# questions are based on linear optimization…

1. (Line balance) For a job that can be decomposed into the following 7 tasks/elements:

 Work Element Precedence Time A – 3 B A 2 C A 1 D B, C 3 E B, C 1 F E 1 G D, F 1

• Construct the precedence diagram (2 pts). Assign tasks to workstations using the “longest operation time first” heuristic (4 pts). What is the efficiency of this assembly line?

• Assign tasks to workstations using the “most number of following tasks first” heuristic (5 pts). What is the efficiency?

• Compare the results using two heuristics (i.e., part b) and c)). What is the takeaway?

• Consider this job a project, identify and specify all tasks that have slack

1. Design a layout on a 2 X 3 grid so that nonadjacent customer movement is minimized. Specify the nonadjacent load.

1. A customer order contains one unit for each of the four products produced by the company. (Hint: Theory of Constraint Scheduling)
 Machine1 Machine 2 Machine 3 A1 ? A3 5 A2 6 C1 5 B2 8 B1 4 D1 2 C2 ? C3 9 D3 4 D4 7 D2 1

• Complete the table and identify the bottleneck

• For the bottleneck machine, discuss the eligibility of each job pertaining to whether a given job can be scheduled first and why ?

• (continued from b) Which job will be your final recommendation for the bottleneck machine to first process ?

1. At Dearborn Hospital, nurses beginning a new shift. Not every nurse is equally efficient with particular kinds of patients. The Hospital has the policy that each nurse can be only assigned to one patient only and all patients need to be taken care of.

(a) Given the following patient roster and time estimates, assign nurses to patients to optimize efficiency.  Specify which nurse should be assigned to which patient (4pts) and the total time required to complete all tasks

 Time required to complete tasks Patient Nurse 1 Nurse 2 Nurse 3 Nurse 4 Mark 5 7 6 5 Helen 3 3 5 4 Joy 5 6 4 4 Andrew 6 5 5 6

(b) To ensure customer (patient) satisfaction, the Hospital also asked its patients to evaluate and indicate preferences for assignment. Reassign the nursing staff to maximize customer satisfaction (the higher the score, the better the satisfaction).  Specify which nurse should be assigned to which patient and the average customer satisfaction

 Patient’s Rating Patient Nurse 1 Nurse 2 Nurse 3 Nurse 4 Mark 88 95 83 84 Helen 89 80 96 85 Joy 87 92 82 84 Andrew 93 82 86 94

1. Compare the assignments from a) and b). Were any nurses assigned to the same patient (1pt)? What is the takeaway(s) of this comparison

1. (continued from above b; 9pts). Assume the perfect score is 100.  Complete below two tables.   Do you think the assignment using the below tables will yield the same result with that from part b)? (1pt)   If yes, discuss whether it is a coincidence.  If no, discuss what results in different assignments.
 Patient’s Rating  (2pts) Patient Nurse 1 Nurse 2 Nurse 3 Nurse 4 Mark 12 5 17 16 Helen 11 20 4 15 Joy Andrew
 Row deduction (4pts) Patient Nurse 1 Nurse 2 Nurse 3 Nurse 4 Mark Helen Joy Andrew

1. Look at the assignment from b). Do you notice any issue(s) related to this assignment approach?

1. If the Hospital can relax one constraint from its current policy to address issue(s) you observed in part e), which constraint will you relax and how would you modify the assignment? Be specific

1. If the Hospital insists that none of the policy constraints can be relaxed. Propose how the assignment algorithm can be modified to address issue(s) you observed in part e).  Be specific.

5.Jobs processed through Kibby &Strand machine shop pass through at least 3 operations: cutting, sewing, and packing. Depending on the final products, an additional task, pressing, is also needed.  Available operations time at each machine is 2400 minutes per week, and the setup time is 20 minutes.  The time (minutes) required for each of these operations per unit as well as the due date is as follows:

• Sequence the job by shortest processing time. Make a Gant chart for the cutting and pressing machines

• Make a Grant chart for the cutting and pressing machines if you were to schedule jobs following the Theory of Constraints’ approach

Compare results between b) and c).  Discuss differences between two scheduling approaches

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