Name:______ID:______

Operations Management II 73-431 Winter 2001

Faculty of Business Administration

University of Windsor

Midterm Exam Solution

Thursday, February 22, 1:00 – 2:20 pm

Instructor: Mohammed Fazle Baki

Aids Permitted: Calculator, straightedge, and a one-sided formula sheet.

Time available: 1 hour 20 min

Instructions:

·  This exam has 9 pages.

·  Please be sure to put your name and student ID number on each page.

·  Show your work.

Grading:

Question Marks:

1  /10

2  /4

3  /2

4  /3

5  /15

6  /6

Total: /40


Question 1: ( 10 points)

All-Weather Oil and Gas Company is planning delivery routes to four natural gas customers. The customer locations and gas requirements (in gallons) are given below:

Customer / Location / Requirements (gallons)
1 / (4,13) / 550
2 / (11,26) / 400
3 / (4,31) / 650
4 / (34,11) / 250

Assume that the depot is located at the origin of the grid and that the delivery trucks have capacity 1,200 gallons. Also assume that the cost of travel between any two locations is the straight-line (Euclidean) distance between them. Find the route schedule obtained from the savings matrix method and the nearest neighbor method.




Answer

Solution: Route of one vehicle is D-2-3-D and the route of another vehicle is D-1-4-D.
Question 2: ( 4 points)

The following matrix contains the material handling costs (in thousand dollars) associated with assigning Machines 1, 2, 3 and 4 to Locations A, B, C and D. Assign machines to locations to minimize material handling costs. State the optimal assignment and the associated cost.

Locations
Machines
/ A / B / C / D
1 / $1,400 / $1,800 / $700 / $1,000
2 / 600 / 2,200 / 1,500 / 1,300
3 / 800 / 1,100 / 1,200 / 500
4 / 1,000 / 1,800 / 2,100 / 1,500

Answer


Question 3: (2 points)

Mighty Metal Company is under a tremendous pressure to complete a government contract for 5 orders. To complete the contract, the parts must first be deburred and, then, heat treated. The processing times are as follows:

Job / Deburr / Heat Treat
1 / 2 / 3
2 / 3 / 4
3 / 6 / 1
4 / 3 / 6

Find the sequence of the jobs that minimizes makespan.

Answer

Step 1: Job 3 has the minimum processing time and the operation is on machine 2.

So, assign Job 3 to the 4th (last available) position.

Step 2: Among the remaining jobs (i.e., Jobs 1, 2, 4), Job 1 has the minimum processing time and the operation is on machine 1. So, assign Job 1 to the 1st (the first available) position.

Step 3: Among the remaining jobs (i.e., Jobs 2, 4), Job 2 (or Job 4) has the minimum processing time and the operation is on machine 1. So, assign Job 2 to the 2nd (the first available) position.

Step 4: Assign the remaining job, Job 4 to the 3rd (only available) position.

Hence, the sequence of jobs is 1, 2, 4, 3. This sequence minimizes makespan.


Question 4: (3 points)


A production facility assembles inexpensive telephones on a production line. The assembly requires 4 tasks with precedence relationships and activity times are shown below:

For each of the line balancing solutions below, determine (i) whether the solution is feasible and (ii) cycle time, if the solution is feasible.

a.  (1 point) Station 1: {A,D}, Station 2: {B,C}

Answer: This solution is not feasible because D cannot be processed before C.

b.  (1 point) Station 1: {A,C}, Station 2: {B,D}

Answer: This solution is feasible. The work-load on station 1 is 20+6=26 units and the work-load on station 2 is 18+4=22 units. Hence, the cycle time = max{22,26} = 26

c.  (1 point) Station 1: {A,B,D}, Station 2: {C}

Answer: This solution is not feasible because D cannot be processed before C.


Question 5: (15 points)

Three trucks, 1, 2 and 3 are waiting on a loading dock at XYZ Company that has only a single service bay. The trucks are labeled in the order that they arrived at the dock. Assume the current time is 1:00 pm. The times required to unload each truck and the times that the goods they contain are due in the plant are given in the table below:

Truck / Unloading Time / Time Material is Due
1 / 10 minutes / 1:30 pm
2 / 25 minutes / 1:40 pm
3 / 30 minutes / 1:50 pm

Determine the schedule for each of the rules FCFS and CR. In each case compute the mean flow time, average tardiness, and number of tardy jobs.

Answer

Question 6 (6 points)

A project has the following precedence relationships and activity times:

Activity / Activity Time (weeks) / Immediate Predecessor(s)
A / 4 / -
B / 10 / -
C / 7 / A
D / 9 / B,C

a. 
(2 points) Draw the network diagram (use activity on arc method).

b.  (2 points) Suppose that the project has another activity, E which has an activity time of 8 weeks and the only immediate predecessor of which is B. Draw the network diagram that contains all five activities A, B, C, D and E.


c.  (2 points) For the network in part a, find the critical path and its length.

Answer: There are only two paths from start to end. One is A-C-D with length 4+7+9=20 weeks and the other is B-D with length 10+9=19 weeks. The critical path is the one that is the longest. Hence, the critical path is A-C-D and its length is 20 weeks.

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