Name:______ID:______

Operations Management II 73-431 Winter 2008

Odette School of Business

University of Windsor

Midterm Exam II Solution

Thursday, March 13, 2:30 pm – 3:50 pm

Odette Building OB B04

Instructor: Mohammed Fazle Baki

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

Time available: 1 hour 20 min

Instructions:

  • This exam has 12 pages.
  • Please be sure to put your name and student ID number on each odd numbered page.
  • Show your work.
  • State results up to four decimal places.

Grading:

QuestionMarks:

1/10

2/15

3/10

4/10

5/10

6/10

Total:/65

Question 1: (10 points) Circle the most appropriate answer

1.1Which of the following is not an input to the MRP system?

  1. Master Production Schedule
  2. Bill of Materials file
  3. Inventory file
  4. None of the above

1.2Which of the following works best if costs change over time?

  1. Lot for lot
  2. EOQ
  3. Least unit cost
  4. Part period balancing

1.3Suppose that the production requirements are 10, 13, 12, 14 in June, July, August and September. If the capacity is 12, does there exist a feasible solution? If not, what is the first month of shortage?

  1. September
  2. August
  3. July
  4. None of the above, there is a feasible solution

1.4Andon

  1. is the authority to stop production line
  2. signals quality problems
  3. makes problem visible
  4. prevents defects

1.5A make-to-stock/assemble-to-stock production system is associated with all of the following except:

  1. high volume of production
  2. standard products
  3. more variation
  4. a predictable pattern of flow of jobs through the machines

1.6Completion time is the same as flow time if

  1. all the jobs have the same due date
  2. all the jobs have the same ready time
  3. a different job has a different due date
  4. a different job has a different ready time

1.7Which rule minimizes total lateness?

  1. Shortest processing time
  2. Earliest due date
  3. Critical ratio
  4. None of the above

1.8Lawler’s is algorithm is a

  1. forward scheduling procedure
  2. backward scheduling procedure
  3. both
  4. none

1.9An extension of Johnson’s rule applies to the three-machine flow shop problem if

  1. Machine 1 dominates Machine 3
  2. Machine 3 dominates Machine 1
  3. Machine 2 dominates Machine 1
  4. Machine 1 dominates Machine 2

1.10Which of the following objectives are equivalent?

  1. Total completion time, maximum tardiness, total flow time, maximum lateness
  2. Maximum lateness, maximum tardiness, maximum completion time, maximum flow time
  3. Total flow time, total completion time, total lateness, makespan
  4. Total flow time, mean lateness, total completion time, mean flow time

Question 2: (15 points)

Each unit of A is composed of two units of B and one unit of C. Items A, B and C have on-hand inventories of 10, 20 and 40 units respectively. Item B has a scheduled receipt of 30 units in period 1, and C has a scheduled receipt of 50 units in Period 1. Lot-for-lot (L4L) is used for Item A. Item B requires a minimum lot size of 50 units. Item C is required to be purchased in multiples of 100. Lead times are two periods for Item A, and one period for each Item B and C. The gross requirements for A are 60 in Period 4, 80 in Period 7, and 90 in Period 9. Find the planned order releases for all items to meet the requirements over the next 10 periods.

  1. (3 points) Construct a product structure tree.
  1. (4 points) Consider Item A. Find the planned order releases and on-hand units in period 10

Period

/ 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Item
A
LT=2
Q=
L4L / Gross Requirements / 60 / 80 / 90
Scheduled receipts
On hand from prior period / 10 / 10 / 10 / 10 / 0 / 0 / 0 / 0 / 0 / 0
Net
requirements / 50 / 80 / 90
Time-phased Net Requirements / 50 / 80 / 90
Planned order releases / 50 / 80 / 90
Planned order delivery / 50 / 80 / 90
  1. (4 points) Consider Item B. Find the planned order releases and on-hand units in period 10.

Period

/ 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Item
B
LT=1
Q  50 / Gross Requirements / 100 / 160 / 180
Scheduled receipts / 30
On hand from prior period / 20 / 50 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0
Net
Requirements / 50 / 160 / 180
Time-phased Net Requirements / 50 / 160 / 180
Planned order releases / 50 / 160 / 180
Planned order delivery / 50 / 160 / 180
  1. (4 points) Consider Item C. Find the planned order releases and on-hand units in period 10.

Period

/ 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Item
C
LT= 1
Q=
100 / Gross Requirements / 50 / 80 / 90
Scheduled receipts / 50
On hand from prior period / 40 / 90 / 40 / 40 / 40 / 60 / 60 / 70 / 70 / 70
Net
requirements / 40 / 30
Time-phased Net Requirements / 40 / 30
Planned order releases / 100 / 100
Planned order delivery / 100 / 100

Question 3: (10 points)

A single inventory item is ordered from an outside supplier. The anticipated demand for this item over the next 5 months is 12, 15, 13, 14, 8. Current inventory of this item is 2, and the ending inventory should be 1. Assume a holding cost of $2 per unit per month and a setup cost of $80. Assume a zero lead time. Determine the order policy for this item over the next 5 months.

Use the Silver-Meal heuristic.

