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Chapter 4. Managing economies of scale in a supply
chain: cycle inventory
Learning objectives:
1. Balance the appropriate costs to choose the optimal amount of
cycle inventory in a supply chain
2. Understand the impact of quantity discount on lot size and
cycle inventory
3. Devise appropriate discounting schemes for a supply chain
4. Understand the impact of trade promotions on lot size and
cycle inventory
5. Identify managerial levers that reduce lot size and cycle
inventory in a supply chain without increasing cost
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Role of cycle inventory
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Why do companies hold inventory?
Why might they avoid doing so?
• WHY? – To take advantage of economic purchase order size :
economy of scale (cycle inventory)
– To meet anticipated customer demand
– To account for differences in production timing(smoothing)
– To protect against uncertainty (demand surge, priceincrease, lead time slippage)
– To maintain independence of operations (buffering)• WHY NOT?
– Requires additional space
– Opportunity cost of capital
– Spoilage / obsolescence
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The role of cycle inventory in a
supply chain
• A lot or batch size is the quantity that a stage of a SC
either produces or purchases at a time.
• The lot size is usually larger than the quantities
demanded by the customer.
• Cycle inventory is the average inventory in a SC due to
this difference.
Key point : Cycle inventory exists in a SC bcs different stages
exploit the economies of scale to lower total cost. The costs
considered include: material cost, fixed ordering cost, and
holding cost.
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The role of cycle inventory in a
supply chain• Example: Consider a computer store selling an average of D = 4
printers a day but ordering Q = 80 printers from the
manufacturer each time.
• Cycle inventory = lot size/2 = Q/2 = 40
• Average flow time = cycle inventory/demand rate = 40/4 = 10days (inventory holding time)
• Inventory turnover (taux de rotation), inventory coverage (taux
de couverture)
O n - h a n d
I n v e n t o r y
Time
Q DemandRate, D
Average Cycle
Inventory, Q/2Q/2
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Two Decisions in
Inventory Management
• When is it time to reorder?
• If it is time to reorder, how much?
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Economies of scale to exploit fixed costs:
Economic Order Quantity Model
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Economies of scale to exploit fixed costs:
Economic Order Quantity Model
O n - h a n d I n v e n t o r y
Time
QDemand
Rate, D
Time Between Orders
(Cycle Time) T = Q/D
Average CycleInventory, Q/2
Reorder
Point, R
PlaceOrder
Receiveorder
Lead
Time,
L
Q/2
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Basic EOQ Assumptions
• Constant Demand Rate
• Constant Lead Time
• Orders received in full after lead-time.
• Constant Unit Price (no discounts)
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Economic Order Quantity Cost Model:
Constant Demand, No Shortages
TC = total annual inventory costD = annual demand (units / year)Q = order quantity (units)K = cost of placing an order or setup cost ($)c = cost per unit
I = annual interest rate
Total Annual
Inventory
Cost
=
Annual
Ordering
Cost
TC = ( D / Q) K + (Q / 2) Ic
Annual
Holding
Cost
+
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Cost Relationships for Basic EOQ(Constant Demand, No Shortages)
Total
Cost
CarryingCost
Ordering
Cost
EOQ balances carrying
costs and ordering
costs in this model.
Q* Order Quantity (how much)
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Trade-off in EOQ Model:
Inventory Level vs. Number of Orders
Time
Q
O
n - h a n d I n v e n t o r y
Time
Q
O n - h a n d
I n v e n t o r y
Many orders,
low inventory
level
Few orders,
h igh inventorylevel
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EOQ Results ( How Much to Order)(Constant Demand, No Shortages)
Economic Order Quantity
Number of Orders per year
Length of order cycle
Total cost = TC = (D / Q* ) K + (Q* / 2) Ic
T = Q* / D
= D / Q*
= Q* =2 D K
Ic
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Example:
Determining When to Reorder
• Quantity to order (how much…) determined by EOQ
• Reorder point (when…)determined by finding theinventory level that is adequate to protect thecompany from running out during delivery lead time
• With constant demand and constant lead time,(EOQ assumptions), the reorder point is exactly theamount that will be sold during the lead time.
