View
216
Download
1
Category
Preview:
Citation preview
Inventory Management: Cycle Inventory
Inventory Management: Cycle Inventory
【 本 著 作 除 另 有 註 明 外 , 採 取 創用 CC
「姓名標示-非商業性-相同方式分享」台灣 3.0
版授權釋出】
第四單元: Inventory Management: Cycle Inventory
郭瑞祥教授
1
Understocking: Demand exceeds amount available
–Lost margin and future sales
Overstocking: Amount available exceeds demand
– Liquidation, Obsolescence, Holding
Role of Inventory in the Supply Chain
2
► Economies of scale
► Stochastic variability of supply and demand》 Batch size and cycle time》 Quantity discounts》 Short term discounts / Trade promotions》Service level given safety inventory》Evaluating Service level given safety inventory
Why hold inventory?
3
Improve Matching of Supplyand Demand
Improved Forecasting
Reduce Material Flow Time
Reduce Waiting Time
Reduce Buffer Inventory
Economies of ScaleSupply / Demand
Variability Seasonal Variability
Cycle Inventory Safety Inventory Seasonal Inventory
CostEfficiency
CostEfficiency
AvailabilityResponsiveness
AvailabilityResponsiveness
Improve Matching of Supplyand Demand
Role of Inventory in the Supply Chain
4
Cycle Inventory
Improve Matching of Supplyand Demand
Improved Forecasting
Reduce Material Flow Time
Reduce Waiting Time
Reduce Buffer Inventory
Economies of ScaleSupply / Demand
Variability Seasonal Variability
Safety Inventory Seasonal Inventory
CostEfficiency
AvailabilityResponsiveness
Cycle inventory is the average inventory that built up in the supplychain because a stage of the supply chain either produces or
purchases in lots that are larger than those demanded by the customer.
Cycle Inventory
Inventory
Time t
Cycle inventory = lot size/2 = Q/2Cycle inventory = lot size/2 = Q/2
Q
5
Little’s Law
► Average flow time = Average inventory / Average flow rate
Average flow time resulting from cycle inventory
Q: Lot size
D: Demand per unit time
► For any supply chain, average flow rate equals the demand,
= Cycle inventory / Demand = Q / 2D
6
Holding Cycle Inventory for Economies of Scale
Holding Cycle Inventory for Economies of Scale
► Fixed costs associated with lots
► Quantity discounts
► Trade Promotions
7
Economics of Scale to Exploit Fixed Costs
— Economic Order Quantity—
» D= Annual demand of the product
» S= Fixed cost incurred per order
» C= Cost per unit
» h=Holding cost per year as a fraction of product cost
» H=Holding cost per unit per year =hC
» Q=Lot size
» n=Order frequency
8
Cost
Lot Size
Lot Sizing for a Single Product (EOQ)
Lot Sizing for a Single Product (EOQ)
► Annual order cost =(D/Q)S=ns
Annual holding cost = (Q/2)H =(Q/2)hC
Annual material cost = CD
TC =CD + (D/Q)S + (Q/2)hC
Holding Cost
Material Cost
Order Cost
Total Cost
9
Cost
Lot Size
► Annual order cost =(D/Q)S
Annual holding cost = (Q/2)H =(Q/2)hc
Annual material cost = CD‧
TC =CD + (D/Q)S + (Q/2)hc
Holding Cost
Material Cost
Order Cost
Total Cost
Lot Sizing for a Single Product (EOQ)
Lot Sizing for a Single Product (EOQ)
Total annual cost, TC =CD + (D/Q)S + (Q/2)hcOptimal lot size, Q is obtained by taking the first derivative
hCQDS
dQTCd
02
)(2
hCDS
Q2*
Average flow time = Q*/2D S*
DhCQD
n2
*
10
Example
Demand , D =1,000 units/month = 12,000 units/year
Fixed cost, S = $4,000/order Unit cost, C = $500 Holding cost, h = 20% = 0.2
》 Optimal order size
》 Cycle inventory
》 Numbers of orders per year
》 Average flow time Q / 2D = 490 / 12000 =0.041 (year) =0.49(mounth)
Q = = 9800.2X500
2X12000X4000
Q/2 =490
D / Q = 12000 / 980 =12.24
11
Example - Continued
Demand , D =1,000 units/month = 12,000 units/year
Fixed cost, S = $4,000/order Unit cost, C = $500 Holding cost, h = 20% = 0.2
》 Optimal order size
》 Cycle inventory
》 Numbers of orders per year
》 Average flow time Q / 2D = 490 / 12000 =0.041 (year) =0.49(mounth)
Q = = 9800.2X500
2X12000X4000
Q/2 =490
D / Q = 12000 / 980 =12.24
► If we want to reduce the optimal lot size from 980 to 200,
then how much the order cost per lot should be.
