MGT 3110: Exam 2 Study Guide
1.
A company has 12 items in its inventory. Using the data given below classify the items into A, B,
and C classes.
SKU
D120
E111
C140
E151
B180
B120
E149
A180
E110
A155
F120
B150
Annual usage (units)
6850
371
1292
62
12667
9625
7010
5100
258
862
1940
967
Unit $ value
1.20
8.60
13.18
91.80
3.20
10.18
1.27
0.88
62.25
18.10
0.38
2.20
2.
Herbert Adams sells bicycles. One particular model is highly popular with annual sales of 2,000
units per year. Annual holding cost is $200 per unit and the ordering cost is $40. The store is open
250 days a year.
a.
What is the economic order quantity?
b.
What is the average number of orders per year?
c.
What is the average time between orders in days?
d.
What is the annual total cost?
3.
Montegut Manufacturing produces a product for which the annual demand is 10,000. Production
averages 100 per day, while demand is 40 per day. Holding costs are $1.50 per unit per year; setup costs $200.00. If they wish to produce this product in economic batches, what size batch
should be used? What is the length of time in days to producing one lot? What is the maximum
inventory level? What is the time between orders in days? How many order cycles are there per
year? Determine the total annual inventory cost?
4.
The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D =
600 units, S = $10/order and holding cost is 30% of item price. Price is established by the following
quantity discount schedule. What should the order quantity be in order to minimize the total
annual cost?
Quantity
Unit price
5.
1 to 49
$5.00
50 to 249
$4.50
250 and up
$4.10
A warehouse store sells laser printer cartridges in bulk. The company places restocking orders
1000 boxes at a time. The annual demand is 8000 boxes. The demand during lead time is given
below. The average demand during lead time is 60 boxes. Assume holding cost of $50 per box per
year and a stock out cost of $40 per box.
Demand during lead time
Probability
40
0.1
50
0.2
60
0.2
70
0.2
80
0.2
90
0.1
Determine the least cost safety stock and the corresponding ROP.
6.
The Winfield Distributing Company has maintained an 80% service level policy for inventory of
string trimmers. Mean demand during the reorder period is 130 trimmers, and the standard
deviation is 80 trimmers. What is the value of ROP and SS?
7.
The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically
correct office chair which costs $300. The annual holding cost rate is 40%, annual demand is 600,
and the order cost is $20 per order. The store is open 300 days per year and PCE has decided to
establish a customer service level of 90%.
a.
Suppose that the lead time is a constant 4 days and the demand is variable with a standard
deviation of 2.4 chairs per day. What is the safety stock and reorder point?
b.
Suppose that the lead time is a variable with an average of 4 days and standard deviation of
3 days. Further suppose that the demand is constant. What is the safety stock and reorder
point?
c.
Suppose that the lead time is a variable with an average of 4 days and standard deviation of
3 days. Further suppose that the demand is also variable with a standard deviation of 2.4
chairs per day. What is the safety stock and reorder point?
8.
An oyster bar buys fresh oysters for $3 per pound and sells them for $10 per pound. Unsold
oyster at the end of the day is sold to a grocery store for $1.20 per pound. Determine the
pounds of oysters that must be ordered each day if the daily demand follows normal distribution
with mean of 150 pounds and standard deviation of 12 pounds.
9.
Leisure Travels, Inc. manufactures and sells Recreation Vehicles. The demand for the next four
quarters is forecasted as 160, 180, 220, and 200. The labor required to produce one unit is 100
hours. Each worker works 8 hours per day for 65 days per quarter. Regular wages is $15 per hour
and O.T. wages is $20 per hour. O.T. is limited to 20% regular hours. Limited subcontracting is
available at the rate of $2500 per unit. Holding cost per unit per quarter is $100. Cost of hiring a
worker is $350 and firing worker will cost $500. The company currently has 30 employees.
a. Determine the production rate per worker per day and per quarter.
b. Determine the regular time wage per worker per day and per quarter.
c. Determine the O.T. cost per unit.
d. Develop a “Chase” plan and the corresponding cost summary. Round up workers needed.
e. Develop a “Level” plan and the corresponding cost summary.
f. Develop a “Mixed” plan with a constant work force of 31 workers, but produce only what the
net demand is each month, i.e. not accumulate any inventory in excess of the safety stock. If
regular time capacity is not sufficient, use O.T. production first and use subcontracting only of
O.T. capacity is not enough to make up the shortage. Round to 2 decimal places.