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EOQ Example
D = 1,000 units per year
S = $20 per order
IC = $8.33 per unit per month
BE CAREFUL!
HOW MUCH TO ORDER?
WHEN TO ORDER?
Number of orders per year =
Length of order cycle = T =
Total cost =
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Exercise
Question: What if the company can only order in multiples
of 12? (That is, order either 0 or 12 or 24 or 36, etc…)?
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Robustness of EOQ model
Order Quantity
Total
Cost
Q*Q*-DQ Q*+DQ
DTC
Would have to m is-speci fy Q* by qu i te a bi t
before tota l annual inventory co sts wou ld
change signi f icant ly.
Very Flat Curve - Good!!
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Example: EOQ Robustness
• Suppose that in the last problem, you have mis-specified theorder costs by 100% and the holding costs by 50%. That is,
– S used in the computation = $40/order (actual cost = $20 / order)
– IC used in computation = $150 / unit / year (actual = $ 100) – Then, using these wrong costs, you would have gotten
2(1,000)40' 23.1
150Q
Your actual TC (computed substituting Q’ into TC, using correct costs of S = $20, and h = $100:
1,000 2320 100 $2,019
23 2TC Only 1% above minimum TC!
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Key points
KP1 : Total ordering and holding costs are relatively stable around theeconomic order quantity. A firm is often better served by ordering aconvenient lot size close to the EOQ rather than the precise EOQ(robustness).
KP2 : If the demand increases by a factor of k, the optimal lot sizeincreases by a factor of k0,5 . The number of orders placed per yearincreases by a factor of k0,5. Flow time due to cycle inventory decreasesby a factor of k0,5.
KP3 : To reduce the optimal lot size by a factor of k, the fixed cost K mustbe reduced by a factor of k2.
KP4 : Aggregating replenishment across products, retailers, or suppliers ina single order allow for a reduction of lot size of individual products bcs
the fixed costs are now spread across differents aggregated entities.
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Lot sizing with multiple products or
customers
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• In general, the ordering, transportation, and
receiving cost of an order grows with thevariety of products or pickup points.
• A portion of the fixed cost of an order can be related to
transportation (this depends only on the load but noton the product variety)
• A portion of the fixed cost is related to loarding and
receiving (this cost increases with variety on the truck)
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Assumptions :
• similar to EOQ model except the followings.
• Di : annual demand for product i
• S: order cost incurred each time an order is placed,independent of the variety of products included
• si: additional order cost incurred if product i is
included in the order.
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Three approaches :
1. Each product manager orders his model
independently (highest cost)
2. The product managers jointly order every product ineach lot (easy to administer and implement, but not
selective enough and expensive joint ordering if
product specific order cost high)
3. Product managers order jointly but not every ordercontains every product, i.e. each lot contains a
selected subset of products.
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Example:
• Best Buy sells 3 models of computers, the Litepro, theMedpro, the Heavypro.
• The annual demands are DL = 12000, DM = 1200, DH =
120.
• Each model costs Best Buy 500$.
• A fixed transportation cost of 4000$ is incurred each
time an order is delivered. For each model ordered and
delivered on the same truck, an additional fixed cost of1000$ is incurred for receiving and storage.
• Best Buy has an annual holding cost of 20%.
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Approach 1 : Independent ordering
• QL = 1095, QM = 346, QH = 110.• Oder frequencies : 11/year, 3,5/year, 1.1/year.
• Total inventory cost = 155140 $
• Other measures of interest : cycle inventory, annualholding cost/prod, annual ordering cost, flow time.
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Approach 2 : Lots ordered and delivered for all
• Combined fixed order cost/order : K = S + si
• The optimal order frequency is (to explain, express
total cost in T):
• Example : n* = 9.75, annual inventory cost = 136528$,
i.e. a reduction of 13% over approach 1.
