Name (print, please) _______________________________________________ ID ___________________________
Production Management 73-604 Fall 2004
Odette School of Business
University of Windsor
Midterm Exam 2 Solution
Thursday, November 25, 5:30 – 6:50 pm
Instructor : Mohammed Fazle Baki
Aids Permitted : Calculator, straightedge, and a two-sided formula sheet.
Time available : 1 hour and 20 minutes
Instructions:

This exam has 14 pages including this cover page and two pages of tables

Please be sure to put your name and student ID number on each page.

Show your work.
Grading:
Question
1
Marks:
/10
2
3
4
/10
/10
/10
7
8
5
6
/10
/5
/5
/5
Total: /65

Name:_________________________________________________ ID:_________________________
Question 1: (10 points)
Multiple choice questions (circle the most appropriate answer)
1.1
Two questions in inventory planning and control are: a. How to count and when to count b. How to order and when to order c. How much to sell and when to sell d. How much to order and when to order
1.2 If order size is more than EOQ, then the annual ordering cost is a. more than the annual holding cost b. less than the annual holding cost c. equal to the annual holding cost d. b and c
1.3 The single-period inventory model is suitable for a. flowers b. light bulbs c. washing machines d. prescription drugs
1.4 Which of the following assumptions are used in the EOQ model? a. Ordering costs is constant b. Demand for the product is uniform throughout the period c. Lead time is constant d. All of the above
1.5 The fixed-time period models (P-models) require a. a higher level of safety stock b. a continual tracking of inventory on hand c. kanbans d. a and b
2

Name:_________________________________________________ ID:_________________________
1.6 Which of the following Priority Rules used in scheduling the sequence of production is calculated as the difference between the time remaining before the due date minus the processing time remaining, where the smallest value is run first? a. STR b. CR c. SOT d. LCFS
1.7 Assume you have a job to sequence using Johnson’s Rule. The job requires 7 hours to assemble and then is followed by 8 hours in the painting department. Which is of the following is where you would schedule the job? a. As late as possible in the unfilled job sequence b. As early as possible in the unfilled job sequence c. Does not matter, early or late d. Since it involves work in two departments, Johnson’s Rule does not apply
1.8 Jidoka a. prevents defects b. allows for planning, problem solving & maintenance c. is the authority to stop a production line d. makes problems visible
1.9 If Inventory costs change over time, use the following lot sizing technique: a. L4L b. EOQ
c. LUC d. LTC
1.10 The objectives of scheduling include which of the following? a. Minimize work-in-process inventory b. Minimize lead time c. Minimize due date
d. All of the above
3

Name:_________________________________________________ ID:_________________________
Question 2: (10 points) The weekly demand for a product is 500 units with a standard deviation of
100 units. The cost to place an order is $25, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $5.2 per unit. a. (5 points) Compute the optimal order quantity.
Q

2 DS

H
2

500

52
5 .
2

500 units
1 point for each of the formula, D, S, H and the final answer. b. (5 points) Compute the reorder point necessary to provide a 97 percent service probability.
For a 97 percent service probability, the area under the normal distribution curve on the left side of z , F
 

0 .
97
Hence, look for area = 0.97-0.50 = 0.47 in the standard normal table
From the standard normal table, z

1 .
88 for area = 0.47.
Hence, R
 d L
 z

L

500

4

1 .
88

100 4

2 , 376 units
1 point for each of the formula, d L , z ,

L
and the final answer.
Question 3: (10 points) University Drug Pharmaceuticals orders its antibiotics every three weeks (21 days) when a salesperson visits from one of the pharmaceutical companies. Tetracycline is one of the most prescribed antibiotics, with average daily demand of 2,000 capsules. The standard deviation of daily demand was derived from examining prescriptions filled over the past three months and was found to be 500 capsules. It takes four days for the order to arrive. University Drug would like to satisfy 98 percent of the prescriptions. The salesperson just arrived, and there are currently 10,000 capsules in stock? Compute an optimal order size.
T

21 days, L

4 days
For a 98 percent probability of not stocking out, the area under the normal distribution curve on the left side of z , F
 

0 .
98
Hence, look for area = 0.98-0.50 = 0.48 in the standard normal table
From the standard normal table, z

