Ex 1 – Exercise on customer service levels

1. Draw a graph

2. Interpret the drawn lines

Both expected revenue and anticipated costs increase as customer service level rises.
When customer service level < 54%, ABC bank is expected to suffer loss as anticipated costs are higher than
expected revenue.
When customer service level > 54%, ABCbank is expected to enjoy profit as expected revenue is higher than
anticipated costs.
 When customer service level < 85%, the slope expected revenue is bigger than anticipated costs, which
resulted in an increase of profit.
 When customer service level > 85%, the slope expected revenue is smaller than anticipated costs, which
resulted in an decrease of profit.
 When customer service level up to 85%, the expected revenue increase outpaces the rise in anticipated
costs, making this range more cost-efficient.
⇒ This highlights the importance of balancing customer service levels with cost management to maximize
efficiency and profit.
3. The bank ABC should establish the customer service levels at 85% to maximize its profitability at 4.2
million USD.
Customer Service levels
50 60 70 80 85 90 95 100
(%)
Expected Revenue
4,8 8,0 10 11 12,5 12.8 12.9 13.5
(million USD)
Anticipated Costs
5,8 6,0 6,6 7,4 8,3 10.5 11.8 13.3
(million USD)
 Profit -1.0 2.0 3.4 3.6 4.2 2.3 1.1 0.2
4. Three factors influencing the customer service levels of Bank ABC could include:
 Technology Infrastructure: Efficient systems for account management, loan processing, and transaction
handling impact the quality and speed of service.
 Employee Expertise and Training: Skilled staff equipped to handle customer queries and provide
personalized assistance ensure higher service levels.
 Customer Expectations: The level of service customers demand and expect, based on market standards
and competition, influences the service level the bank must maintain.

Ex 2 – Exercise on transportation decisions

Situation:
A manufacturing company needs 250 components per day (d), the cost of purchasing a unit of this component
product is $4.5 (C), and the purchased components stored in the warehouse cost an estimated 25% (I) of the
total storage cost. To ensure continuous production, the company determines an average safety reserve of
15,000 units (Q/2) of components. The company operates 300 days a year (T). Currently, the company is
considering 2 forms of transportation with the relevant parameters given in the following table:
Forms of Cost per shipping Shipping time to the company's Frequency of Average safe reserve units
transport unit ($/dvsp) (R) warehouse (days) (T) trips in the year of components (Q/2)
Truck 0.3 6 20 7,500
Train 0.1 25 10 15,000
Question: Please tell us which transportation option the company will choose.
To answer the question above, we compute the following steps
 Step 1: Expected volume to be shipped in a year: D = d.T (number of working day)
 Step 2: Transportation cost: R.D
 Step 3: In-transit inventory cost: (I.C.D.T)/365
 Step 4: Source inventory cost: I.C.Q/2
 Step 5: Destination inventory cost: I.(C+R).Q/2
 Step 6: Total cost for each form of transport = Sum of Transportation cost, in-transit inventory cost,
source inventory cost and destination inventory cost.
SOLVE
 The total product demand for a year (Nhu cầu sản phẩm/ năm) = D = d.T = 250 x 300 = 75000 (units)

⇒ Average inventory of truck is 15,000/(20/10) = 7,500 (units)

 Average inventory of train (Q/2) = 15,000 (units)