2D
hC(Q*)2
S = 0.2X500X2002
2X12000= = $166.7
If we increase the lot size by 10% (from 980 to 1100), what the total cost would be.
Annual cost = $ 98,636 (from $ 97,980)(an increase by only 0.6%) (Note: material cost is not included)
Microsoft 。Microsoft 。
Microsoft 。Microsoft 。
CoolCLIPS
Microsoft 。
12
Key Points from EOQ
Total order and holding costs are relatively stable around the economic order quantity. A firm is often better served by ordering a convenient lot size close to the EOQ rather than the precise EOQ.
To reduce the optimal lot size by a factor of k, the fixed order cost
S must be reduced by a factor of k2 .
If demand increases by a factor of k, the optimal lot size increases
by a factor of . The number of orders placed per year should
also increase by a factor of . Flow time attributed to cycle
inventory should decrease by a factor of .
k
k
k
13
Aggregating Multiple Products in a Single Order
► One of major fixed costs is transportation
► Ways to lower the fixed ordering and transportation costs:
► Ways to lower receiving or loading costs:
》ASN (Advanced Shipping Notice) with EDI
》Aggregating across the products from the same supplier
》Single delivery from multiple suppliers
》Single delivery to multiple retailers
Microsoft 。
Microsoft 。
Microsoft 。
14
Example: Lot Sizing with Multiple Products
Three computer models (L, M, H) are sold and the demand per year:
–DL = 12,000; DM = 1,200; DH = 120
► Common fixed (transportation) cost, S = $4,000
► Holding cost, h = 0.2
► Unit cost 》 CL = $500; CM = $500; CH = $500
► Additional product specific order cost
》 sL = $1,000; sM = $1,000; sH = $1,000
L M H
Microsoft 。Microsoft 。Microsoft 。
15
Delivery Options
► No aggregation
► Complete aggregation
► Tailored aggregation
》Each product is ordered separately
》All products are delivered on each truck
》Selected subsets of products on each truck
16
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 1: No Aggregation Result
Litepro Medpro Heavypro
Demand per year 12000 1200 120
Fixed cost / order $5,000 $5,000 $5,000
Optimal order size 1,095 346 110
Order frequency 11.0/year 3.5/year 1.1/year
Annual holding cost $109,544 $34,642 $10,954
Annual total cost = $155,140 (no material cost)
17
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 2: Complete Aggregation
》Combined fixed cost per order is given by
》Let n be the number of orders placed per year. We have Total annual cost = Annual order cost + Annual holding cost
=
HML sssSS *
)]2/()2/()2/[()( * nhCDnhCDnhCDnS HHMMLL
hCDS
Q2*
**2S
hCDhCDhCDn HHMMLL
n
S
DhC2
*
18
Option 2: Complete Aggregation
► No aggregation
► Complete aggregation
► Tailored aggregation》Combined fixed cost per order is given by
》Let n be the number of orders placed per year. We have Total annual cost = Annual order cost + Annual holding cost
=
HML sssSS *
)]2/()2/()2/[()( * nhCDnhCDnhCDnS HHMMLL
**2S
hCDhCDhCDn HHMMLL
n
S
DhC2
*
19
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 2: Complete Aggregation Result
Litepro Medpro Heavypro
Demand per year 12000 1200 120
Order frequency 9.75/year 9.75/year 9.75/year
Optimal order size 1,230 123 12.3
Annual holding cost $61,512 $6,151 $615
Annual order cost = 9.75×$7,000 = $68,250Annual total cost = $68,250+$61,512+$6,151+$615=$136,528
20
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 3: Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.
► Step 1: Identify most frequently ordered product.
21
Option 3: Tailored aggregation
► No aggregation
► Complete aggregation
► Tailored aggregation
►A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.
0.11 1.1 3.5, ,0.11)(2
nHnMnLsSLDLhC
Ln
► Step 1: Identify most frequently ordered product.
