Transcript chopra_scm5_ch11.pptx

Summary
• Managing Economies of Scale in a Supply Chain:
Cycle Inventory
• Role of Cycle Inventory in a Supply Chain
• Estimating Cycle Inventory Related Costs in Practice
• Economies of Scale to Exploit Fixed Costs
• Lot Sizing for a Single Product
• EOQ Example
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11
Managing
Economies of Scale
in a Supply Chain:
Cycle Inventory
PowerPoint presentation to accompany
Chopra and Meindl Supply Chain Management, 5e
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1-2
Role of Cycle Inventory
in a Supply Chain
• Lot or batch size is the quantity that a
•
stage of a supply chain either produces or
purchases at a time
Cycle inventory is the average inventory in
a supply chain due to either production or
purchases in lot sizes that are larger than
those demanded by the customer
Q: Quantity in a lot or batch size
D: Demand per unit time
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Inventory Profile
Figure 11-1
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Role of Cycle Inventory
in a Supply Chain
lot size Q
Cycle inventory =
=
2
2
average inventory
Average flow time =
average flow rate
Average flow time cycle inventory Q
=
=
resulting from
demand
2D
cycle inventory
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11-5
Role of Cycle Inventory
in a Supply Chain
• Lower cycle inventory has
•
– Shorter average flow time
– Lower working capital requirements
– Lower inventory holding costs
Cycle inventory is held to
– Take advantage of economies of scale
– Reduce costs in the supply chain
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Role of Cycle Inventory
in a Supply Chain
• Average price paid per unit purchased is a key
•
•
cost in the lot-sizing decision
Material cost = C
Fixed ordering cost includes all costs that do
not vary with the size of the order but are
incurred each time an order is placed
Fixed ordering cost = S
Holding cost is the cost of carrying one unit in
inventory for a specified period of time
Holding cost = H = hC
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11-7
Role of Cycle Inventory
in a Supply Chain
• Primary role of cycle inventory is to allow
•
•
•
different stages to purchase product in lot
sizes that minimize the sum of material,
ordering, and holding costs
Ideally, cycle inventory decisions should
consider costs across the entire supply chain
In practice, each stage generally makes its
own supply chain decisions
Increases total cycle inventory and total costs
in the supply chain
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11-8
Role of Cycle Inventory
in a Supply Chain
• Economies of scale exploited in three
typical situations
1. A fixed cost is incurred each time an order
is placed or produced
2. The supplier offers price discounts based
on the quantity purchased per lot
3. The supplier offers short-term price
discounts or holds trade promotions
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Estimating Cycle Inventory Related Costs
in Practice
• Inventory Holding Cost
– Cost of capital
WACC =
E
D
(R f + b ´ MRP) +
Rb (1– t)
D+ E
D+E
where
E = amount of equity
D = amount of debt
Rf = risk-free rate of return
b = the firm’s beta
MRP = market risk premium
Rb = rate at which the firm can borrow money
t = tax rate
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11-10
Estimating Cycle Inventory Related Costs
in Practice
• Inventory Holding Cost
– Cost of capital
Adjusted for pre-tax setting
Pretax WACC = after-tax WACC / (1– t)
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Estimating Cycle Inventory Related Costs
in Practice
• Inventory Holding Cost
– Obsolescence cost
– Handling cost
– Occupancy cost
– Miscellaneous costs
• Theft, security, damage, tax, insurance
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Estimating Cycle Inventory Related Costs
in Practice
• Ordering Cost
– Buyer time
– Transportation costs
– Receiving costs
– Other costs
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Economies of Scale
to Exploit Fixed Costs
• Lot sizing for a single product (EOQ)
Annual demand of the product
Fixed cost incurred per order
Cost per unit
Holding cost per year as a fraction of
product cost
Basic assumptions
D
S
C
H
•
=
=
=
=
– Demand is steady at D units per unit time
– No shortages are allowed
– Replenishment lead time is fixed
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Economies of Scale
to Exploit Fixed Costs
• Minimize
– Annual material cost
– Annual ordering cost
– Annual holding cost
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Lot Sizing for a Single Product
Annual material cost = CD
D
Number of orders per year =
Q
æ Dö
Annual ordering cost = ç ÷ S
èQø
æQ ö
æQö
Annual holding cost = ç ÷ H = ç ÷ hC
è2ø
è2ø
æ Dö
æQ ö
Total annual cost, TC = CD + ç ÷ S + ç ÷ hC
èQø
è2ø
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Lot Sizing for a Single Product
Figure 11-2
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Lot Sizing for a Single Product
•
The economic order quantity (EOQ)
2DS
Optimal lot size, Q* =
hC
•
The optimal ordering frequency
D
n* =
=
Q*
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DhC
2S
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EOQ Example 11-1
The demand for deskpro computers at best buy is 1000 units per month.