1*2
k
i i i
i
D I c
n K
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Approach 3 : Lots ordered and delivered jointly for a
selected subset of productsStep 1. Identify most frequently ordered product
assuming each being ordered independently.
The most frequently order products i* is included each
time an order is placed
max
2
ii
i i i
i
i
n n
D I cn
S s
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Step 2. Identify the frequency with which other products
are included.• Calculate the order frequency as a multiple of
• As the most frequently ordered product is in each
order, the inclusion of a product i incurs an additional
product specific fixed order cost of si.
• Product i is included once every mi orders
2
i i
i i i
i
i
m n n
D I cn
s
n
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Step 3. Recalculate the order frequency of the most
frequently order product n.
Why? (order cycle T for n, order cycle miT for i)
2
i i i i
i i
D I c m
n S s m
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Step 4. For each product, evaluate the order frequency ni
= n/mi and the total cost of such an ordering policy.
Example :
n = 11.47, mL = 1, mM = 2, mH = 5,
annual total inventory cost = 130767$, a reduction of
4% over approach 2.
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Key point:
• A key to reducing cycle inventory is the reduction of
lot size.
• A key to reducing lot size without increasing costs isto reduce the fixed cost associated with each lot.
• This may be achieved by reducing the fixed cost itself
or by aggregating lots across products, customers,
suppliers.• When aggregating, tailored aggregation is best,
especially if product specific costs are large.
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Economies of scale to exploit quantity
discounts
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Introduction
• Pricing schedule often displays economies of scale, with pricesdecreasing as lot size increases.
• A discount is lot size based if the pricing schedule offers
discounts based on the quantity ordered in a single lot.
• A discount is volume based if the discount is based on the totalquantity purchased over a given period.
• Two commonly used lot size based discount schemes : all unit
quantity discounts, marginal unit quantity discount or
multiblock tarriffs
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Two basic questions
• Given a pricing schedule with quantity discount, what is theoptimal purchasing decision for a buyer? How does this affect
the SC in terms of lot size, cycle inventories, flow times?
• Under what conditions should a supplier offer quantitydiscounts? What are appropriate pricing schedules that a
supplier should offer?
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EOQ with all quantity discount
• Pricing schedule :The unit purchase cost is Ci if the order quantity is at least qi
with q0 = 0 < q1 < q2 < … < qr = ∞ and c0 > c1 > c2 > …
• The retailer’s objective is to maximise its profit, i.e. minimisethe sum of material, order, and holding costs.
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Example
• Drug Online (DO) is an online retailer of prescription drugs.Demand for vitamins is 10000 bottles per month. DO incurs a
fixed order cost of 100$ each time an occurs is placed with the
manufacturer. DO has an annual holding cost of 20%.
• The pricing schedule of the manufacturer is the all unit discountschedule:
Order quantity Unit Price ($)
0-5000 3
5000-10000 2,9610000 or more 2,92
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Solution
Step 1. Determine the EOQ Qi for each price Ci
Step 2. Determine the total annual cost TCi for each price range
Case 1: Qi >= qi+1, ignored as it is considered for Qi+1
Case 2: Qi < qi,
Case 3: qi <= Qi < qi+1,
Step 3. Determine the optimal order quantity.
2i
i
DK Q
Ic
2
ii i i
i
Q DTC K Ic Dc
Q
2
i
i i i
i
q DTC K Ic Dc
q
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Example (draw TC(Q))
Step 1: Q0 = 6324, Q1 = 6367, Q2 = 6410Step 2:
Q0 >= 5000, TC0 ignore
5000 < Q1 < 10000, TC1 = 358969 $
Q2 < 10000, TC2 = 354520$
Step 3: Optimal order size = q2 = 10000, TC = TC2.
Remarks :
• Presence of quantity discount leads to Larger order size of
10000 units than the normal EOQ = 6324
• If S = 4$, order size under all unit discount schedule is still
10000 units and is 8 times the normal EOQ = 1265.