}2(S+si)
{i
hCiDiniMaxn
22
Option 3: Tailored aggregation
► No aggregation
► Complete aggregation
► Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.
0.11 1.1 3.5, ,0.11)(2
nHnMnLsSLDLhC
Ln
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
2.4 7.72
HM
MMM n
s
DhCn
55.4 Hm 24.1 7.7/0.11/
MM nnm
► Step 1: Identify most frequently ordered product.
n= hCiDi
2si
23
Option 3: Tailored aggregation► No aggregation
► Complete aggregation
► Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
Step 4: Identify ordering frequency of all products.
► Step 1: Identify most frequently ordered product.
0.11 1.1 3.5, ,0.11)(2
nHnMnLsSLDLhC
Ln
Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
2.4 7.72
HM
MMM n
s
DhCn
7.7/0.11/ MM nnm
► Step 3: Recalculate order frequency of most frequently ordered product.
)]/([2
ii
iii
msS
mDhCn
55.4 Hm 24.1
TC= order cost + holding cost
Derivation of n
24
Option 3: Tailored aggregation► No aggregation
► Complete aggregation
► Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.
► Step 1: Identify most frequently ordered product.
0.11 1.1 3.5, ,0.11)(2
nHnMnLsSLDLhC
Ln
Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
2.4 7.72
HM
MMM n
s
DhCn
7.7/0.11/ MM nnm
Step 3: Recalculate order frequency of most frequently ordered product.
)]/([2
ii
iii
msS
mDhCn
Derivation of n
+= 2ni
i
hCiDiMi
mi
nnS
TC= order cost + holding cost
(hCi)i
nisii 2ni
DinSTC=( )++
si
55.4 Hm 24.1 7.7/0.11/
MM nnm
25
Option 3: Tailored aggregation No aggregation
Complete aggregation
Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
Step 3: Recalculate order frequency of most frequently ordered product.
Step 4: Identify ordering frequency of all products.
► Step 1: Identify most frequently ordered product.
0.11 1.1 3.5, ,0.11)(2
nHnMnLsSLDLhC
Ln
Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
2.4 7.72
HM
MMM n
s
DhCn
7.7/0.11/ MM nnm
► Step 3: Recalculate order frequency of most frequently ordered product.
)]/([2
ii
iii
msS
mDhCn
Derivation of n
+= 2ni
i
0
nTC
hCiDiMi
mi
nnS
TC= order cost +
(hCi)i
nisii 2ni
DinSTC=( )++
si
=0S+i mi
si
2n2i
hCiDiMi
holding cost
)]/([2
ii
iii
msS
mDhCn
26
Option 3: Tailored aggregation► No aggregation
► Complete aggregation
► Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
Step 3: Recalculate order frequency of most frequently ordered product.
Step 4: Identify ordering frequency of all products.
► Step 1: Identify most frequently ordered product.
0.11 1.1 3.5, ,0.11)(2
nHnMnLsSLDLhC
Ln
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
2.4 7.72
HM
MMM n
s
DhCn
7.7/0.11/ MM nnm
► Step 3: Recalculate order frequency of most frequently ordered product.
)]/([2
ii
iii
msS
mDhCn =11.47
L
55.4 Hm 24.1
Derivation of n
+= 2ni
i
0
nTC
hCiDiMi
mi
nnS
TC= order cost +
(hCi)i
nisii 2ni
DinSTC=( )++
si
=0S+i mi
si
2n2i
hCiDiMi
holding cost
)]/([2
ii
iii
msS
mDhCn
Microsoft 。
27
Option 3: Tailored aggregation No aggregation
Complete aggregation
Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
Step 3: Recalculate order frequency of most frequently ordered product.
Step 4: Identify ordering frequency of all products.
0.11 1.1 3.5, ,0.11)(2
nHnMnLsSLDLhC
Ln
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
2.4 7.72
HM
MMM n
s
DhCn
7.7/0.11/ MM nnm
► Step 3: Recalculate order frequency of most frequently ordered product.
)]/([2
ii
iii
msS
mDhCn =11.47
► Step 4: nL=11.47/year, nM=11.47/2=5.74/year,
nH=11.47/5=2.29/year .
► Step 1: Identify most frequently ordered product.