⚠️(20/10) = Frequency of trips in the year of truck / Frequency of trips in the year of train
Cost type Method of computation Truck Train
Transportation = 0.3 x 75,000 = 0.1 x 75,000
RxD
(Chi phí vận tải) = 22,500 = 7,500
In-transit inventory = (0.25 x 4.5 x 75000 x = (0.25 x 4.5 x 75000 x
(Chi phí dự trù trên đường) (ICDT)/365 6) / 365 25) / 365
= 1,387 = 5,779
Plant inventory = 0.25 x 4.5 x 7500 = 0.25 x 4.5 x 15000
ICQ/2
(Chi phí dự trù tại nguồn) = 8,437.5 = 16,875
 Field inventory = 0.25 x 4.8 x 7500 = 0.25 x 4.6 x 15000
I(C+R)Q/2
(Chi phí dự trù tại đích) = 9,000 = 17,250
Total $41,324.5 $47,404
Situation
ABC company needs 2500 materials units for their production (labelled as “d”). The buying price of
each materials unit is 45$ (labelled as “C”), the holding cost for this type of materials accounts for 25% of
total purchasing costs (labelled as “I”), the average quantity of materials being stocked in warehouses is
150,000 units (labelled as “Q/2”), and this company operates 300 days in a year (labelled as “T”). ABC
company is negotiating with a logistics service provider and receives a detailed information about rates and time
across different modes of transport. See table below.
Transport modes Rates ($/unit) Time to complete (days) Number of shipments per year (n)
Train 0.1 25 10
Semi-trailer 0.15 16 20
Truck 0.3 6 20
Plane 1.2 2 40
SOLVE
 The total product demand for a year (Nhu cầu sản phẩm/ năm)
= D = d.T = 2,500 x 300 = 750,000 (units)

⇒ Average inventory of semi-trailer (Q/2) = 150,000/(20/10) = 75,000 (units)

 Average inventory of train (Q/2) = 150,000 (units)

⇒ Average inventory of truck (Q/2) = 150,000/(20/10) = 75,000 (units)

⇒ Average inventory of plane (Q/2) = 150,000/(40/10) = 37,500 (units)
Method of
Cost type Train Semi-trailer Truck Plane
computation
Transportation = 0.1 x 750,000 = 0.15 x 750, 000 = 0.3 x 750,000 = 1.2 x 750,000
RxD
(Chi phí vận tải) = 75,000 = 112,500 = 225,000 = 900,000
In-transit = (0.25 x 45 x = (0.25 x 45 x
= (0.25 x 45 x = (0.25 x 45 x
inventory 750,000 x 6)/365 750,000 x 2)/365
(ICDT)/365 750,000 x 25)/365 750,000 x 16)/365
(Chi phí dự trù = 138,698.6301 = 46,232.8767
= 577,910.9589 = 369,863.0137
trên đường)
Plant inventory = 0.25 x 45 x = 0.25 x 45 x = 0.25 x 45 x = 0.25 x 45 x
(Chi phí dự trù tại ICQ/2 150,000 75,000 75,000 37,500
nguồn) = 1,687,500 = 843,750 = 843,750 = 421,875
Field inventory = 0.25 x 45.1 x = 0.25 x 45.15 x = 0.25 x 45.3 x = 0.25 x 46.2 x
(Chi phí dự trù tại I(C+R)Q/2 150,000 75,000 75,000 37,500
đích) = 1,691,250 = 846,562.5 = 849,375 = 433,125
Total $4,031,600,959 $2,172,675.514 $2,056,823.63 $1,801,232.877

Ex 3 – Exercise on Inventory decisions

Situation
 ABC company needs 18 units to keep its production line run on a normal business day. The buying cost
for each unit is 5.000 $ (labelled as “C”). The inventory cost accounts for 18% of total purchasing cost
(labelled as “I”). Whenever the company places a new order, it costs 1.500 $, known as sourcing cost
(labelled as “S”). The lead time is 8 days and labelled as “T”. The company works 320 days in a year.
d = 18 units C = $5,000
I = 18% = 0.18 S = $1,500
T (Lead Time) = 8 days Number of working days per year = 320
H = IC
SOLVE
D = d x Number of working days per year = 18 x 320 = 5760 (Days)
1. The optimal order quantity (EOQ) is:

Q* =
√ 2 DS
H
=
√ 2 DS
IC
=
√ 2 x 5760 x 1500
0.18 x 5000
= 139 (units)