Order quantity Unit Price ($)
0-5000 3
5000-10000 2,96
10000 or more 2,92
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EOQ with marginal quantity discount
• Pricing schedule :The pricing schedule contains specified break points q0 = 0 <
q1 < q2 < … < qr = ∞. The marginal cost of a unit decreases at
the break points to ci if the order quantity is at least qi with c0
> c1 > c2 > …
• The purchasing cost Vi of qi units is determined as follows:
V0 = 0, Vi+1 = Vi + ci (q i+1 – qi), for i = 0, 1, …
• Purchasing cost of an order of Q such that qi <= Q < qi+1 is:C(q) = Vi + ci(Q-qi)
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Solution
Step 1. Determine the EOQ Qi for each price range Ci (why?)
Step 2. Determine the total annual cost TCi for each price range
Case 1: Qi < qi, Qi* = qi
Case 2: Qi > qi+1, Qi* = qi+1
Case 3: qi <= Qi < qi+1, Qi* = Qi
Step 3. Determine the optimal order quantity.
2 i i i
i
i
D K V q cQ
Ic
12
1
2
i i i i i ii
i i i
i i i
V Q q c V Q q c K TC Q I QQ D Q Q D
V Q q c K I V Q q c
Q D Q D
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Example (draw TC(Q))
V0 = 0, V1 = 15000, V2 = 29800
Step 1: Q0 = 6324, Q1 = 11028, Q2 = 16961
Step 2:
Q0 >= 5000, TC0 = 363900$
Q1 > 10000, TC1 = 361780 $
10000 < Q2, TC2 = 360365$Step 3: Optimal order size = Q2 = 16961, TC = TC3.
Remarks :
• Much larger order size of 16961 units than the normal EOQ =6324
• If S = 4$, order size 15755 is 12,5 times the normal EOQ =
1265.
Order quantity Unit Price ($)
0-5000 3
5000-10000 2,96
10000 or more 2,92
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Key point
• There can be significant increase of order size andcycle inventory in the absence of fixed order costs as
long as quantity discounts are offered.
• Quantity discounts lead to a significant buildup of
cycle inventory in a supply chain.• In many SC, quantity discounts contribute more to
cycle inventory than fixed ordering cost.
• Value of quantity discount in a supply chain?
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Why quantity discount?
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Coordination to increase total SC profits
Quantity discount for commodity products
• For commodity products, a competitive market exists,
the market sets the price, the firm’s objective is the
lower costs.
• For the retailer DO (Drug Online), its lot sizing
decision is based on costs it faces.
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Coordination to increase total SC profits
Quantity discount for commodity products
DO : D = 10000 bottles vitamins/month, Kr = 100$, I = 20%, cr
= 3$, EOQ = 6324, TC_inv = 3795 $.
Manufacturer : processing, packing & shipping DO orders
• A line packing bottles at a steady rate matching the demand.• Fixed setup cost Km = 250$ / order
• Production cost cm = 2$/bottle
• Holding cost = 20%
• Annual setup cost = 120000/6324*250 = 4744$
• Annual holding cost = 6324/2*0,2*2 = 1265$
• Total manufacturer setup & holding cost = 6009$
Total SC cost = 6009 + 3795 = 9804$
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Coordination to increase total SC profits
Quantity discount for commodity products
DO : TC_inv = D/Q*100 +0,2*3*Q/2
Manufacturer :
• Fixed setup cost Km = 250$ / order
• Production cost cm = 2$/bottle
• Holding cost = 20%
• Total setup & holding cost = D/Q*250+0,2*2*Q/2
Total SC cost = D/Q*350 + (0,2*3+0,2*2)*Q/2
SC lot size Q = [2*D*350/ (0,2*3+0,2*2)]0,5=9165
Opt SC cost = 9165 $, gain = 9804 – 9165 = 638$
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Coordination to increase total SC profits
Quantity discount for commodity products
Pricing scheme for achieving opt SC profit:
• C = 3$/bottle if Q < 9165, C = 2.9978$ otherwise.