Best buy incurs a fixed order placement, transportation, and receiving cost
of $4000 each time an order is placed. Each computer costs Best buyer
$500 and the retailer has a holding cost of 20 percent. Evaluate the
number of computers that the store manager should order in each
replenishment lot.
Annual demand, D = 1,000 x 12 = 12,000 units
Order cost per lot, S = $4,000
Unit cost per computer, C = $500
Holding cost per year as a fraction of unit cost, h = 0.2
2 ´12,000 ´ 4,000
Optimal order size = Q* =
= 980
0.2 ´ 500
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Q * 980
Cycle inventory =
=
= 490
2
2
D
Number of orders per year =
= 12.24
Q*
æQ *ö
D
Annual ordering and holding cost =
S +ç
÷ hC = 97,980
Q*
è 2 ø
Average flow time =
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Q*
490
=
= 0.041= 0.49 month
2D 12,000
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If the demand increases by a factor of k, the optimal lot size increases by a factor
of √k. The number of orders placed per year should also increase by a factor of
√k. Flow time attributed to cycle inventory should decrease by a factor of √k.
Now assume that the manager would like to reduce the lot size to 200 to reduce
flow time.
Lot size reduced to Q = 200 units
æQ *ö
D
Annual inventory-related costs =
S +ç
÷ hC = 250,000
Q*
è 2 ø
A significant increase in the cost as compared to $97,980. If the fixed cost
associated with each lot is reduced to $1000 (from a current of $4000), the
optimal lot size reduces to 490 (from a current of 980).
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Relationship Between Desired Lot Size
and Ordering Cost
The store manager at best buy would like to reduce the optimal lot
size from 980 to 200. For this lot size reduction to be optimal, the
store manager wants to evaluate how much the ordering cost per
lot should be reduced.
If the lot size Q* = 200, how much should the ordering
cost be reduced?
Desired lot size, Q* = 200
Annual demand, D = 1,000 × 12 = 12,000 units
Unit cost per computer, C = $500
Holding cost per year as a fraction of inventory value, h = 0.2
hC(Q*)2 0.2 ´ 500 ´ 2002
S=
=
= 166.7
2D
2 ´12,000
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Production Lot Sizing
•
•
•
The entire lot does not arrive at the same time
Production occurs at a specified rate P
Inventory builds up at a rate of P – D
2DS
Q =
(1– D / P)hC
P
Annual setup cost
æ Dö
ç P ÷S
èQ ø
Annual holding cost
æQP ö
(1– D / P) ç
÷ hC
è 2 ø
For the remainder of this chapter we restrict our attention to the case in which the entire
replenishment lot arrives at the same time, a scenario that applies in most supply chain
settings
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Aggregating Multiple Products
in a Single Order
• Savings in transportation costs
– Reduces fixed cost for each product
– Lot size for each product can be reduced
– Cycle inventory is reduced
• Single delivery from multiple suppliers or
•
single truck delivering to multiple retailers
Receiving and loading costs reduced
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Lot Sizing with Multiple
Products or Customers
•
•
Ordering, transportation, and receiving costs
of an order grows with the variety of products
or pickup points, because the inventory
update and restocking effort.
The objective is to arrive at a Lot sizes and
ordering policy that minimize total cost.
Assume the following inputs.
Di : Annual demand for product i
S : Order cost incurred each time an order is placed,
independent of the variety of products in the order
si : Additional order cost incurred if product i is included in the
order
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Lot Sizing with Multiple
Products or Customers
• Three approaches
1. Each product manager orders his or her
model independently
2. The product managers jointly order every
product in each lot
3. Product managers order jointly but not
every order contains every product; that is,
each lot contains a selected subset of the
products
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1 Example 11.3 Multiple Products Ordered
and Delivered Independently
Evaluate the lot sizes that the best buy manager should
order if lots for each product are ordered and delivered
independently. Also evaluate the annual cost of such a policy
Demand
DL = 12,000/yr, DM = 1,200/yr, DH = 120/yr
Common order cost
S = $4,000
Product-specific order cost
sL = $1,000, sM = $1,000, sH = $1,000
Holding cost
h = 0.2
Unit cost
CL = $500, CM = $500, CH = $500
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Litepro
Medpro
Heavypro
Demand per year
12,000
1,200
120
Fixed cost/order
$5,000
$5,000
$5,000
1,095
346
110
548
173
55
$54,772
$17,321
$5,477
11.0/year
3.5/year
1.1/year
$54,772
$17,321
$5,477
2.4 weeks
7.5 weeks
23.7 weeks
$109,544
$34,642
$10,954
Optimal order size
Cycle inventory
Annual holding cost
Order frequency