10.
e.
Consider the following Solver model for an aggregate planning problem given in the next page.
a. What is the Solver Target cell?
b. What are the Solver changing cells?
c. What are the Solver constraints?
d. What options of Solver must be checked?
Determine the excel formula for the following cells:
B17
B18
B19
F29
G29
H29
B22
E22
B23
C26
D26
E26
B29
C29
G33
B35
B36
B37
B38
B39
B40
B41
11.
A concert organizing company wishes to study the effect of discount pricing on net revenue
generated. Currently the company charges uniform fee of $100 per ticket and has averaged 500
tickets sold. The company is considering a three tier pricing structure, (a) a deeply discounted $70
per ticket if purchased at least 1 month in advance, (b) $90 per ticket if purchase at least a week in
advance and $120 at the box office on the day of the event. The company has estimated a
demand of 300 tickets sold at least a month in advance, 200 at least a week in advance and 100 on
the day of the event. The company estimates the variable cost to be $3 per ticket under all the
three prices. Using the yield revenue approach determine what the effect of the proposed price
structure will be on net revenue.
12.
A Bill of Materials is desired for a bracket (A) that is made up of a base (B), two springs (C) and
four clamps (D). The base is assembled from one clamp (D) and two housings (E). Each clamp has
one handle (F) and one casting (G). Each housing has two bearings (H) and one shaft (I).
a. Develop a product structure tree.
b. The lead time for the parts are given below. Develop a time-phased product structure.
c. The available inventory for each part is given in the table below. Determine the net
requirement quantities of all parts required to assemble 50 units of bracket A.
Item
A
B
C
D
E
F
G
H
I
13.
Lead time
1
2
3
2
1
2
1
1
2
Available
5
5
10
20
50
150
50
5
0
A product (A) consists of a base (B) and a casting (C). The base consists of a plate (P) and three
fasteners (F). The lead time, current on-hand inventory and scheduled receipts are given below.
All components are lot for lot. The MPS requires start of production of 100 units of product A in
week 4 and 150 in week 6. Produce the MRP for the upcoming six weeks. Produce a list of all
planned order releases.
Part
B
C
P
F
14.
Lead time
1
3
2
4
Scheduled receipts
50 in week 1
20 in week 1, 30 in week 2
50 in week 1
30 in week 1, 40 in week 3
For the following item the inventory holding cost is $0.80 per week and the setup cost is $300.
Determine the lot sizes and total cost for this item under (i) Lot-for-Lot, (ii) EOQ, and (iii) POQ
methods.
Item
Week:
Gross requirement
Scheduled receipts
Projected on-hand 100
Net Requirement
Planned receipts
Planned order releases
15.
On-hand
100
30
0
0
LT =
1
100
1
2
250
3
200
4
150
5
250
6
200
7
200
8
150
Consider the following planned and actual hours of input and output.
Week ending
Planned input
Actual input
Planned output
Actual output
1
500
700
650
600
2
800
700
650
700
3
700
700
650
800
4
600
800
650
700
5
600
600
650
650
6
800
500
700
500
Prepare the Input/Output Control chart for this workstation. Assume an initial actual backlog of
120 hours and zero for the two cumulative deviations.
16.
The following jobs are waiting to be processed on day 50
Job
Production days needed
Date job due
A
30
90
B
20
215
C
40
175
D
35
180
Sequence the jobs in the order of SPT, EDD, and Critical Ratio, and compute (i) Average flow time,
(ii) Average lateness, (iii) Average number of jobs in the system, and (iv) Utilization, for each of the
three schedule of jobs.
17.
An antique restoration operation uses a two-step sequence that all jobs in a certain category
follow. For the group of jobs listed.
a. Find the sequence that will minimize total completion time.
b. Determine the amount of idle time for workstation 102.
c. What jobs are candidates for splitting‘? Why? If they were split, how much would idle time
and makespan time be reduced? Assume the very first job can be split 50% and the remaining
jobs can be spit 60%.