2 .
055 for area = 0.48.
Q
 d

T

L

 z

T

L

I

2 , 000

21

4


2 .
055 21

4

10 , 000

45 , 137 .
5 units
2 point for each of the formula, d

T

L

, z ,

T

L
and the final answer.
4

Name:_________________________________________________ ID:_________________________
Question 4: (10 points) A purchasing agent for a particular type of silicon wafer used in the production of semiconductors must decide among three sources. Source A will sell silicon wafers for
$2.50 per wafer, independently of the number of wafers ordered. Source B will sell the wafers for
$2.25 each but will not consider an order for fewer than 3,000 wafers, and source C will sell the wafers for $2.20 each but will not accept an order for fewer than 9,000 wafers. Assume an order setup cost of $50 and an annual requirement of 20,000 wafers. Assume a 20 percent annual interest rate for holding cost calculations. Which source should be used, and what is the size of the standing offer? What is the optimal value of the holding cost, setup cost and buying cost for wafers when the optimal source is used?
Source
A
B
C
Quantity
0-2,999
3,000-8,999
9,000+
Unit Price c
1

2 .
50 c
2

2 .
25 c
3

2 .
20

First, consider the cheapest price level of c
3

$2.20 per unit.
H
3

Ic
3

0 .
20

2 .
2

$ 0 .
44 /unit/year
EOQ
3

2 DS

H
3
2

20 , 000
0 .
44

2 , 132 .
01 units
Since the price level of c $2.20 is not available for an order quantity Q

3

EOQ
3
is infeasible and a candidate for optimal order quantity is Q
3

9 , 000
EOQ
3
= 2,132 units,
, because 9,000 is the minimum order quantity for the price level of c
3

$2.20.

Now, consider the next price level, c
2

$2.25 per unit. H
2

Ic
2

0 .
20

2 .
25

$ 0 .
45 /unit/year
EOQ
2

2 DS
H
2

2

20 , 000
0 .
45

2 , 108 .
19 units
Since the price level of c
2

$2.25 is available for an order quantity Q

EOQ
2 is feasible and a candidate for optimal order quantity is Q
2

3 ,
EOQ
000
2
= 2,108 units,
, because 3,000 is the minimum order quantity for the price level of c
2

$2.25.

Now, consider the next price level, c
1

$2.5 per unit. H
1

Ic
1

0 .
20

2 .
5

$ 0 .
50 /unit/year
EOQ
3

2 DS
H
3

2

20 , 000
0 .
50

2 , 000 units
Since the price level of c
1

$2.5 is available for an order quantity Q
 is feasible and a candidate for optimal order quantity is Q
1

2 , 000 .
EOQ
1
= 2,000 units, EOQ
1
2 points up to this
5

Name:_________________________________________________ ID:_________________________
Use this page, if necessary

Now, compute total cost for each candidate for optimal order quantity:
Candidate Holding cost Ordering cost Cost of item Total cost j
Q j
H j
Q j
2
DS
Q j
Dc j
Holding cost +
Ordering cost +
Cost of item
3
2
1
Q
3

9 , 000
(2 points)
Q
2

3 , 000
(2 points)
Q
2

2 , 000
(2 points)
0

.
44

2
1 , 980
9 , 000
0 .
45

3 , 000

675
2
0 .
50

2 , 000

500
2
20 , 000

50
9 , 000

111 .
11
20 , 000

50
3 , 000

333 .
33
20 , 000

50
2 ,

500
000

20 , 000

2 .
2

20 , 000

44 , 000
20 , 000

2 .
25
45 , 000

2 .
5
50 , 000
$46,091.11
$46,008.33
$51,000

Conclusion: The total cost is minimum, $46,008.33 for quantity is Q
2

3 , 000 from Source B. (2 points)
Q
2

3 , 000 . Therefore, an optimal order
6

Name:_________________________________________________ ID:_________________________
Question 5: (10 points) Each unit of A is composed of three units of B and two units of C. Items A,
B and C have on-hand inventories of 35, 30 and 50 units respectively. Item B has a scheduled receipt of 40 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 one period for each of the Items A, B and C. The gross requirements for A are 30 in Period 2, 25 in Period 5, and
70 in Period 8. Find the planned order releases for all items to meet the requirements over the next
10 periods. a. (3 points) Construct a product structure tree.
B(3)
A
C(2) b. (3 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
30 25 70 Item
A
LT=
1
Q=
L4L
Gross
Requirements
Scheduled receipts
On hand from prior period
Net requirements
Time-phased Net
Requirements
Planned order releases
Planned order delivery
35 35 5 5
20
20
5
20
20
0 0
70
70
0
70
70
0 0
(Continued…)
7