2. The reorder point (ROP) is:

ROP = d x LT = 18 x 8 = 144 (units)
3. The total inventory cost (TC) is:
DS
5760 x 1500 139 x 0.18 x 5000
TC = Q∗H = + = $124,708.2734
Q∗¿+ ¿ 139 2
2
4. Number of times that the company order in a year:
N = D/Q* = 5760/139 = 41,44 times
5. The optimal time between two orders (T*)
T* = Q*/D = 0.024 (year)
⇒ 0.024 x 52 = 1,24 (weeks)
⇒ 0.024 x 365 = 8.76 (days)
6. Meaning
EOQ is the order quantity that minimizes the total inventory costs, which include both ordering costs
(costs associated with placing and receiving orders) and holding costs (costs of storing and maintaining
inventory). Significance: By ordering the EOQ, a company ensures it is not overstocking (increasing holding
costs) or ordering too frequently (increasing ordering costs), thus achieving cost efficiency.
ROP is the inventory level at which a new order should be placed to replenish stock before it runs out,
considering the lead time for delivery. Significance: It ensures the company does not face stockouts during the
lead time, keeping operations running smoothly.
T∗ is the optimal time interval between placing consecutive orders. Significance: It helps in planning
the inventory replenishment cycle. Companies can ensure a steady flow of inventory without over-ordering or
under-ordering.
N∗ represents the number of times the company needs to order inventory in one year to maintain the
optimal inventory levels. Significance: It shows the frequency of orders, helping the company streamline its
ordering processes and align them with demand.
The total inventory cost is the sum of all costs associated with managing inventory. These typically
include ordering costs, holding costs, and sometimes purchase costs (if they vary by order size). When using
 the EOQ model, the formula simplifies to focus on ordering costs and holding costs, as purchase costs are
constant.

Ex 4 – Exercise on Warehousing decisions

Situation
ABC company considers allocating a shipment of new arrivals being 26,000 product units for three
stores that are situated in Hai Phong, Quang Ninh, and Hanoi. The information given below in the table
represents the current level of stocks at each store, the forecasted demand, the variance of the forecasted
demand, the customer service level, and the standardization also known as Z_score
The current production run = 125,000 units.
The current level The forecasted the standard deviation_SD The customer
Stores Z_score
of stocks (units) demand (units) of the forecasted demand service level (%)
1 1,000 2,000 400 90 1.28
2 3,000 10,000 300 95 1.65
3 6,000 14,000 4,000 90 1.28
Question: Determine the volume of products to be allocated for each store.
SOLVE
Step 1: Total requirements = Forecast + (z * Forecast error).
Store The forecasted demand (units) Forecast error Z_score Total requirements (units)
s
= 2000 + (400 x 1.28)
1 2,000 400 1.28
= 2,512
= 10000 + (300 x 1.65)
2 10,000 300 1.65
= 10,495
= 14000 + (4000 x 1.28)
3 14,000 4,000 1.28
= 19,120
Total 26,000 32,127

Step 2: Net requirements = Total requirements – Current stock level

Stores Total requirements (units) The current level of stocks (units) Net requirements
1 2,512 1,000 1,512
2 10,495 3,000 7,495
3 19,120 6,000 13,120
Total 32,127 22,127

Step 3: The excess production that needs to be prorated to the warehouses = The current production run (đề bài
cho) – Total net requirements
= 125,000 – 22,127 = 102,873

Step 4: Proration of excess = (Forecasted demand / Total forecasted demand) * The excess production
Stores The forecasted demand (units) The excess production Proration of excess
102,873 = (2,000 /26,000) x 102,873
1 2,000
= 7,913.31
102,873 = (10,000 /26,000) x 102,873
2 10,000
= 39,566.54
102,873 = (14,000 /26,000) x 102,873
3 14,000
= 55,393.15
Total 26,000

Step 5: Total allocation to a warehouse = Net requirements + Proration of excess

Stores Net requirements Proration of excess Allocation
1 1,512 7,913.31 9,425.31
2 7,495 39,566.54 47,061.54
3 13,120 55,393.15 68,513.15
Total 22,127 125,000

Ex 5 – Exercise on Inventory decisions (part 1)