JOB TIMES (minutes)
Workstation 101
Workstation 102
A
27
45
B
18
33
C
70
30
D
26
24
E
15
10
Answers
1.
No. SKU
1 B120
2 B180
3 C140
4 E110
5 A155
6 E149
7 D120
8 E151
9 A180
10 E111
11 B150
12 F120
Annual
usage
(units) Unit $ value
9625
10.18
12667
3.20
1292
13.18
258
62.25
862
18.10
7010
1.27
6850
1.20
62
91.80
5100
0.88
371
8.60
967
2.20
1940
0.38
Annual Dollar
volume
97,982.50
40,534.40
17,028.56
16,060.50
15,602.20
8,902.70
8,220.00
5,691.60
4,488.00
3,190.60
2,127.40
737.20
220565.66
2.
D = 2000, No. of days = 250, H = $200, S = $40
a.
EOQ =
Dollar %
44.4%
18.4%
7.7%
7.3%
7.1%
4.0%
3.7%
2.6%
2.0%
1.4%
1.0%
0.3%
100%
Cum. %
for $
44.4%
62.8%
70.5%
77.8%
84.9%
88.9%
92.6%
95.2%
97.3%
98.7%
99.7%
100.0%
2(2000)40
 28
200
b.
N = D/Q = 2000/28 = 71.4
c.
d = D/No. of days per year = 2000/250 = 8, T = Q/d = 28/8 = 3.5 days
d.
Annual total cost = (D/Q)S + (Q/2)H = (2000/28)40 + (28/2)200 = $5,657
3.
D = 10,000, H = $1.50, S = $200, p = 100/day, d = 40/day
EPQ = √
2𝐷𝑆
𝑑
𝑝
𝐻(1− )
2(10000)200
=√
1.50(1−
40
)
100
= 2108
Production time = Q/p = 2108/100 = 21.08 days
Imax = (Q/p)(p - d) = (2108/100)(100 - 40) = 1264.80
Average number of orders per year = D/Q = 10000/2108 = 4.74
Time between orders = Q/d = 2108/40 = 52.7 days
Cum. % for
no. of items
8.3%
16.7%
25.0%
33.3%
41.7%
50.0%
58.3%
66.7%
75.0%
83.3%
91.7%
100.0%
Class
A
A
B
B
B
B
C
C
C
C
C
C
Annual holding cost = (Imax/2) x H = (1264.80/2) x 1.50 = $948.60
Annual setup cost = (D/Q) x S = (10000/2108) x 200 = $948
Total cost = 948.60 + 948 = $1,896.60
4.
D = 600
Q
S = 10
Price Holding cost
1 - 49
5.00
1.50
50 - 249
250 &
above
4.50
1.35
4.10
1.23
Q
1 – 49
50 - 249
>= 250
EOQ =
Holding cost = 30%
Formula Q
Candidate Q
Formula Q > upper limit -89 not a candidate
Formula Q is within range, =
94 Candidate Q = Formula Q
Formula Q < lower limit,
99 Candidate Q = lower limit
Price Candidate Q Ordering cost
5.00
4.50
94
63.83
4.10
250
24.00
250 @ P = $4.10
Holding cost
63.45
153.75
5. Number of orders per year = 8000/1000 = 8, H = $50, Cs = $40
Safety
ROP
stock
Carrying cost
Expected stock out
60
0
0
(10x.2 + 20x.2 + 30x.1) = 9
70
10
10 x $50 = $500 (10x.2 + 20x.1) = 4
80
20
20 x $50 = $1000 (10x.1) = 1
90
30
30 x $50 = $1500 0
94
250
Item cost
Total cost
2700
2460
2827.28
2637.75
Stock out cost/year
9 x 8 x 40 = $2,880
4 x 8 x 40 = $1,280
1 x 8 x 40 = $320
$0
Least cost safety stock = 20, ROP = 80
6.
Given dL = 130, dLT = 80, and for 80% service level, Z = 0.84
ROP = 130 + 0.84 x 80 = 197.2, or round up to 198 for at least 80% service level
7.
d = D/No. of days per year = 600/300 = 2 per day, Z for 90% service level = 1.285
a.
