41. (7 points) A distribution center in a supply chain has the following jobs waiting to be processed. All jobs (sets of products requiring repackaging) must first be sorted into groups at one workstation, then packaged at a second workstation.
Job J1 J2 J3 J4 J5
Cleaning Time 9 4 5 3 8
Waxing Time 6 5 10 2 3
a. The distribution center would like to repackage the products for these five jobs in the shortest total time possible. What processing sequence will minimize the makespan for these jobs?
b. What is the minimum makespan for this set of five jobs?
43. (7 points) From a process known to be in control, 5 samples of 7 units each were taken at random intervals and the units in the samples were weighed. The mean (Xbar) and range (R) for each of the six samples are given in the following table.
Sample Mean Range
1 7.1 0.5
2 7.5 1.0
3 7.0 1.1
4 7.4 0.9
5 7.3 0.6
_
a. Calculate the 3? X-chart and R-chart control limits.
b. Calculate the mean (X) and range (R) for the following sample, which was taken from the same process at a later time.
Item number: 1 2 3 4 5 6 7
Weight: 7.6 7.9 8.1 7.6 7.5 7.7 8.0
44. (7 points) A company stocks a component that costs $6 per unit. Annual usage of this item is expected to be 3640 units. The firm is open for business 52 weeks per year, so weekly demand is 70 units per week, with a standard deviation of 10 units. The firm's cost accountants have estimated that it costs $80 every time an order is placed for more components, and that carrying the item in inventory costs about $15 per unit per year. Past experience with their supplier indicates that the time from ordering more items to receipt of the shipment of those items is 21 days (assume they are open 7 days per week).
a. What quantity should be ordered each time? (Assume that the EOQ assumptions apply.)
b. What is the minimum total annual cost (ordering + holding + purchase) for managing this inventory item?
c. If the company decided that their JIT program required frequent small orders and deliveries (assume that this would mean ordering a quantity of 20 units every other day, instead of the EOQ quantity on a less frequent basis), and the costs remain the same as described above, how much higher would the total annual cost be for this item?
d. If a 90% service level is required, what reorder point should be used?
45. The following table represents the set of activities required to complete a project, along with their time estimates for PERT calculations.
a. Using the data, calculate the expected time and variance for each activity.
Job Number Predecessor Job(s) a m b ET variance
A --- 1 2 3
B A 4 5 6
C A 1 4 7
D B 1 3 5
E B, C 3 4 11
F D,E 2 4 6
b. Sketch the network diagram for the project.
c. Indicate the critical path. (You can do this by inspecting the paths - you do not have to calculate ES, EF, LS, LF). What is the expected completion time for the project?
d. What is the probability that the project will take more than 19 days to complete?
46. Of the topics that we covered in this course, which one or ones were the most interesting and/or useful to you? Why?