Net requirements: 12-2=10,15,13,14,8+1=9

Months / Q / I1 / I2 / I3 /
I4
/ I5 / Holding Cost / Ordering Cost / Per period cost
1-1 / 10 / 0 / 0 / 80 / 80
1-2 / 25 / 15 / 0 / 30 / 80 / 55
1-3 / 38 / 28 / 13 / 0 / 82 / 80 / 54
1-4 / 52 / 42 / 27 / 14 / 0 / 166 / 80 / 61.5 (stop) Q=38
4-4 / 14 / 0 / 0 / 80 / 80
4-5 / 23 / 9 / 0 / 18 / 80 / 49
  1. (5 points) Use the table above to show your computation and summarize your order policy here:

Month 1: Order 38

month 4: order 23

  1. (5 point) Use the table below to show the ending inventory that results from your order policy at the end of each of the 7 months:

Month

/ 1 / 2 / 3 / 4 / 5
Gross Requirements / 12 / 15 / 13 / 14 / 8
Beginning Inventory / 2 / 28 / 13 / 0 / 9
Net Requirements / 10 / 14
Time-phased Net Requirements / 10 / 14
Planned order Release / 38 / 23
Planned Deliveries / 38 / 23
Ending Inventory / 28 / 13 / 0 / 9 / 1>=1

Question 4: (10 points)

Three jobs must be processed on a single machine that starts at 8:30 am. The processing times and due dates are given below:

Job / Processing Time (Hours) / Due Date
J1 / 4 / 1:30 pm
J2 / 3 / 2:30 pm
J3 / 5 / 3:30 pm
  1. (7 points) Assuming that the jobs are processed in the sequence J1, J2, J3, compute makespan, total completion time, maximum lateness, and average tardiness.

Job / Start Time
(Hours) / Processing Time
(Hours) / Completion Time
(Hours) / Due Date
(Hours) / Lateness
(Hours) / Tardiness
(Hours)
J1 / 0 / 4 / 4 / 5 / -1 / 0
J2 / 4 / 3 / 7 / 6 / 1 / 1
J3 / 7 / 5 / 12 / 7 / 5 / 5
Maximum / 12 / 5 / 5
Total / 23 / 6

Makespan = 12 hrTotal completion time = 23 hr

Maximum lateness = 5 hrAverage tardiness = 6/3 = 2 hr

  1. (3 points) Find the sequence in which the jobs are processed when the critical ratio rule is applied.

Iteration 1

Current time / 0
Job / Processing Time (Hours) / Due Date (Hours) / Critical ratio
J1 / 4 / 5 / (5-0)/4 = 1.25 / Assign
J2 / 3 / 6 / (6-0)/3 = 2.00
J3 / 5 / 7 / (7-0)/5 = 1.40

Iteration 2

Current time
Job / Processing Time (Hours) / Due Date (Hours) / Critical ratio
J2 / 3 / 6 / (6-4)/3=0.67
J3 / 5 / 7 / (7-4)/5=0.60 / Assign

Final sequence:

J1 / J3 / J2

Question 5: (10 points)

Irving Bonner, an independent computer programming consultant, has contracted to complete four computer programming jobs.

Job / Time required (days) / Due date (days)
1 / 8 / 25
2 / 10 / 12
3 / 11 / 35
4 / 12 / 26

Assume that some jobs must be completed in a certain sequence because they involve program modules that will be linked. Precedence restrictions: 14 32

  1. (7 points) Using Lawler’s algorithm, find the sequence in which he should be performing the jobs in order to minimize the maximum lateness subject to the precedence constraints.

Iteration 1:

Job / Candidate? / Due date / Completion time if scheduled / Lateness if scheduled
1
2 / Yes / 12 / 41 / 41-12 = 29
3
4 / Yes / 26 / 41 / 41-26 = 15(*)

Decision in iteration 1:

4

Iteration 2:

Job / Candidate? / Due date / Completion time if scheduled / Lateness if scheduled
1 / Yes / 25 / 29 / 29-25 = 4(*)
2 / Yes / 12 / 29 / 29-12 = 17
3

Decision in iteration 2:

1 / 4

Iteration 3:

Job / Candidate? / Due date / Completion time if scheduled / Lateness if scheduled
2 / Yes / 12 / 21 / 9
3

Decision in iteration 3:

3 / 2 / 1 / 4

Final Sequence:

3 / 2 / 1 / 4
  1. (3 points) What is the maximum lateness of the sequence you found in Part a?

Job / Start
time
(days) / Time required
(days) / Completion time
(days) / Due date
(days) / Lateness
(days)
3 / 0 / 11 / 11 / 35 / -24
2 / 11 / 10 / 21 / 12 / 9
1 / 21 / 8 / 29 / 25 / 4
4 / 29 / 12 / 41 / 26 / 15

Hence, maximum lateness = 15

Question 6: (10 points)

Three jobs are to be scheduled on two machines M1 and M2. Assume that every job is first processed on M1 and then on M2. The processing times are as stated below:

Job / M1 / M2
J1 / 3 / 8
J2 / 7 / 4
J3 / 5 / 6

Find a schedule that minimizes makespan. Compute the optimal makespan.

Min 3, J1 on M1. Hence assign J1 in the beginning.  1xx

Min 4, J2 on M2. Hence assign J2 in the end.  1x2

Final sequence 1-3-2

Machine 1 / Machine 2
Start / Proc / End / Start / Proc / End
J1 / 0 / 3 / 3 / 3 / 8 / 11
J3 / 3 / 5 / 8 / 11 / 6 / 17
J2 / 8 / 7 / 15 / 17 / 4 / 21

1