Given: L = 4 days Constant, d = 2.4 per day, therefore dLT = 2.4 √4 = 4.8
Safety stock = Z dLT = 1.285 x 4.8 = 6.2 or 7 (round up for at least 90% service level)
ROP = dL + SS = (2 chairs/day * 4) + 7 = 15
b.
Given: L = 4 days with L = 3 and demand is constant, dLT = 2 (3) = 6
Safety stock = Z dLT = 1.285 x 6 = 7.7 or 8 (round up for at least 90% service level)
Total cost
$2,880
$1,780
$1320
$1500
ROP = dL + SS = (2 chairs/day * 4) + 8 = 16
c.
Given: L = 4 days with L = 3 , and d = 2.4 per day,
therefore dLT = √4(2.4)2 + 22 32 = 7.684
Safety stock = Z dLT = 1.285 x 7.684 = 9.9 or 10 (round up for at least 90% service level)
ROP = dL + SS = (2 chairs/day * 4) + 10 = 18
8.
Cs = Lost profit = Selling price per unit – Cost per unit = 10 – 3 = $7
Co = Cost/unit – salvage value/unit = 3 – 1.20 = $1.80
Optimum service level = 7/(7 + 1.80) = 0.795 = 79.5%
From normal table, for 79.5% service level, Z = 0.83
Stock =  + Z  = 150 + 0.825 (12) = 159.9 or 160
9.
Hiring cost/worker =
350
Worker hours/quarter =
520
Firing cost/worker =
500
Standard hours/unit =
100
RT Wage/hour =
15
Holding cost =
100
OT wage rate/hour =
20
Sub-contracting cost/unit =
2500
a. Production rate/worker/day = 8 hours per day/100 hours per unit = 0.08 per worker/day
Production rate/worker/quarter = 0.08/worker/day x 65 days/quarter = 5.2/worker/ quarter
b. Wage rate per worker per day = $15/hour x 8 hours/day = $120
Wage rate per worker per quarter = $15/hour x 8 hours/day x 65 days/quarter = $7800
c. OT cost/unit = $20/hour x 100 hours/unit = $2000
d. Chase plan
Period
Demand
Production
required
1
2
3
4
160
180
220
200
160–(0–0) =
160
180
220
200
Cost summary
Regular wages
O.T. cost =
S.C. cost
Hiring cost
Firing cost
Carrying cost
Total cost
Workers
needed
Workers needed
(Rounded)
30
160/5.2=30.77
180/5.2=34.62
220/5.2=42.31
200/5.2=38.46
31
35
43
39
148
148 workers-quarters x $7800 =
13 workers x $350 =
4 workers x $500 =
Hired
Fired
workers workers
1
4
8
0
13
0
0
0
4
4
1,154,400
4,550
2,000
$1,160,950
e. Level Plan
Sum of demand = 760
Average demand = 760/4 = 190 i.e. = production per quarter
Period
Demand
1
2
3
4
160
180
220
200
RT Production
E.I.
0
30
40
10
0
190
190
190
190
No. of workers needed = 190/5.2 = 36.54 or 37
Cost summary
Regular wages
37 workers x 4 quarters x $7800 =
Hiring cost
(37 workers – 30 workers) x $ 350 =
Firing cost
Carrying cost
80 x $100 =
Total cost
1,154,400
2,450
8,000
$1,164,850
f. Mixed Plan
No. of workers = 31
Production per quarter with 31 workers = 31 x 5.2 = 161.2
O.T. capacity/quarter = 161.2 x 20% = 32.2
Period
1
2
3
4
Demand
160
180
220
200
Shortage
160 – 160=0
180-161.2=18.8
220-161.2=58.8
200-161.2=38.8
Cost summary
Regular wages
O.T. cost =
S.C. cost
Hiring cost
Firing cost
Carrying cost
Total cost
Production capacity
161.2
161.2
161.2
161.2
O.T Capacity
32.2
32.2
32.2
32.2
RT Production
Min(160,161.2) =160
Min(180,161.2) =161.2
Min(220,161.2) =161.2
Min(200,161.2) =161.2
643.6
O.T. Production
0
Min(18.8,32.2) = 18.8
Min(58.8,32.2)=32.2
Min(38.8,32.2)=32.2
82.8
31 workers x 4 quarters x $7800 =
82.8 units x $2000
33.6 units x $2500 =
(31 – 30) x $350 =
S.C.