DO :
• has an incentive to order Q = 9165,
• material cost reduction just enough to offset the
increase of ordering & holding cost
Total SC cost = opt SC cost = 9165 $
In practice, the manufacturer may have to share the
increase of SC profit of 638$.
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Coordination to increase total SC profits
Quantity discount for commodity products
Key point
• For commodity products for which price is set by the
market, manufacturer with large fixed costs per lot can
use lot-size quantity discounts to maximise total SC profits.
• Lot size-based discounts, however, increase cycle
inventory in the SC.
• The benefit of quantity discount decreases as the setup
cost of the manufacturer decreases. (Importance of
coordination between marketing & production)
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Coordination to increase total SC profits
Quantity discount for products for which the firm has market
power
• Consider the scenario in which the manufacturer has
invented a new vitamin pill, vitaherb, for which few
competitors exist.• The price p at which DO sells vitaherb influence
demand.
• Assume that: D = 360000 – 60000p.
• Production cost Cs = 2$/bottle
• The manufacturer decides the price Cr to charge DO
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Coordination to increase total SC profits
Quantity discount for products for which the firm has market
power
When decisions are coordinated:
• SC profil :
Prof_SC = (p – Cs)(360000 – 60000p)
Results:
• p = 3 + Cs/2 = 4
• D = 120000,
• Prof_SC = 240000$
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Coordination to increase total SC profits
Quantity discount for products for which the firm has market
power
When decisions are made independently:
• Manufacturer :
MAXCr Prof_m = (Cr – Cs)(360000 – 60000p)
• DO :MAX p Prof_r = (p – Cr)(360000 – 60000p)
Results:
• p = 3 + Cr/2, Cr = 3 + Cs/2 = 4, p = 5
• D = 60000,• Prof_m = 120000$, Prof_r = 60000$, SC profil = 180000
• Loss of 60000$ due to independent price setting, phenomenon
known as double marginalization
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Coordination to increase total SC profits
Quantity discount for products for which the firm has market
power
Key point
• The supply chain profit is lower if each stage of the
supply chain makes its pricing decisionsindependently, with the objective of maximizing its
own profit.
• A coordinated solution results in higher profit.
C i i i SC fi
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Coordination to increase total SC profits
Quantity discount for products for which the firm has market
power
Pricing schemes to achieve the coordinated solution
Two-part tariff :
• The manufacturer charges its entire profit as an up-front
franchise fee and then sells to the retailer at cost.
• It is then optimal for the retailer to price as though the two
stages are coordinated.
Example :
• Opt Prof_SC = 240000 $, Prof_DO = 60000$ (when nocoordination)
• Pricing scheme: charge the DO of the franchise fee of 180000$
and material cost of Cr = 2$/bottle.
• DO maximises its profit if it sets p = 4$.
C di i i l SC fi
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Coordination to increase total SC profits
Quantity discount for products for which the firm has market
power
Pricing schemes to achieve the coordinated solution
Volume-based quantity discount:
• The two-tariff is a volume-based quantity discount as the
average material cost of DO declines as the purchase increases.
• Design discount scheme to encourage DO the purchase the opt
quantity 120000.
• Pricing scheme : Cr = 4$ if the purchase < 120000, and Cr =3.5$ otherwise.
• DO optimal solution: p = 4, Prof_DO = 60000$, D = 120000,
Prof_SC = 240000$.
C di i i l SC fi
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Coordination to increase total SC profits
Quantity discount for products for which the firm has market
power
Key point
• For products for which the firm has market power, two-part tariffs or
volume-based discounts can be used to achieve SC coordination and
maximize SC profits.
• Lot size-based discounts are not optimal even in the presence ofinventory costs. In such as setting, either two-part tariff or a volume-
based discount, with the supplier passing on some of its fixed cost to
the retailer, is needed for the SC to be coordinated.
• Lot size based discount tends to raise the cycle inventory. In contrast,volume based discounts are compatible with small lots. Use lot size
based discount only when the supplier has high fixed cost.