55.4 Hm 24.1
28
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 3: Tailored Aggregation Result
Litepro Medpro Heavypro
Demand per year 12000 1200 120
Order frequency 11.47/year 5.74/year 2.29/year
Optimal order size 1,046 209 52
Annual holding cost $52,310 $10,453 $2620
Annual order cost = nS + nLsL+ sMsM + nHsH =$65,380
Annual total cost = $130,763Complete aggregation (Annual total cost) =$136,528
29
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 3: Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.
─ A fixed cost of (S+si) is allocated to each product i, and
)(2 frequency order frequently most The
i
iii
i sSDhC
nMaxn
► Step 1: Identify most frequently ordered product.
30
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 3: Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.2si
hCi Dini
mi n / ni
mi mi
► Step 1: Identify most frequently ordered product.
31
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 3: Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.
)]/([2
ii
iii
msS
mDhCn
► Step 1: Identify most frequently ordered product.
32
► No aggregation
► Complete aggregation
► Tailored aggregation
Option 3: Tailored aggregation
A heuristic that yields an ordering policy whose cost is close to optimal.
► Step 2: Identify frequency of other products as a multiple of the order frequency of the most frequently ordered product.
► Step 3: Recalculate order frequency of most frequently ordered product.
► Step 4: Identify ordering frequency of all products.
ni=n/mi
► Step 1: Identify most frequently ordered product.
33
Impact of Product Specific Order Cost
Product specificorder cost =$1,000
Product specificorder cost =$3,000
No aggregation $155,140 $183,564
Complete aggregation $136,528 $186,097
Tailored aggregation $130,763 $165,233 Ss ??
34
Lessons From Aggregation
Aggregation allows firm to lower lot size without increasing cost
Tailored aggregation is effective if product specific fixed cost is large
fraction of joint fixed cost
Complete aggregation is effective if product specific fixed cost is a
small fraction of joint fixed cost
35
► Economies of scale
► Stochastic variability of supply and demand
Why hold inventory?
》 Batch size and cycle time》 Quantity discounts》 Short term discounts / Trade promotions
36
Quantity Discounts
► Lot size based
► Volume based
How should buyer react? How does this decision affect the supply chain
in terms of lot sizes, cycle inventory, and flow time?
What are appropriate discounting schemes that suppliers should offer?
》Based on total quantity purchased over a given period
> All units> Marginal unit
》Based on the quantity ordered in a single lot
37
All Unit Quantity Discounts
C0
C1
C2
q1 q2 q3
Average Cost per Unit
Quantity Purchased
Total Material Cost
Order Quantityq1 q2 q3
If an order that is at least as large as qi but smaller than qi+1 is placed,
then each unit is obtained at the cost of Ci. 38
► Evaluate EOQ for price in range qi to qi+1 ,
》Case 1:If qi Qi < qi+1 , evaluate cost of ordering Qi
》Case 2:If Qi < qi, evaluate cost of ordering qi
》Case 3:If Qi qi+1 , evaluate cost of ordering qi+1
► Choose the lot size that minimizes the total cost over all price ranges.
Evaluate EOQ for All Unit Quantity Discounts
hCi
DSQi
2
DCihCiQiSD
TCi
2Qi
DCihCiqiSD
TCi
2qi
DCi+1hCiSD
TCi
qi+12
qi+1
Order Quantity
Total CostLowest cost in the range
EOQi
qi qi+1
Total Cost Lowest cost in the range
EOQi
qi qi+1
Order Quantity
Total Cost Lowest cost in the range
EOQi
qi qi+1
39
Assume the all unit quantity discounts
Based on the all unit quantity discounts, we have
If i = 0, evaluate Q0 as
Since Q0 > q1, we set the lost size at q1=5,000 and the total cost
Example
Order Quantity Unit Price
0-5,000 $ 3.00
5,000-10,000 $ 2.96
10,000 or more $ 2.92
D = 120,000/ yearS = $100/loth = 0.2
q0=0, q1=5,000, q2=10,000
C0=$3.00, C1=$2,96, C2=$2.92
hC0
DSQ0
2 = 6,324
C0
C1
C2
q1 q2 q3
Average Cost per Unit
Quantity Purchased
40
Evaluate EOQ for All Unit Quantity Discounts
hCi
DSQi
2 Evaluate EOQ for price in range qi to qi+1 ,
》Case 1:If qi Qi < qi+1 , evaluate cost of ordering Qi
》Case 2:If Qi < qi, evaluate cost of ordering qi
》Case 3:If Qi qi+1 , evaluate cost of ordering qi+1
Choose the lot size that minimizes the total cost over all price ranges.