Situation: Company ABC has a list of items stocked in its warehouse as displayed in the table below.
Items Sales ($)
D-212 3.424
D-191 893
D-192 843
D-193 727
D-196 214
D-199 172
D-200 170
D-205 159
D-204 5.056
D-185-0 1.052
D-179-0 451
D-186-0 205
D-198-0 188
D-195 412
SOLVE
 Step 1: Determine products type, quantity and value
 Step 2: Determine percent of product value over total value
 Step 3: Sort in descending order by percentage of product value
 Step 4: Determine the cumulative percentage by value
 Step 5: Determine the cumulative item proportion
  Step 6: Categorize products into 3 groups A,B,C
Rank by Cumulative % Cumulative %
Items Sales %Sale Classification
sales of Total Sales of Total Items
204 1 5056 36.20% 36.20% 7.14%
A
212 2 3424 24.52% 60.72% 14.29%
185 3 1052 7.53% 68.25% 21.43%
191 4 893 6.39% 74.65% 28.57%
192 5 843 6.04% 80.68% 35.71% B
193 6 727 5.21% 85.89% 42.86%
179 7 451 3.23% 89.12% 50.00%
195 8 412 2.95% 92.07% 57.14%
196 9 214 1.53% 93.60% 64.29%
186 10 205 1.47% 95.07% 71.43%
198 11 188 1.35% 96.41% 78.57% C
199 12 172 1.23% 97.64% 85.71%
200 13 170 1.22% 98.86% 92.86%
205 14 159 1.14% 100.00% 100.00%
Total 13966 100 100 100

Ex 6 – Exercise on Inventory decisions (part 2)

Suppose that an inventory of 10 items, 15% of the items account for 80% of the sales volume. The
total sales of all 10 items is $90,000 per year. How much inventory can be expected if turn over for A items =
8, B items = 5, and C items = 2?

SOLVE
0.15(1−0.8)
A= = 0.0462
0.8−0.15
Projected
Cumulative fraction Projected Projected Average
No Pr cumulative sales ABC Turnover ratio
of items (X) Cumulative sales item sales inventory
fraction (Y)

(3)=(1)/total no. of (4) (using the (6) = Số sau

(1) (2) (5)=(4)*90000 (7) (8) = (6)/(7)
items formula) – Số trước

1 A 0.1 0.7156 64403.557 64403.557 8 8050.445

A
2 B 0.2 0.8499 76489.033 12085.477 8 1510.685
3 C 0.3 0.9066 81592.721 5103.688 5 1020.738
4 D 0.4 0.9379 84408.785 2816.064 B 5 563.213
5 F 0.5 0.9577 86193.702 1784.917 5 356.983
6 G 0.6 0.9714 87426.184 1232.482 2 616.241
7 J 0.7 0.9814 88328.330 902.146 2 451.073
8 K 0.8 0.9891 89017.254 688.923 C 2 344.462
9 L 0.9 0.9951 89560.558 543.304 2 271.652
10 M 1.0 1.0000 90000.000 439.442 2 219.721
90000.000 13405.212

Suppose that an inventory of 11 items. 21% of the items account for 68% of the sales volume (X=0,21
Y=0,68). The total sales of all 11 items is 25000/year. How much inventory can be expected if turn over for
A items = 7, B items = 5, C items = 3

No Pr Cumulative Projected Projected Projected item Turnover ratio Average

fraction of items cumulative sales Cumulative sales sales inventory
(X) fraction (Y)
(1) (2) (3)=(1)/total no. (4) (using the (5)=(4)*25000 (6) (7) (8) = (6)/(7)
of items formula)
1 A 0,0909 0,4443 11.107 A 11.107 7:1
2 B 0,1818 0,6398 15.996 B-A 4.889 7:1
15.996 2.285
3 C 0,2727 0,7499 18.747 C-B 2.751 5:1
4 D 0,3636 0,8204 20.510 1.764 5:1
5 F 0,4545 0,8695 21.737 1.227 5:1
6 G 0,5455 0,9056 22.640 903 5:1
6.644 1.329
7 J 0,6364 0,9333 23.332 692 3:1
8 K 0,7273 0,9552 23.880 548 3:1
9 L 0,8182 0,9730 24.324 444 3:1
10 M 0,9091 0,9876 24.691 367 3:1
11 N 1,0000 1,0000 25.000 309 3:1
2.360 787
4.401