• Volume-based discounts suffer from orders peak toward the end of
financial horizon. Volume discount based on a rolling horizon could
help.
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Short-term discounting: trade
promotions
I t d ti
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Introduction
• Manufacturers use trade promotions to offer a discounted price
and a time period over which the discount is effective.
• Ex: 10% off for any purchase from 12/15 to 01/25.
• The goal is to influence retailers to act in a way that helps the
manufacturer achieve its objectives.
I t d ti
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Introduction
Key goals (from the manufacturer perspective)
• Induce retailers to use price discount, displays or advertising to
spur sales
• Shift inventory from the manufacturer to the retailer and the
customer
• Defend a brand against competition
Need to understand the impact of trade promotion on the behaviour of a retailer and SC performances.
I t d ti
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Introduction
Retailer’s options facing a trade promotion
1. Pass through some or all of the promotion to customers to spur
sales (increase the sales of the whole SC)
2. Pass through very little of the promotion to customer but
purchase in greater quantity during promotion period to exploit
the temporary reduction in price (forward buy and no increase
of sales)
F d b
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Forward buy
• d$: discount per product offered
• Q* : EOQ at normal price
• Qd : lot size ordered at discounted price
Assumptions:• Discount is offered once
• Retailer takes no action to influence demand
• Qd is an integer multiple of Q*.
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Time
Q*
Qd
Forward buy
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Forward buy
Forward buy = Qd – Q*
• Why? Profit maximization (gain in fix cost, gain in purchase,
loss of inventory cost).
*d dD cQQ
c d I c d
Forward buy
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Forward buy
• Let T = Q/D be the period covered by short-term promotion
• Cost during T without promotion
• Cost during T with promotion
• Cost Gain during T
• The optimal Q is obtained from
* 1 0.5 *Q Q Q K Qd I c d Q IcQ T D
* 0.5 *Q Q K Qc Ic Q T
0.5 K Q c d I c d QT
* 0.5 * (optimal EOQ) KD Q Ic Q
0Q QD
Forward buy
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Forward buy
Example:
• DO is a retailer selling vitaherb. Demand is 120000 bottles/year.
The manufacturer currently charges 3$/bottle and DO has an
annual holding cost of 20%. Fixed order cost K = 1000 $. What
is the current lot size Q* of DO, cycle time, average flow time?
• The manufacturer has offered a discount of 0.15$ for all bottles purchased by the retailer over the coming month. How many
bottles should DO order given the promotion?
Answer:
• Q* = 6324, Qd = 38236, Forward buy = 31912
Remark:
• 5% discount causes the lot size to increase by 500+%.
Forward buy
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Forward buy
Key point :
• Trade promotions lead to a significant increase in lot size and
cycle inventory because of forward buying by retailer.
• This generally results in reduced SC profits unless the trade
promotion reduces demand fluctuations.
Impact on the demand
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Impact on the demand
Example:
• Assume DO selling at price p faces a demand of D = 300000 –
60000p. The normal price charged by the manufacturer is Cr =
3$/bottle. Ignoring the inventory related costs, evaluate the
optimal response of DO to a discount of 0.15$ per bottle.
Answer:
• Without discount and Cr = 3$, p = 4$, D = 60000
• With discount of 0.15$ and Cr = 2.85$, p = 3.925$, D = 64500.
• 7.5% increase in demand, DO pass only half of the trade
promotion discount to Customers.
Impact on the demand
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Impact on the demand
Key point
• Faced with a short term discount, it is optimal for retailers to
pass through only a fraction of the discount to the customer,
keeping the rest for themselves.
• Simultaneously, it is optimal for retailers to increase the
purchase lot size and forward bur for future periods.
• Thus, trade promotions often lead to an increase of cycle
inventory in a SC without a significant increase in customer
demand.
• Trade promotion should be designed so that retailers limit theirforward buying and pass along more of the discount to end
customers.
