1 Chapter 3. Managing economies of scale in a supply chain: cycle inventory Learning objectives: 1....

1

Chapter 3. 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

2

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, price

increase, lead time slippage)– To maintain independence of operations (buffering)

• WHY NOT?– Requires additional space– Opportunity cost of capital– Spoilage / obsolescence

4

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.

5

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 = 10

days (inventory holding time)• Inventory turnover (taux de rotation), inventory coverage (taux

de couverture)

On-

hand

Inv

ento

ry

Time

QDemand Rate, D

Average CycleInventory, Q/2Q/2

6

Two Decisions in Inventory Management

• When is it time to reorder?

• If it is time to reorder, how much?

7

Economies of scale to exploit fixed costs:Economic Order Quantity Model

8

Economies of scale to exploit fixed costs:Economic Order Quantity Model

On-

hand

Inv

ento

ry

Time

QDemand Rate, D

Time Between Orders

(Cycle Time) T = Q/D

Average CycleInventory, Q/2

ReorderPoint, R

PlaceOrder

Receiveorder

LeadTime, L

Q/2

9

Basic EOQ Assumptions

• Constant Demand Rate• Constant Lead Time• Orders received in full after lead-time.• Constant Unit Price (no discounts)

10

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 unitI = annual interest rate

Total Annual Inventory Cost

=AnnualOrderingCost

TC = (D / Q) K + (Q / 2) Ic

AnnualHoldingCost

+

11

Cost Relationships for Basic EOQ(Constant Demand, No Shortages)

TC

– A

nn

ual

Co

st

Total Cost

CarryingCost

OrderingCost

EOQ balances carryingcosts and ordering costs in this model.

Q* Order Quantity (how much)

12

Trade-off in EOQ Model: Inventory Level vs. Number of Orders

Time

Q

On-

hand

Inv

ento

ry

Time

Q

On-

hand

Inv

ento

ry

Many orders, low inventory level

Few orders, high inventory level

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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

14

Example:

Determining When to Reorder

• Quantity to order (how much…) determined by EOQ • Reorder point (when…)determined by finding the

inventory level that is adequate to protect the company from running out during delivery lead time

• With constant demand and constant lead time, (EOQ assumptions), the reorder point is exactly the amount 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 =

16

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

Annual Cost

Total Cost

Q*Q*-DQ Q*+DQ

DTC

Would have to mis-specify Q* by quite a bit before total annual inventory costs would change significantly.

Very Flat Curve - Good!!

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Example: EOQ Robustness• Suppose that in the last problem, you have mis-specified the

order 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 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 (robustness).

KP2 : If the demand increases by a factor of k, the optimal lot size increases by a factor of k0,5 . The number of orders placed per year increases by a factor of k0,5. Flow time due to cycle inventory decreases by a factor of k0,5.

KP3 : To reduce the optimal lot size by a factor of k, the fixed cost K must be reduced by a factor of k2.

KP4 : Aggregating replenishment across products, retailers, or suppliers in a 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 the variety 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 not on 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 in each 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 order contains 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, the

Medpro, 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 of 1000$ 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, annual

holding 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 ii

D I cn

K

27

Approach 3 : Lots ordered and delivered jointly for a selected subset of products

Step 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 ii

i

n n

D I cn

S s

28

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 ii

i

m n n

D I cn

s

n

29

Step 3. Recalculate the order frequency of the most frequently order product n.

Why? (order cycle T for n, order cycle miT for i)

2i i i i

i i

D I c mn

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 is to 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 prices

decreasing 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 total

quantity 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 the

optimal 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 quantity discounts? 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. minimise the 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 discount schedule:

Order quantity Unit Price ($)

0-5000 3

5000-10000 2,96

10000 or more 2,92

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SolutionStep 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

DKQ

Ic

2i

i i ii

QDTC K Ic Dc

Q

2i

i i ii

qDTC K Ic Dc

q

38

Example (draw TC(Q))Step 1: Q0 = 6324, Q1 = 6367, Q2 = 6410

Step 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 2,9610000 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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SolutionStep 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 ii

i

D K V q cQ

Ic

1

2

1

2

i i i i i ii

i i ii i i

V Q q c V Q q cKTC Q I Q

Q D Q Q D

V Q q cKI 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 2,9610000 or more 2,92

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Key point

• There can be significant increase of order size and cycle 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?

44

Coordination to increase total SC profitsQuantity discount for commodity products

• For commodity products, a competitive market exists, the market sets the price, the firm’s objective is the lower costs.

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A two-stage supply chain exampleRetailer• 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%.

• Normal wholesale price of the manufacturer cr = 3$ per unit.

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%

DO makes its lot sizing decision based on costs it faces.

