 rule refers to the fact that 80% of the problems are caused by 20% of the potential causes. True. (g) The greedy method of project crashing will always produce an optimal solution. False. See the counterexample given in class. (h) A fishbone diagram is helpful in identifying the root cause of a defect. True. (i) The main goal of 6 sigma is to reduce the number of defects in manufacturing processes by reducing process variability. True. (j) Loss of customer loyalty is one of the four costs of poor quality. 2

False. The four costs of poor quality are prevention costs, appraisal costs, internal failure costs and external failure costs. 3

2. (35 points total) Best Buy has decided to open up a new store in lower Manhattan. The project of opening up a new store consists of 7 activities which are given below. The duration of each activity is given in weeks and the precedence relationships amongst each of the activities are given as well. Activity Description Immediate Predecessors Duration (weeks) A Hire Employees – 3 B Purchase Inventory – 1 C Remodel Interior A 7 D Ship & Receive Inventory B 10 E Paint Exterior A 5 F Finishing Touches E 3 G Stock the Store C,D 2 a. (10 points) Using the activity-on-arc method, label the network diagram below appropriately. Then, using the critical path method learned in class, determine the earliest start, earliest finish, latest start and latest finish time of each activity. Finally, in the table given below, list the slack of each activity. Figure 1: Network Diagram Activity Slack A 1 B 0 C 1 D 0 E 2 F 2 G 0 4

b. (5 points) What is the minimum possible amount of time that Best Buy may open its store in? Also, what are the critical activities for opening up the store and what are the critical paths for opening up the store? The minimum amount of time that Best Buy may open its store in is 13 weeks. The critical activities for opening the store are B,D and G and the critical path is B-D-G. c. (5 points) Suppose that due to a lack of cash, Best Buy is not able to simultaneously Hire Employees and Purchase Inventory at the same time. In addition, Best Buy may not simultane- ously place the Finishing Touches on the store at the same time as it Stocks the Store. Given both of these requirements, will Best Buy still be able to open its store in the amount of time given in your answer in part c above? No. If Best Buy may not simultaneously Hire Employees and Purchase Inventory at the same time and also Best Buy may not simultaneously place the Finishing Touches on the store at the same time as it Stocks the Store, then it will not be able to open its store in 13 weeks. This is because if Best Buy may not simultaneously Hire Employees and Purchase Inventory at the same time, then it must start Hiring Employees right after week 1 if it wishes to open the store in 13 weeks. However, this will require Best Buy to start placing the Finishing Touches on the store after week 9 which will cause some overlap with Stocking the Store. d. (15 points) Suppose now that Best Buy has gained some cash and is now able to simulta- neously Hire Employees and Purchase Inventory at the same time. In addition, if it wants to, Best Buy can place the Finishing Touches on the store at the same time as it Stocks the Store. However, suppose now that a competitor to Best Buy is planning on opening up a new store in lower Manhattan 10 weeks from now. For each week beyond 10 weeks from now that Best Buy opens up its store, it faces a $950 penalty. Best Buy is therefore considering crashing some of its activities in order to move up the opening date of its store. The following table details Best Buy’s options when it comes to reducing activity durations. Activity Immediate Duration Crash Duration Normal Crash Crash Cost Predecessors (weeks) (weeks) Cost Cost per Week A – 3 1 $200 $1,400 $600 B – 1 1 – – – C A 7 3 $200 $3,000 $700 D B 10 5 $500 $2,500 $400 E A 5 2 $200 $1,100 $300 F E 3 2 $100 $500 $400 G C,D 2 1 $100 $1,000 $900 Using the greedy method learned in class, crash Best Buy’s store opening project for as many weeks as it is profitable to do so. For each week of crashing, identify the activities to be crashed, the cost of crashing and the resulting critical path(s) after you have performed the crashing. If it no longer becomes profitable to crash the project, then clearly state why. You may use the following 5

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