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Managing multiechelon cycle inventory
A mutliechelon distribution supply chain
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A mutliechelon distribution supply chain
stage
1stage2
stage
3
stage
4
A multiechelon supply chain has multiple stages and possibly manyplayers et each stage.
Goal: decrease the total costs by coordinating orders across the SC
One manufacturer supplying one retailer
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One manufacturer supplying one retailer
(Instantaneuous production, lotsize Q)
No synchronization : production right after delivery, average INV = 3Q/2
shipping
production
mfginventory
retailerinventory
Synchronization : production after before delivery, average INV = Q/2
Simple multiechelon with one player at each stage
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Simple multiechelon with one player at each stage
Integer replenishment policy:
• lot size at each stage = integer multiple of the lot size of its
immediate customer
• Coordination of ordering across stages allows for a portion of
the delivery to a stage to be cross-docked on to the next stage
• Extent of cross-docking depends on the ratio of fixed ordering
cost S and holding cost H at each stage. The closer the ratio, the
higher the optimal percentage of cross-docked product.
Shown to be quite close to optimal.
distributor replenshment order arrives
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Distributer replenishes every two weeks
Retailer replenishes every week
Retailer replenishes every two weeks
Retailer replenishes every four weeks
p
retailer shipment is cross-docked
retailer shipment is from inventory
retailer shipment is cross-docked
retailer shipment is cross-docked
One distributor supplies multiple retailers
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One distributor supplies multiple retailers
Integer replenishment policy:
• Distinguish retailers with high demand from those with low
demand
• Group retailers such that all retailers in one group order together
• fr = n*fd or fd = n*fr, for each retailer r where n is an integer
and fr and fd are retailer and distributor order frequencies
• Each player orders periodically with reorder interval equal to an
integer multiple of some base period
Shown to be near optimal by Roundy.
Integer replenishment policies
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Integer replenishment policies
• Divide all parties within a stage into groups such that all parties of a
group order from the same supplier and have the same reorder interval• Set reorder intervals across stages such that the receipt of a
replenishment order at any stage is synchronized with the shipment of a
replenishment order to at least one of its customers. The synchronized
portion can be cross-docked.
• For customers with a longer reorder interval than the supplier, make the
customer reorder interval an integer multiple of the suppliers' interval
and synchronize their replenishment to facilitate cross-docking
• For customers with a shorter reorder interval, make the supplier's
reorder interval an integer multiple of the customer's interval andsynchronize the replenishment
• The relative frequency of reordering depends on the setup cost, holding
cost and demand at different parties.
Key points
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Key points
• Integer replenishment policies can be synchronized in multiechelon
supply chains to keep cycle inventory and order costs low.• Under such policies, the reorder interval at any stage is an integer
multiple of a base reorder interval.
• Synchronized integer replenishment policies facilitate a high level of
cross-docking.
• Whereas the integer policies synchronize replenishment and decrease
cycle inventories, they increase safety inventories because of the lack of
flexibility with the timing of a reorder
• These policies make the most sense for supply chains in which cycle
inventories are large and demand is relatively predictable.
Integer replenishment policies
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Integer replenishment policies
• Divide all parties within a stage into groups such that all parties of a
group order from the same supplier and have the same reorder interval• Set reorder intervals across stages such that the receipt of a
replenishment order at any stage is synchronized with the shipment of a
replenishment order to at least one of its customers. The synchronized
portion can be cross-docked.
• For customers with a longer reorder interval than the supplier, make the
customer reorder interval an integer multiple of the suppliers' interval
and synchronize their replenishment to facilitate cross-docking
• For customers with a shorter reorder interval, make the supplier's
reorder interval an integer multiple of the customer's interval andsynchronize the replenishment
• The relative frequency of reordering depends on the setup cost, holding
cost and demand at different parties.
Echelon inventory
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Echelon inventory
• Ordering policies based on echelon inventory (s, S), (r, Q)
• Problems: where to locate the inventory, how to allocate the inventory
supplier warehouse
warehouse echelon inventory