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productionfor next DO delivery

ManufacturerInventory

DO Inventory

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DO Local optimum face wholesale unit price cr = 3$

DO : D = 120000/year, Kr = 100$, I = 20%, cr = 3$

EOQ = 6324,

TC-DO = 3795 $ (DO cost excluding purchasing cost crD)

Manufacturer : • Setup cost Km = 250$ / order, unit production cost cm = 2$

• Annual setup cost = KmD/EOQ = 4744$

• Annual holding cost = (Icm)EOQ/2 = 1265$

• TC-M = 6009$ (Manuf cost excluding sales revenue crD)

Total SC cost = TC-DO + TC-M = 6009 + 3795 = 9804$

48


Supply Chain Global Optimum

DO cost : TC-DO = KrD/Q + (Icr)Q/2

Manufacturer cost: TC-M = KmD/Q + (Icm)Q/2

SC cost: TC-SC = TC-DO + TC-M = (Km+Kr)D/Q + I(cr+cm)Q/2

SC lot size Q = [2D(Km+Kr)/ (Icr+Icm)]0,5=9165

Opt SC cost = 9165 $

Gain of SC optimum = 9804 – 9165 = 638$

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Pricing scheme for achieving opt SC profit:• C = 3$/bottle if Q < 9165, C = 2.9978$ otherwise.

DO : • has an incentive to order EOQ = 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$.

50


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 profitsQuantity 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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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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power

When decisions are made independently:• DO sets p : MAXp Prof_r = (p – Cr)(360000 – 60000p)

p = 3+0.5Cr• Manufacturer sets Cr: MAXCr Prof_m

• Prof_m = (Cr – Cs)(360000 – 60000p)

= (Cr – Cs)(180000 – 30000Cr)• Cr = 3 + 0.5Cs = 4 p = 5, D = 60000

Results:• 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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power

Key point

• The supply chain profit is lower if each stage of the supply chain makes its pricing decisions independently, with the objective of maximizing its own profit.

• A coordinated solution results in higher profit.

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power

Pricing schemes to achieve the coordinated solutionTwo-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 no

coordination)• Pricing scheme: charge the DO of the franchise fee of 180000$

and material cost of Cr = 2$/bottle.• DO maximises its profit if it sets p = 4$ (Why?).

56


power

Pricing schemes to achieve the coordinated solutionVolume-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$, D = 120000, Prof_SC = 240000$ (Why?).

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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 of inventory 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

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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.

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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.

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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)

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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

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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 cQ

Qc d I c d

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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

* 1 0.5 *

* 1 0.5 *

Q Q Q K Qd I c d Q IcQ T

QQ Q K Qd I c d Q IcQ

D

**

2

QQ Q K Qc Ic T

2

QK Q c d I c d T

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Forward buy

• The optimal Q is obtained from

** 0.5

1* 0.5 *

1* (From property of EOQ, * 0.5 *)

I c d QIcQQ Q K Q d

D DI c d Q

KD Q IcQ dD D

I c d QIcQ d KD Q IcQ

D D

10 * 0

I c d QQ Q IcQ d

D D

*IcQ dD

QI c d

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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+%.

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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.

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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.

Why:• Maxp Profit-DO = (p – Cr)*(300000 – 60000p) p = 2.5+0.5Cr

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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 buy 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 their forward buying and pass along more of the discount to end customers.

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Managing multiechelon cycle inventory

72

A mutliechelon distribution supply chain

stage 1

stage 2

stage 3

stage 4

A multiechelon supply chain has multiple stages and possibly many players et each stage.

Goal: decrease the total costs by coordinating orders across the SC

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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

mfg inventory

retailer inventory

Synchronization : production after before delivery, average INV = Q/2

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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.

Distributer replenishes every two weeks

Retailer replenishes every week

Retailer replenishes every two weeks

Retailer replenishes every four weeks

distributor replenshment order arrives

retailer shipment is cross-docked

retailer shipment is from inventory



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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.

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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 and synchronize the replenishment

• The relative frequency of reordering depends on the setup cost, holding cost and demand at different parties.

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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.

79

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 and synchronize the replenishment

• The relative frequency of reordering depends on the setup cost, holding cost and demand at different parties.

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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

warehouse echelon lead time

Echelon inventory

Local installation based-stock policy:

• Order-up-to local base stock Sj if the local inventory position < Sj• Local inventory position of j = inventory on hand at stage j + on order

of stage j + in transit to stage j – backorder (on order) of stage j-1

3 24 1Demand DL1L2

L3L4

j j j DS L E D z L

On order

in transit

On hand

Echelon 3

Echelon inventory

Echelon based-stock policy:

• Order-up-to echelon base stock ESj if the echelon inventory position < ESj

• Echelon inventory position of j = on order of stage j + inventories at stages (j, j-1, …, 1) + in transit to stages (j, j-1, …, 1) – backorder of stage 1

3 24 1Demand DL1L2L3L4

1 1 1 1... ...j j j j j DES L L L E D z L L L

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