0
0
58.8 – 32.2=26.8
38.8 - 32.2=6.8
33.6
967,200
165,600
84,000
350
$1,217,150
10.
B17
B18
B19
B22
E22
B23
C26
D26
E26
B29
C29
(B13*B12)/B11
B13*B3*B12
B11*B4
E11
B22+C22-D22
E22
SUM(C22:C25)
SUM(D22:D25)
SUM(E22:E25)
E12
E22*$B$17
F29
G29
H29
G33
B35
B36
B37
B38
B39
B40
B41
E4
SUM(B29:E29)-F29
C29*$B$14
SUM(G29:G32)
E26*B18
D33*B19
E33*B5
C26*B7
D26*B8
G33*B6
SUM(B35:B40)
a. B41
b. C22:D25, D29:E32
c. D29:D32 <= H29:H32
G29:G32 >= E13
C22:D25 = Integer (if needed)
D29:E32 = Integer (if needed)
d. Changing cells non-negative
Simplex LP
11. Current pricing:
Price = $100
Demand = 500
Revenue = 500 x $100 = 50,000
Variable cost = $3 x 500 = 1500
Net revenue = 50,000 – 1,500 = $48,500
Proposed pricing:
Price
Demand
Revenue
70
300
21000
90
200
18000
120
100
12000
Total revenue = 51000
Variable cost = $3 x 600 tickets sold = 1800
Net revenue = 51,000 – 1,800 = $49,200
12. (a)
A
B
C2
D1
F
D4
E2
G
H2
I
F
G
(b).
F
D
G
B
H
E
I
C
A
F
D
G
1
2
3
4
5
Lead time = 7 weeks
(c)
Part
A
B
C
D
E
F
G
H
I
Gross
50
1 x A = 45
2 x A = 2 x 45 = 90
4 x A + 1 x B = 4 x 45 + 40 = 220
2 x B = 80
1 x D = 200
1 x D = 200
2 x E = 2 x 30 = 60
1 x E = 30
Available
5
5
10
20
50
150
50
5
0
Net
50 – 5 = 45
45 – 5 = 40
90 – 10 = 80
220 – 20 = 200
80 – 50 = 30
200 – 150 = 50
200 – 50 = 150
60 – 5 = 55
30 – 0 = 30
6
7
13.
1
2
3
MPS start for A
Item B GR =
Week:
Gross requirement
Scheduled receipts
Projected on-hand
100
Net requirement
Planned receipts
Planned order releases
Item C
Week:
Gross requirement
Scheduled receipts
Projected on-hand
30
Net requirement
Planned receipts
Planned order releases
Item P
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Net requirement
Planned receipts
Planned order releases
Item F
Week
Gross requirement
Scheduled receipts
Projected on-hand
Net requirement
Planned receipts
Planned order releases
0
0
Lead time =
3
0
2
0
4
100
5
6
150
4
100
5
0
6
150
1
1
0
50
100
150
150
150
50
0
0
0
0
0
0
0
0
0
100
50
100
100
0
4
100
5
0
6
150
0
0
150
80
20
20
0
0
0
0
150
150
0
Lead time =
3
0
4
0
5
100
6
0
50
50
50
0
0
1
0
20
30
2
0
30
50
0
20
0
0
Lead time =
3
0
80
2
0
3
2
1
0
50
0
50
50
50
0
0
0
0
0
50
0
0
0
0
1
0
30
0
Lead time =
2
3
0
0
40
30
30
4
0
5
300
6
0
70
0
0
230
0
0
0
0
70
230
230
0
Planned order releases:
A has releases of 100 in week 4, 150 in week 7
B has a release of 100 in week 5
C has releases of 20 in week 1, 150 in week 3
P has a release of 50 in week 3
F has a release of 230 in week 1
0
0
4
0
0
14. (i) L-4-L
Item
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Net Requirement
Planned receipts
Planned order releases
100
No. of setup =
Carrying cost =
Setup cost = 7 x $300 =
Total cost =
LT =
1
100
1
2
250
3
200
4
150
5
250
6
200
7
200
8
150
100
0
0
250
0
250
250
200
0
200
200
150
0
150
150
250
0
250
250
200
0
200
200
200
0
200
200
150
0
150
150
0
5
250
0
150
100