Name:_________________________________________________ ID:_________________________ c. (2 points) Consider Item B. Find the planned order releases and on-hand units in period 10.
Period
Item
B
LT=
1
Q >=
50
Gross
Requirements
Scheduled receipts
On hand from prior period
Net
Requirements
Time-phased Net
Requirements
Planned order releases
1
40
30
2
70
3
70
4
20(3)
= 60
70
5
10
6
10
200
200
7
70(3)
= 210
10
200
8
0
9
0
10
0
Item
C
LT=
1
Q=
100
Planned order delivery
200 d. (2 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
Gross
Requirements
Scheduled receipts
On hand from prior period
Net requirements
Time-phased Net
Requirements
Planned order releases
50 50
20(2)
= 40
50 50 10
70(2)
= 140
10
130
200
10
130
70 70 70
Planned order delivery
200
8

Name:_________________________________________________ ID:_________________________
Question 6: (5 points) A single inventory item is ordered from an outside supplier. The anticipated demand for this item over the next 7 months is 13, 11, 14, 12, 7, 8, 5. Current inventory of this item is
3, and the ending inventory should be 4. Assume a holding cost of $2 per unit per month and a setup cost of $75. Assume a zero lead time. Determine the order policy for this item over the next 7 months.
Use the Least Unit Cost (LUC) heuristic.
First, compute net requirements. Subtract beginning inventory from the demand of the first month and add ending inventory to the demand of the last month. So, the net requirements over the next 7 months are: 13-
3=10, 11, 14, 12, 7, 8,= and 5+4=9.
Months Q
(1 point)
I1 I2 I3 I4 I5 I6 I7 Holding cost
(1 point)
Ordering cost
Unit Cost
(1 point)
1 to 1 10 0 0 75 7.5
1 to 2 21 11 0 22 75 4.6190
1 to 3 35 25 14 0 78 75 4.3714
(1 point)
1 to 4
4 to 4
47
12
37 26 12 0
0
150
0
75
75
4 to 5 19
27
7 0
15 8 0
14
46
75
75 4 to 6
(1 point)
4 to 7 36 24 17 9 0 100 75
7 to 7 9 0 0 75
Use the table above to show your computation and summarize your order policy below:
Month
1
4
7
Order
35
27
9
4.7872
6.25
4.6842
4.4815
4.8611
8.3333
9

Name:_________________________________________________ ID:_________________________
Question 7: (5 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
J2
4
2
12:30 pm
1:30 pm
J3 1 4:30 pm
Assuming that the jobs are processed in the sequence J1, J2, J3, compute makespan, total completion time, maximum lateness, and average tardiness.
Job j
Start Time
(Hours)
Processing
Time
(Hours)
Completion
Time
(Hours)
C j
Due Date
(Hours) d j
Lateness
(Hours)
L j

C j
 d j
Tardiness
T j

(Hours) max
  j
J1 0 4 4 4 0 0
5
8
1
-1
1
0
J2 4 2
J3 6 1
Makespan = C max
 max(4, 6, 7) = 7 hours
6
7
Total completion time =

C j

4 + 6 + 7 = 17 hours
Maximum lateness = L max
 max( 0, 1, -1) = 1 hour
Average tardiness = T

0

1

0
3

0 .
3333 hour
10

Name:_________________________________________________ ID:_________________________
Question 8: (5 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 follows:
Job M1 M2
J1
J2
7
4
5
8
J3 9 6 a. (3 points) Using Johnson’s algorithm for two-machine flow-shop, find a sequence of jobs in order to minimize makespan. In each iteration, show the job you assign and position to which the job is assigned.
Iteration 1: Show which job is assigned to which position in iteration 1
1
J2
Positions
2 3
Iteration 2: Show which job is assigned to which position in iteration 2
Positions
1 2 3
J1
Iteration 3: Show which job is assigned to which position in iteration 3
Positions
1 2
J3
3 b. (2 points) Compute makespan given by the sequence obtained in part a .
Job
J2
J3
Start
0
4
J1 13
Hence, makespan = 25
M1
Process
4
9
7
Finish
4
13
20
Start
4
13
20
M2
Process
8
6
5
Finish
12
19
25
11