DCi+1hCiSD
TCi
qi+12
qi+1
DCihCiqiSD
TCi
2qi
DCihCiQiSD
TCi
2Qi
41
DC1hC1q1SD
TC0
2q1
Assume the all unit quantity discounts
Based on the all unit quantity discounts, we have
If i = 0, evaluate Q0 as
Since Q0 > q1, we set the lost size at q1=5,000 and the total cost
Example
Order Quantity Unit Price
0-5,000 $ 3.00
5,000-10,000 $ 2.96
10,000 or more $ 2.92
D = 120,000/ yearS = $100/loth = 0.2
q0=0, q1=5,000, q2=10,000
C0=$3.00, C1=$2,96, C2=$2.92
hC0
DSQ0
2 = 6,324
= $359,080
42
Assume the all unit quantity discounts
Based on the all unit quantity discounts, we have
If i = 0, evaluate Q0 as
Since Q0 > q1, we set the lost size at q1=5,000 and the total cost
Example
Order Quantity Unit Price
0-5,000 $ 3.00
5,000-10,000 $ 2.96
10,000 or more $ 2.92
D = 120,000/ yearS = $100/loth = 0.2
q0=0, q1=5,000, q2=10,000
C0=$3.00, C1=$2,96, C2=$2.92
hC0
DSQ0
2 = 6,324
= $359,080DC1hC1q1SD
TC0
2q1
43
All Unit Quantity Discounts
Total Material Cost
C0
C1
C2
q1 q2 q3
Average Cost per Unit
Quantity Purchased Order Quantityq1 q2 q3
If an order is placed that is at least as large as qi but smaller than qi+1, then each unit is obtained at a cost of Ci.
44
Example
Order Quantity Unit Price
0-5,000 $ 3.00
5,000-10,000 $ 2.96
10,000 or more $ 2.92
D = 120,000/ yearS = $100/loth = 0.2
q0=0, q1=5,000, q2=10,000
C0=$3.00, C1=$2,96, C2=$2.92
hC0
DSQ0
2 = 6,324
= $359,080
Assume the all unit quantity discounts
Based on the all unit quantity discounts, we have
If i = 0, evaluate Q0 as
Since Q0 > q1, we set the lost size at q1=5,000 and the total cost
DC1hC1q1SD
TC0
2q1
45
Example - Continued
For i = 1, we obtain Q1 = 6,367
Since 5,000 < Q1 <10,000 , we set the lot size at Q1 = 6,367.
Observe that the lowest total cost is for i = 2.
The optimal lot size = 10,000 (at the discount price of $2.92)
For i = 2, we obtain Q2 = 6,410
Since Q2 < q2 , we set the lot size at q2=10,000.
= $358,969DC1hC1Q1SD
TC1
2Q1
46
DC2hC2q2SD
TC2
2q2
= $358,969DC1hC1Q1SD
TC1
2Q1
Example - Continued
For i = 1, we obtain Q1 = 6,367
Since 5,000 < Q1 <10,000 , we set the lot size at Q1 = 6,367.
► Observe that the lowest total cost is for i = 2.
The optimal lot size = 10,000 (at the discount price of $2.92)
For i = 2, we obtain Q2 = 6,410
Since Q2 < q2 , we set the lot size at q2=10,000.
= $354,520
47
Example - Continued
For i = 1, we obtain Q1 = 6,367
Since 5,000 < Q1 <10,000 , we set the lot size at Q1 = 6,367.
► Observe that the lowest total cost is for i = 2.
The optimal lot size = 10,000 (at the discount price of $2.92)
For i = 2, we obtain Q2 = 6,410
Since Q2 < q2 , we set the lot size at q2=10,000.
= $354,520
= $358,969
DC2hC2q2SD
TC2
2q2
DC1hC1Q1SD
TC1
2Q1
48
Example - Continued
For i = 1, we obtain Q1 = 6,367
Since 5,000 < Q1 <10,000 , we set the lot size at Q1 = 6,367.
► Observe that the lowest total cost is for i = 2.
The optimal lot size = 10,000 (at the discount price of $2.92)
For i = 2, we obtain Q2 = 6,410
Since Q2 < q2 , we set the lot size at q2=10,000.