375
0
6
200
0
275
0
0
375
7
200
0
75
125
375
0
8
150
0
250
0
0
0
7
0
2100
2100
(ii) EOQ:
Total demand for 8 weeks = 1500, d = 1500/8 = 187.5
H = $0.80/week
S = 300
2(187.5)300
0.8
Q= √
Item
Week:
Gross requirement
Scheduled receipts
Projected on-hand
Net Requirement
Planned receipts
Planned order releases
= 375
100
LT =
1
100
0
100
0
0
375
1
2
250
0
0
250
375
375
3
200
0
125
75
375
0
4
150
0
300
0
0
375
Setup cost per week = (d/Q) S = (187.5/375) x 300 =
Holding cost per week = (Q/2)H per week = (375/2) x 0.80 =
Total cost per week= 150 + 150 =
Cost for 8 weeks = Total cost per week x 8 weeks = 300 x 8 =
(iii) POQ
No. of periods = EOQ/d = 375/187.5 = 2 weeks
Item
LT =
1
Week:
1
2
Gross requirement
100
250
Scheduled receipts
0
0
Projected on-hand 100
100
0
Net Requirement
0
250
Planned receipts
0
450
3
200
0
200
0
0
4
150
0
0
150
400
150
150
300
2400
5
250
0
250
0
0
6
200
0
0
200
400
7
200
0
200
0
0
8
150
0
0
150
150
Planned order releases
450
No. of setup =
Setup cost = 4 x $300 =
Sum of ending inventory
Carrying cost = 650 x 0.8 =
Total cost =
#15.
Week ending
Planned input
Actual input
Cumulative deviation
Planned output
Actual output
Cumulative deviation
Backlog
400
400
150
4
1200
650
520
1720
120
1
500
700
200
650
600
-50
220
2
800
700
100
650
700
0
220
3
700
700
100
650
800
150
120
4
600
800
300
650
700
200
220
5
600
600
300
650
650
200
170
6
800
500
0
700
500
0
170
#16. SPT
Processing
time (Days)
20
30
35
40
125
Job
B
A
D
C
Average flow time =
Average lateness =
Average WIP =
Utilization =
Days till due
date
165
40
130
125
Completion time
(Flowtime)
20
50
85
125
280
Lateness
0
10
0
0
10
70
2.5
2.240
44.6%
EDD
Job
A
C
D
B
Processing
time (Days)
30
40
35
20
125
Days till due
date
40
125
130
165
Average flow time =
Average lateness =
Average no. of jobs in the system =
Utilization =
82.5
0
2.640
37.9%
Completion time
(Flowtime)
30
70
105
125
330
Lateness
0
0
0
0
0
CR
Job
A
B
C
D
Processing time
30
20
40
35
Processing
time (Days)
30
40
35
20
125
Job
A
C
D
B
Date job due
90
215
175
180
Days till due
date
40
125
130
165
Average flow time =
Average lateness =
Average no. of jobs in the system =
Utilization =
Due date
40
165
125
130
CR
1.333333
8.25
3.125
3.714286
Completion time
(Flowtime)
30
70
105
125
330
Lateness
0
0
0
0
0
82.5
0
2.640
37.9%
#17. JOB TIMES (minutes)
A
27
45
Workstation 101
Workstation 102
Job
B
A
C
D
E
B
18
33
a. Schedule: B – A – C – D – E
Workstation 101
Processing time
Finish time
18
18
27
45
70
115
26
141
15
156
C
70
30
D
26
24
E
15
10
Workstation 102
Processing time Start time
Finish time
33
18
51
45
51
96
30
115
145
24
145
169
10
169
179
Idle time
18
0
19
0
0
37
b. Total idle time for workstation 102 is 37 minutes
B
A
C
18
45
Idle
B
20
A
Idle
51
30
40
E
115
18
10
D
50
96
60
70
80
90
100
141
D
C
115
110
156
120
145
130
140
150
160
E
169
179
170
180