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Title: quantitative methods of business decisions chapter 13(inventory modeling)
Description: quantitative methods of business decisions chapter 13

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School of Business
Department of Management Information Systems
BMIS355: Quantitative Methods of Business Decisions
Chapter 13 |

Inventory Modeling
Spring 2020 - 2021
BMIS355- CHAPTER 13

Outline
1
...


2
...


How much to order?

❖ Determine the size of the order at replenishment time
...


When to order?

❖ Periodic reviews: order at the start of a time period (week/month)
...


BMIS355- CHAPTER 13

Classical EOQ Model
Classical Economic Order Quantity (EOQ) Model:
The simplest of the inventory models
...


Stock is depleted uniformly at a constant demand rate, D
...
K = Setup cost associated with the placement of an order (dollars per order)
...

Expenses incurred on transportation of purchased orders
...

Cost of stationary, typing, postage, telephone charges etc
...
h = Holding cost (dollars per inventory unit per unit time)
...

◦ Storage and handling of material
...

BMIS355- CHAPTER 13

Classical EOQ Model
Computations:

The total cost per unit time:

❑ TCU(y) = Setup cost per unit time + Holding cost per unit time
❑ TCU(y) =

𝐾
𝑦
ൗ𝐷

𝑦
2

+ ℎ( )

BMIS355- CHAPTER 13

Classical EOQ Model
Where the optimal order quantity is:



𝒚 =

2𝐾𝐷


A positive lead time “L”, occurs between the placement and receipt of an order
...
The physical
plant orders the neon lights periodically
...
A neon
light kept in storage is estimated to cost about $
...
The lead time between placing
and receiving an order is 12 days
...


From the data of the problem, we have:





D = 100 units per day
K = $100 per order
h = $
...
02
BMIS355- CHAPTER 13

= 1000 neon lights

Classical EOQ Model
◦ The associated cycle length is:
• t0 = y/D = 1000/100 = 10 days

◦ Since the lead time L (= 12 days) > t0 (=10 days), then we must compute the effective lead time Le
...
2) = 1

• Le = L - n t0 = 12 – 1 X 10 = 2 days
◦ Reorder point :

Place a new order whenever inventory drops to 200 units

• LeD = 2 X 100 = 200 neon lights
...
02

1000
2

BMIS355- CHAPTER 13

= $20 per day

Outline
1
...


2
...

The difference is that the items compete for a limited storage space
...
+ 𝑇𝐶𝑈𝑖
Subject to:
◦ σ𝑛𝑖=1 𝑎𝑖 𝑦𝑖 ≤ 𝐴 :
◦ before calculating TCU, we must check if there is enough space to store 𝑌𝑖 quantity
...

Otherwise, the constraint is binding and must be accounted for
...

Each brick order costs 15$
...
5 in storage
...
One brick takes 0
...

In addition, the company needs 1,000 bags of cement per month
...
Each cement bag costs $2 in storage
...
One cement bag
takes 6 𝑓𝑡 2 of space
...


Demand per item - 𝑫𝒊 :
• 𝐷𝑒𝑚𝑎𝑛𝑑 𝑓𝑜𝑟 𝑏𝑟𝑖𝑐𝑘𝑠: 𝐷1 = 200,000 brick/month
• 𝐷𝑒𝑚𝑎𝑛𝑑 𝑓𝑜𝑟 𝑐𝑒𝑚𝑒𝑛𝑡 𝑏𝑎𝑔𝑠: 𝐷2 = 1,000 cement bags/month
Setup cost per item - 𝑲𝒊 :
• Setup Cost for bricks: 𝐾1 = $15/𝑜𝑟𝑑𝑒𝑟
• Set up Cost for cement bags: 𝐾2 = $35/𝑜𝑟𝑑𝑒𝑟
Holding cost per item - 𝒉𝒊 :
• Holding cost for bricks: ℎ1 = $0
...

Storage area per inventory unit - 𝒂𝒊 :
• Storage area for bricks: 𝑎1 = 0
...


Compute 𝒀𝒊 :
1
...


Bricks: 𝑦1 =

2𝐾1 𝐷1
ℎ1

Cement Bags: 𝑦2 =

=

2(15)(200,000)
0
...


Compute σ𝑛𝑖=1 𝑎𝑖 𝑦𝑖
◦ 𝑎1
...
𝑦2 = 0
...


Check σ𝑛𝑖=1 𝑎𝑖 𝑦𝑖 ≤ 𝐴:

3200 𝑓𝑡 2 ≤ 8000𝑓𝑡 2
◦ Then the solution satisfies the constraint & 𝑦𝑖 𝑖𝑠 𝑜𝑝𝑡𝑖𝑚𝑎𝑙
...
5/𝑏𝑟𝑖𝑐𝑘/month
• Holding cost for cement bags: h2 = $2/cement bag/month
Leading time for both is zero
...
6𝑓𝑡 2 /brick
• Storage area for cement bags : 𝑎2 = 6𝑓𝑡 2 /𝑐𝑒𝑚𝑒𝑛𝑡 bag
A = 8,000 𝑓𝑡 2

BMIS355- CHAPTER 13

Multi-Item EOQ with Storage Limitation
TCU = 𝑇𝐶𝑈1 + 𝑇𝐶𝑈2
Bricks: 𝑇𝐶𝑈1 =

𝐾1
𝑌1

ൗ𝐷1

Cement bags: 𝑇𝐶𝑈2 =
$374
...


+ ℎ1
𝐾2
𝑌2

ൗ𝐷2

𝑦1
2

= $1732/month
...
16 = $2,106
...
5/𝑏𝑟𝑖𝑐𝑘/month
• Holding cost for cement bags: h2 = $2/cement bag/month
Leading time for both is zero
...
6𝑓𝑡 2 /brick
• Storage area for cement bags : 𝑎2 = 6𝑓𝑡 2 /𝑐𝑒𝑚𝑒𝑛𝑡 bag
A = 8,000 𝑓𝑡 2

BMIS355- CHAPTER 13

Thank you!
BMIS355- CHAPTER 13


Title: quantitative methods of business decisions chapter 13(inventory modeling)
Description: quantitative methods of business decisions chapter 13