Annual ordering cost
Average flow time
Annual cost
•
•
Total annual cost = $155,140
Table 11-1
Independent ordering is simple to execute but ignores the opportunity to
aggregate orders
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(2) Lots Ordered and Delivered Jointly
S* = S + sL + sM + sH
Annual order cost = S * n
DL hC L DM hCM DH hC H
Annual holding cost =
+
+
2n
2n
2n
DL hC L DM hCM DH hC H
Total annual cost =
+
+
+S*n
2n
2n
2n
n* =
DL hC L + DM hCM + DH hC H
2S *
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n* =
å
k
i=1
Di hCi
2S *
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Example 11.4 Products Ordered and
Delivered Jointly
S* = S + sA + sB + sC = $7,000 per order
12,000 ´100 +1,200 ´100 +120 ´100
n* =
= 9.75
2 ´ 7,000
Annual order cost = 9.75 x 7,000 = $68,250
Annual ordering
and holding cost = $61,512 + $6,151 + $615 + $68,250
= $136,528
Reduced annual cost from $155,140 to $136,528 a decrease of
about 12 % by ordering all orders jointly
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Example 11.4 Products Ordered and
Delivered Jointly
Litepro
Medpro
Heavypro
Demand per year (D)
12,000
1,200
120
Order frequency (n∗)
9.75/year
9.75/year
9.75/year
1,230
123
12.3
615
61.5
6.15
$61,512
$6,151
$615
2.67 weeks
2.67 weeks
2.67 weeks
Optimal order size (D/n∗)
Cycle inventory
Annual holding cost
Average flow time
Table 11-2
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Example 11.5 Aggregation with Capacity
Constraint
• W.W. Grainger example
Demand per product, Di = 10,000
Holding cost, h = 0.2
Unit cost per product, Ci = $50
Common order cost, S = $500
Supplier-specific order cost, si = $100
Presence of capacity constraints
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Example 11.5 Aggregation with Capacity
Constraint
S* = S + s1 + s2 + s3 + s4 = $900 per order
n* =
å
4
i=1
D1hC1
2S *
=
4 ´10,000 ´ 0.2 ´ 50
= 14.91
2 ´ 900
Annual order cost = 14.91´
900
= $3,354
4
hCiQ
671
Annual holding
=
= 0.2 ´ 50 ´
= $3,355
cost per supplier
2
2
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Example 11.5 Aggregation with Capacity
Constraint
Total required capacity per truck = 4 x 671 = 2,684 units
Truck capacity = 2,500 units
Order quantity from each supplier = 2,500/4 = 625
Order frequency increased to 10,000/625 = 16
Annual order cost per supplier increases to $3,600
Annual holding cost per supplier decreases to $3,125.
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(3) Lots Ordered and Delivered Jointly for
a Selected Subset
Step 1: Identify the most frequently ordered
product assuming each product is
ordered independently
hCi Di
ni =
2(S + si )
Step 2: For all products i ≠ i*, evaluate the
ordering frequency
hCi Di
ni =
2si
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Step 3: For all i ≠ i*, evaluate the frequency of
product i relative to the most frequently
ordered product i* to be mi
é
ù
mi = ên / ni ú
Step 4: Recalculate the ordering frequency of the
most frequently ordered product i* to be n
n=
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å
(
l
i=1
hCi mi D
2 S + å si / mi
l
i=1
)
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Step 5: Evaluate an order frequency of ni = n/mi
and the total cost of such an ordering
policy
æD ö
TC = nS + å ni si + åç i ÷ hC1
i=1
i-1 è 2ni ø
l
l
Tailored aggregation – higher-demand products
ordered more frequently and lower-demand
products ordered less frequently
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Example 11.6 Ordered and Delivered
Jointly – Frequency Varies by Order
•
•
Consider the data in example 11.3. Product managers have decided
to order jointly but to be selective about which models they include
in each order. Evaluate the ordering policy and cost using the
procedure discussed previously.
Applying Step 1
hC L DL
nL =
= 11.0
2(S + sL )
hCM DM
nM =
= 3.5
2(S + sM )
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hC H DH
nL =
= 1.1
2(S + sH )
Thus
n = 11.0
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• Applying Step 2
hCM DM
hC H DH
nM =
= 7.7 and nH =
= 2.4
2sM
2sH
• Applying Step 3
é ù é
é ù é
ù
n ú 11.0
n ú 11.0 ù
ê
ê
mM =
=ê
=ê
ú = 2 and mH =
ú=5
ê n ú ê 7.7 ú
ê n ú ê 2.4 ú
ê Mú
ê Hú
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Litepro
Medpro
Heavypro
Demand per year (D)
12,000
1,200
120
Order frequency (n∗)
11.47/year
5.74/year
2.29/year
1,046
209
52
523
104.5
26
$52,307
$10,461
$2,615
2.27 weeks
4.53 weeks
11.35 weeks
Optimal order size (D/n∗)
Cycle inventory
Annual holding cost
Average flow time
Table 11-3
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• Applying Step 4
n = 11.47
• Applying Step 5
nL = 11.47 / yr
nM = 11.47 / 2 = 5.74 / yr
nH = 11.47 / 5 = 2.29 / yr
Annual order cost
nS + nL sL + nM sM + nH sH = $65,383.5
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Total annual cost
$130,767
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