DC1hC1Q1SD
TC1
2Q1
= $358,969
= $354,520DC2hC2q2SD
TC2
2q2
49
The Impact of All Unit Discounts on Supply Chain
► In the above example
► If the fixed ordering cost S = $4,
► All unit quantity discounts encourage retailers to increase the size of their lots.
► This also increases cycle inventory and average flow time.
》The optimal order size = 6,324 when there is no discount.》The quantity discounts result in a higher order size = 10,000.
》The optimal order size without discount = 1,265》The optimal order size with all unit discounts = 10,000
50
Marginal Unit Quantity Discounts
C0
C1
C2
q1 q2 q3
Marginal Cost per Unit
Quantity Purchased Order Quantity
q1 q2 q3
Total Material Cost
If an order of size q is placed, the first q1-q0 units are priced at C0, the next q2-q1 are priced at C1, and so on.
51
Optimal lot size
2D(S+Vi-qiCi)
hCi
Qi=
► Evaluate EOQ for each marginal price Ci (or lot size between qi and qi+1)
Evaluate EOQ for Marginal Unit Discounts
》 Let Vi be the cost of order qi units. Define V0 = 0 and
Vi=C0(q1-q0)+C1(q2-q1)+ +C‧‧‧ i-1(qi-qi-1)
》 Consider an order size Q in the range qi to qi+1
Total annual cost = ( D/Q )S (Annual order cost)
+ (Q/2) h‧ ‧[ Vi+(Q-qi)Ci ] / Q (Annual holding cost)
+ D [ ‧ Vi+(Q-qi)Ci ] / Q(Annual material cost)
52
Optimal lot size
2D(S+Vi-qiCi)
hCi
Qi=
► Evaluate EOQ for each marginal price Ci (or lot size between qi and qi+1)
Evaluate EOQ for Marginal Unit Discounts
》 Let Vi be the cost of order qi units. Define V0 = 0 and
Vi=C0(q1-q0)+C1(q2-q1)+ +C‧‧‧ i-1(qi-qi-1)
》 Consider an order size Q in the range qi to qi+1
Total annual cost = ( D/Q )S (Annual order cost)
+ (Q/2) h‧ ‧[ Vi+(Q-qi)Ci ] / Q (Annual holding cost)
+ D [ ‧ Vi+(Q-qi)Ci ] / Q(Annual material cost)
53
Assume the all unit quantity discounts
q0=0, q1=5,000, q2=10,000
C0=$3.00, C1=$2,96, C2=$2.92
V0=0 ; V1=3(5,000-0)=$15,000
V2=3(5,000-0)+2.96(10,000-5,000)=$29,800
If i = 0, evaluate Q0 as
Since Q0 > q1, we set the lost size at q1=5,000 and the total cost
2D(S+V0-q0C0)
hC0
Q0=
Example
Order Quantity Unit Price
0-5,000 $ 3.00
5,000-10,000 $ 2.96
10,000 or more $ 2.92
D = 120,000/ yearS = $100/loth = 0.2
= 6,324
$363,900D
SDTC0
+[ V1+(q1-q1)C1] + [ V1+(q1-q1)C1]= q1q1
h2
54
For i = 1, evaluate
Since Q1 > q2, we evaluate the cost of ordering q2=10,000
For i = 2, evaluate
Optimal order size = 16,961
Example - Continued
2D(S+V1-q1C1)
hC1
Q1= = 11,028
$361,780
2D(S+V2-q2C2)
hC2
Q2= = 16,961
$360,365DSDTC2
+[ V2+(Q2-q2)C2] + [ V2+(Q2-q2)C2 ]=Q2Q2
h2
DSTC1
+[ V2+(q2-q2)C2] + [ V2+(q2-q2)C2]= q2
h2
Dq2
55
頁碼 作品 授權條件 作者 /來源
12本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
12, 14本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
12, 14 本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
12 本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
12CoolCLIPS 。本作品轉載自 CoolCLIPS 網站( http://dir.coolclips.com/Popular/World_of_Industry/Food/Shopping_cart_full_of_groceries_vc012266.html ),瀏覽日期 2011/12/28 。依據著作權法第 46 、 52 、 65 條合理使用。
12 本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
14 本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
版權聲明
56
頁碼 作品 授權條件 作者 /來源
15, 27 本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
15 本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
15 本作品轉載自Microsoft Office 2007多媒體藝廊,依據Microsoft 服務合約及著作權法第 46 、 52 、 65條合理使用。
版權聲明
57
Recommended